European Conference on Mathematical and Theoretical Biology (ECMTB 2026)

Jul 12, 2026, 9:00 AM → Jul 17, 2026, 6:00 PM Europe/Vienna

University of Graz

The European Conference on Mathematical and Theoretical Biology is a joint event of the Society for Mathematical Biology (SMB) and the European Society for Mathematical and Theoretical Biology (ESMTB) that takes place every other year.

This year's 14th edition of the conference takes place in Graz, Austria from 13. July to 17. July 2026. Visit our conference website at https://ecmtb2026.org to learn more and to receive the latest news and updates concerning the conference.

A satellite event, the 2026 OpenVT Workshop on Multiscale Multicellular Model Sharing and Reproducibility, is scheduled to take place on Sunday, 12. July 2026. See https://www.openvt.org/pages/events/workshops/2026openvt-ecmtb-smb-workshop.html for more information.

Sun, July 12

9:00 AM → 4:00 PM Early Career Workshop

Speaker: TBA

9:00 AM → 4:00 PM SMB Board Meeting

Speaker: Brandilyn Stigler (Southern Methodist University)

1:00 PM → 5:00 PM BMB 2026 OpenVT Workshop on Multiscale Model Sharing and Reproducibility

Speaker: James Osborne

Mon, July 13

9:20 AM → 10:10 AM Mathematical modeling of spatial evolution with applications to biomedical systems

Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in life sciences. Mass-action (or mean-field) evolutionary dynamics have been studied over the last 100 years, and produced an enormous wealth of useful results. In this talk, however, I will discuss how spatial interactions may change the laws of evolution, giving rise to a number of interesting and counterintuitive findings. I will discuss both explicitly spatial systems and metapopulations, and demonstrate a number of scaling laws that describe production and spread of disadvantageous, neutral, and advantageous mutants. Applications of these laws to bacterial growth and carcinogenesis will be discussed.

Speaker: Natalia L. Komarova (University of California, San Diego)

10:10 AM → 10:40 AM Coffee Break

10:40 AM → 12:00 PM Advanced Progresses in Population Models Driven by Natural and/or Artificial Intelligence

10:40 AM Long-range forecasting of seasonal influenza vaccine uptake using web search data

The population-level burden of an influenza season depends strongly on the proportion of people vaccinated beforehand. Being able to predict whether a given season is on track to have low, high or average uptake would provide a critical piece of highly actionable intelligence for all stakeholders involved: Governments, public health authorities, healthcare providers, vaccines manufacturers, and not least, the population itself. In particular, sufficiently early advance warning provides the opportunity for interventions—such as increased investment in awareness programs—to proactively boost participation and avert a projected shortfall. We present an ensemble forecast model which utilizes a panel of Google web search queries to make meaningful predictions about US national-level total seasonal vaccine uptake as early as the beginning of the year in which the season begins.

This work was supported by a National Sciences and Engineering Research Council (NSERC) Alliance grant co-funded by Sanofi

EWT is an employee of Sanofi and may hold shares and/or stock options

Speaker: Edward Thommes (University of Guelph and Sanofi)

11:00 AM Comparison of empirical estimates of SARS-CoV-2’s effective reproduction number in the United States with that derived from a transmission model

Mathematical epidemiologists focus on the numbers of secondary infections per primary, R, but the intervals between primary and secondary infections, T, also determine infected population growth rates, r. Empirical estimates of R from reported cases or hospitalizations approximate T from periods between symptom onsets in paired primary and secondary infections. Mechanistic models typically are systems of ordinary differential equations (ODEs) that may be stratified. In such meta-population models, r and R may be derived from the Jacobian matrix, partial derivatives of the linearized system of ODEs for the infected states at equilibrium with respect to the remaining variables. They are the eigenvalue with largest real part and dominant eigenvalue of the matrix product of the infection and inverse of the transmission terms, respectively. The associated left and right eigenvectors are equilibrium contributions and prevalence of infectious states, respectively. And T is the mean generalized-gamma-distributed sojourn of people following all possible paths among infected states weighted by their respective contributions to R. In this presentation, we describe insights from weekly evaluations of the impact of mitigation measures, via effective values of these analytical quantities derived from our meta-population model of SARS-CoV-2 transmission in the United States, that estimates of R via renewal equations with proxy T would miss even if infections were accurately reported.

Joint work with Troy Day (Queens University) and Zhilan Feng (National Science Foundation).

Speaker: John Glasser (Emory University)

11:20 AM Nonlinear Dynamics of Political Instability in a Reduced Structural-Demographic Model

Political instability often exhibits long-term oscillatory patterns, commonly referred to in Structural-Demographic Theory (SDT) as secular cycles. Although existing computational approaches, such as the Multi-Path Forecasting (MPF) framework, can reproduce historical instability trends through high-dimensional simulations, they often lack the analytical tractability needed to clarify the structural mechanisms underlying these oscillations. To address this limitation, we propose a reduced-dimensional continuous-time model consisting of three coupled ordinary differential equations that capture the nonlinear feedback among radicalization, collective violence, and accumulated structural pressure. Using a mean-field approximation for the population reservoir, we derive a minimal dynamical system that preserves the essential structure of the original framework. Stability analysis based on the Routh–Hurwitz criterion shows that equilibrium stability is governed by the rate of exogenous economic decline. We further prove the existence of a supercritical Hopf bifurcation, demonstrating that secular cycles of violence emerge as a stable limit-cycle attractor when structural pressure exceeds a critical threshold. Numerical simulations support the analytical results and provide a rigorous mathematical foundation for the endogenous periodicity of social unrest.

Speaker: Junling Ma (University of Victoria)

11:40 AM Modelling disease transmission with game theoretic determinants: a look at MPOX modelling

Mathematical modelling is a valuable tool in assessing disease dynamics and interventions. Models may be deterministic, stochastic, data driven, network-based, or hybrid, combining multiple approaches. Advances in computing power, data collection, and simulation frameworks have made it possible to create dynamic models that integrate individual behaviour, environmental context and policy scenarios. The agent-based framework was chosen in this work because of its ability to simulate person-to-person behavioural characteristics, personality traits, and individual decision-making.

For a disease such as MPOX, with a strong behavioural component influencing transmission dynamics, we investigate the possible transmission from a small subpopulation to a larger one, by accounting for differing individual decisions leading to differentiated contacts among population members. We then employ calibration methods and scenario testing to investigate the cross-over spread of the disease and possible control strategies. The talk will illustrate our ideas in the case of MPOX transmission with a signaling game.

This talk is joint work with: Bridgette Amoako, Ed Thommes.

Speaker: Monica Cojocaru (University of Guelph)

10:40 AM → 12:00 PM Vertex Models in Tissue Mechanics and Morphogenesis: Bridging Cell-Scale Forces to Multicellular Dynamics

10:40 AM Mechanosensitive Feedback Organizes Cell Shape and Motion During Hindbrain Neuropore Morphogenesis

Neural tube closure in mammals requires the sealing of the hindbrain neuropore (HNP) gap. Failure in this critical process results in fatal birth defects. Yet, the physical forces orchestrating this morphogenetic event at the cellular and tissue level have remained elusive.
Here, we combine live and fixed imaging of mouse embryos with cell-based computational modeling to investigate the mechanisms underlying mouse HNP closure. We find that two force-generating mechanisms drive HNP closure: a high-tension actomyosin purse-string acting along
the gap edge and directional cell migration. While together these reproduce gap-level dynamics, they are insufficient to explain the reproducible pattern of cell elongation along the gap border.
We show that a mechanical feedback loop between shear stress and cytoskeletal organization, where the purse-string serves as a mechanical cue, generates the observed morphological pattern around the gap. Over time, cell neighbor exchanges stall and the tissue solidifies, helping preserve cell shapes and their relative arrangements even away from the high-tension cue. This induces mechanical memory, leading to rostro-caudal midline cell elongation, consistent with observations in both the cranial and spinal mouse regions. We validate this feedback model by comparing mouse to chick embryos, which naturally lack the purse-string.

Speaker: Fernanda Pérez Verdugo (Institute of Science and Technology Austria)

11:00 AM Linking vertex models with experiments in tissue morphogenesis

Collective cell movements play a critical role in guiding embryonic development, wound repair, and disease progression, such as cancer metastasis. The coordination of these movements is strongly influenced by mechanical forces. Biological tissues can be viewed as soft, out-of-equilibrium systems whose constituent cells continuously generate forces and undergo rearrangements. During development, tissue material
properties can change drastically, reminiscent of rigidity transitions in physics. Measuring the impact of these transitions on cell behaviour, or identifying how to control them, remains experimentally challenging in developing organisms. In this talk, I will present our work developing vertex models in close collaboration with experimentalists, where model predictions and in vivo measurements inform one another iteratively. By integrating experimental measurements into our models and generating testable predictions, we investigate the interplay between tissue material properties, cell-scale forces, and tissue boundary formation across a range of morphogenetic processes.
Together, these efforts yield mechanistic insights with implications for understanding congenital disorders and cancer.

Speaker: Gonca Erdemci-Tandogan (Western University)

11:20 AM MS127-3

Speaker: Osvaldo Chara (University of Nottingham)

11:40 AM A quantitative vertex model of neural tube closure informed by imaging data

Tissue morphogenesis emerges from the collective mechanical behaviour of epithelial cells, where gene expression, cytoskeletal dynamics and cell cycle progression combine to drive coordinated tissue-scale deformations. Neural tube closure is a paradigmatic example whose failure gives rise to severe congenital conditions including spina bifida. Yet quantitative links between gene-level perturbations, single-cell mechanics and tissue-scale closure outcomes remain missing. Here we develop a data-driven vertex model that bridges these scales, parameterised directly from quantitative imaging across developmental stages. Incorporating cell cycle dynamics and apical constriction as mechanistically grounded inputs, the model recapitulates tissue-scale deformation during closure and correctly predicts neuropore widening under pharmacological inhibition of contractility.

This provides a framework in which genetic perturbations altering cytoskeletal tension or cell cycle progression can be mapped directly onto closure outcomes offering a quantitative route to understanding how mutations disrupting neuroepithelial mechanics lead to neural tube defects.

Speaker: Rubén Perez-Carrasco (Imperial College London)

10:40 AM → 12:00 PM Metabolic Foundations of Microbial Community Interactions: From Theory to Practice

10:40 AM Microbial community metabolic models of the human gut microbiome: From objectives to validation

From the first hours of life until the last, the human body is colonized by microbes that consume and produce a wide array of metabolites, predominantly within the gastrointestinal tract. These microbial metabolites are intimately linked to inflammation and immune signaling. Molecules such as short-chain fatty acids (SCFAs) and indoles have been shown to attenuate host inflammatory responses, making the gut microbiome a promising target for clinical interventions. However, metabolic output within microbial communities results from a complex interplay between hundreds of species, host factors, and dietary intake. Consequently, metabolic function cannot be accurately predicted from microbiome composition alone. Microbial Community Metabolic Models (MCMMs) offer a mechanistic solution to this challenge, yet their utility has been hindered by poorly defined optimization objectives and a lack of robust validation. Here, we demonstrate that ecological two-step objectives significantly enhance the predictive accuracy of MCMMs, rendering them suitable for clinical intervention modeling. We validate our flux predictions using large-scale ex vivo microbiome cultivation and engraftment studies. Our results establish MCMMs as a potent, mechanism-based strategy for predicting personalized intervention effects within the human gut microbiome.

Speaker: Dr Christian Diener (Diagnostic & Research Institute of Hygiene, Microbiology and Environmental Medicine, Medical University of Graz)

11:00 AM Thermodynamic Feasibility in Genome-Scale Microbial Consortia

Systematically mapping species interactions in microbial communities remains a central challenge. Community-level elementary flux modes (cEFMs) provide a complete description of community metabolism, but are intractable at genome-scale, necessitating optimization-based approaches. However, the latter introduce thermodynamically infeasible cycles (TICs) across organisms, leading to spurious cross-feeding predictions.

Here, we show that blocking external metabolite inflow allows cEFMs to fully characterize all TICs in a community model. We leverage this insight to derive simple activity-based constraints that yield cycle-free solutions at genome-scale, when integrated into a mixed-integer linear program.

The resulting computational framework links metabolic function, species interactions, and thermodynamic feasibility for the analysis and design of microbial consortia.

Speaker: Jürgen Zanghellini (Department of Analytical Chemistry, University of Vienna)

11:20 AM Elementary vectors reveal minimal interactions in microbial communities

Understanding microbial communities is crucial for advancing fields like ecology, biotechnology, and human health. Recently, constraint-based metabolic models of individual organisms have been combined in various ways to study microbial consortia. In this work, we present a comprehensive geometric approach to characterize all feasible microbial interactions. First, we project community models onto the relevant variables for interaction, namely exchange fluxes and community compositions. Next, we compute ’elementary’ compositions/exchange fluxes, thereby extending the concept of minimal metabolic pathways from single species to entire communities. Every feasible community is a combination of these elementary compositions/exchange fluxes, and, surprisingly, every elementary vector represents a fundamental ecological interaction (such as specialization, commensalism, or mutualism). Hence, our geometric approach allows us to decode the metabolic interactions underlying microbial cooperation. Moreover, it provides a foundation for rational community design. Since it treats exchange fluxes and community compositions equally, we can directly apply existing constraint-based methods and algorithms.

Speaker: Stefan Müller (University of Vienna, Faculty of Mathematics)

Elementary vectors reveal minimal interactions in microbial communities

The geometry of cooperation: decoding microbial interactions

11:40 AM MS146-4

10:40 AM → 12:00 PM Advanced Topics in Stochastic Chemical Reaction Networks

10:40 AM The Dummy species extension of the Chemical reaction networks; Adding additional species to derive its stationary distribution.

Stochastic chemical reaction networks (CRNs) provide a fundamental framework for modeling stochastic dynamics in systems biology, population dynamics, and chemistry. A stationary distribution of stochastic CRN describes its long-term behavior. An analytic formula for a stationary distribution can be obtained for only in limited cases, linear or finite-state systems.

Interestingly, the analytic form of stationary distribution can be obtained when the underlying network satisfies topological conditions, specifically weak reversibility and deficiency zero, and kinetic conditions such as mass-action or kinetics satisfying factorizability. Moreover, other studies resolved certain violations of topological conditions with the network translations. In this talk, I will introduce a “dummy species extension” framework to overcome violations of kinetic conditions. By adding an additional species, originally non-factorizable networks are transformed into factorizable systems within this framework, enabling the analytic derivation of their stationary distribution. I will demonstrate its applications with several examples from biological network systems.

Speaker: Hoejin Kim (POSTECH)

11:00 AM Bang–bang population control with reduced fluctuations: lessons from bacteria

A bang–bang control in a reaction system refers to rapid switching between two extreme behavioral regimes of a species in order to optimize an objective, such as population growth. Because such transitions occur abruptly, intrinsic stochasticity typically induces large fluctuations in the system. We have recently identified a class of bacteria that employs a remarkable strategy to suppress these fluctuations while achieving population dynamics equivalent to those generated by bang–bang control. In this talk, we examine how biological systems mitigate noise while reproducing bang–bang–like behavior. To this end, we compare two reaction network models describing bacterial division mechanisms, each formulated as a continuous-time Markov chain. Although both models yield qualitatively similar mean population dynamics, their fluctuation levels differ substantially: one exhibits significantly reduced noise. This lower-variance regime corresponds to the so-called size-control mechanism, which is supported by experimental data reported in prior studies.

Speaker: Jinsu Kim (Pohang University of Science and Technology)

11:20 AM On the abelian structure of noncompetitive chemical reaction networks.

Chemical reaction networks (CRNs) are foundational models for describing complex biochemical processes. We study noncompetitive CRNs, a class of networks whose static states are rate-independent, and that can implement ReLU neural networks. A central contribution of this work is that noncompetitive CRNs are special instances of Abelian networks (ANs)—a well-established framework for self-organized criticality. CRNs of interest in biochemistry and systems biology are embedded in complex networks so that local CRNs have to respond to internal and environmental cues. We describe the network’s response to such perturbations using a Markov chain whose state space is the set of CRN’s static states, from where no reaction is possible. The addition of molecules to a static state induces reactions that move the system into a new static state. For noncompetitive CRNs of finite state space, we use AN theory to get that only a fraction of the static states are recurrent, suggesting that these states might be the biologically relevant configurations.

We obtain furthermore that the set of recurrent states is in one to one correspondence with the critical group of the AN. Overall, this work establishes a unified algebraic and probabilistic framework for analyzing the long-term behavior of noncompetitive CRNs.

Speaker: Louis Faul (Université de Fribourg)

11:40 AM On the Stability Properties of Stochastic Chemical Reaction Networks with Phosphorylation

We investigate a class of chemical reaction networks models associated to a phosphorylation mechanism with three steps. This is an important mechanism in many biological cells. A chemical species, the substrat has three possible configurations: ${\mathcal S}_1$, ${\mathcal S}_2$ and ${\mathcal S}_3$. There are transformations by two types of chemical species (enzymes) ${\mathcal A}$ and ${\mathcal B}$:

$$\begin{aligned} &A{+}S_1\mathrel{\mathop{\rightleftarrows}_{\alpha_{1}^-}^{\alpha_{1}^+}} AS_1\stackrel{\lambda_1}{\rightharpoonup} A{+}S_2 \mathrel{\mathop{\rightleftarrows}_{\alpha_{2}^-}^{\alpha_{2}^+}} AS_2\stackrel{\lambda_2}{\rightharpoonup}A{+}S_3\\ & B{+}S_1\stackrel{\mu_2}{\leftharpoonup} BS_2\mathrel{\mathop{\rightleftarrows}_{\beta_{2}^+}^{\beta_{2}^-}} B{+}S_{2} \stackrel{\mu_1}{\leftharpoonup}BS_3\mathrel{\mathop{\rightleftarrows}_{\beta_{1}^+}^{\beta_{1}^-}} B{+}S_3. \end{aligned}$$ In this work, in a Markovian setting, we assume that the initial total number of copies of substrat is $N$ and that the total number of copies of each type of enzymes is proportional to $N$. We investigate the asymptotic behavior, when $N$ gets large, of the concentrations of the chemical species $(\mathcal{S}{i})$. The dependence of the possible asymptotic regimes on the reaction rates is investigated. It turns out that there are significant differences with deterministic models of the literature. The detailed stability properties of a deterministic dynamical system in ${\mathbb{R}}{+}^{4}$ plays an important role in several of our scaling results.

Joint work with Lucie Laurence (University of Bern)

Speaker: Philippe Robert (INRIA)

10:40 AM → 12:00 PM Modelling Ocular Disease: From Mechanisms to Treatment

10:40 AM A model of the unconventional aqueous outflow enhanced by a suprachoroidal stent

Ocular hypertension can arise when the conventional outflow route for the aqueous humor of the eye becomes partially blocked, leading to an increase in interocular pressure (IOP) with associated risk of developing Glaucoma. Increasing the unconventional outflow route is a potential mechanism to decrease IOP, and certain types of Minimally Invasive Glaucoma Surgery (MIGS) are designed to exploit this by creating a fluid bypass, which decreases or removes resistance to fluid entering the unconventional pathway.

We present an extension of a mathematical model of the unconventional flow, previously developed by Tweedy et al., 2025. The model includes fluid flow and albumin transport in the choroid and suprachoroidal space and is extended to include a simple example of a suprachoroidal stent (an example of MIGS) which allows fluid from the anterior chamber to enter the uveo-scleral pathway directly.

The presence of the stent leads to additional complications for numerical analysis, such as loss of symmetry in the ocular fluid flow, strong pressure gradients near the stent and nonlinear interactions between the interocular pressure and unconventional flow.

Numerical results are presented which capture key features of the unconventional flow and show a reduction in IOP. This suggests that tapping the unconventional outflow could be effective at mitigating ocular hypertension.

Speaker: Ben Ashby (University of Bath)

11:00 AM Heterogeneity, Bias, and Translation Bottleneck in Age-Related Macular Degeneration

Age-related macular degeneration (AMD) is a primary cause of irreversible vision loss worldwide, causing years of progressive visual decline and reduced quality of life that may culminate in severe visual impairment or blindness. Available therapeutic options are limited to late-stage disease, when irreversible damage to ocular tissues has already occurred and patients experience significant vision loss. Moreover, these treatments often suffer from limited efficacy and a high treatment burden. With an estimated attrition rate of 85-90%, the translation pipeline for AMD therapeutics faces a persistent bottleneck, hindering the development of effective alternative treatments. In this talk, we demonstrate that this translational bottleneck is driven largely by substantial variability in disease presentation and clinical progression among affected individuals. This population-level heterogeneity propagates bias across multiple stages of the translational pipeline, from clinical study design and patient recruitment to molecular analyses and biomarker validation. Integrative analyses across genetics, transcriptomics, proteomics, and clinical phenotyping suggest that this heterogeneity arises from a lack of integration among three core disease dimensions: age, genetic risk profile, and staging of AMD severity. We argue that frameworks combining these axes are required to identify knowledge gaps, clarify disease mechanisms, and support effective therapy development.

Speaker: Moussa Zouache (University of Utah)

11:20 AM How Mechanical Forces Shape Stratification and Wound Healing Dynamics in the Corneal Epithelium

The corneal epithelium is a self-renewing tissue maintained with remarkable precision. Its regeneration is driven by limbal epithelial stem cells (LESCs), which reside at the corneal periphery and give rise to transit amplifying cells (TACs) that migrate centripetally toward the centre. These TACs continually replenish the tissue and, together with vertical delamination between layers, sustain the five to seven stratified layers of the epithelium. Despite this highly coordinated renewal process, the mechanical mechanisms regulating epithelial stratification remain poorly understood.

In this talk, I present simulation results demonstrating that stratification is strongly coupled to TAC proliferation, whereas LESC activity remains largely unchanged, consistent with their slow-cycling behaviour. Weakening cell–substrate adhesion increases epithelial turnover without the need for external growth factor stimulation. In addition, increased surface shedding promotes both cell division and delamination, while excessive shedding induces mechanical compensation in the form of cell stretching in the upper epithelial layer.

The model further predicts a direct relationship between the shedding rate and the centripetal velocity of clonal expansion, reflecting a wound-healing-like acceleration of epithelial migration. Overall, these results highlight how intercellular mechanical forces coordinate cell size, migration, and turnover to maintain and rapidly restore epithelial integrity. Finally, I introduce an extension of the model to a five-layer epithelial structure and demonstrate the resulting wound healing dynamics.

Speaker: Neda Khodabakhsh Joniani (The University of Sydney)

11:40 AM Estimating effective diffusion in the vitreous: A profile likelihood approach

Wet age-related macular degeneration is a chronic ocular disease treated by repeated intravitreal injections. The relatively short intravitreal half-life of these therapeutics leads to frequent administration, creating a substantial treatment burden. Accurate estimation of the effective diffusion coefficient is central to predicting intravitreal half-life and to the rational design of longer-lasting treatments.

Quantitative investigation of intraocular drug transport is challenging: experimental access to the eye is limited, and the vitreous humour is a structurally complex, heterogeneous medium. Classical approaches estimate diffusion coefficients in substitute materials or extracted samples, which do not faithfully represent the intact vitreous. Recently, collaborators developed a method to measure diffusion in intact ex vivo vitreous. We analyse these data for molecules of varying sizes using a profile likelihood framework to estimate effective diffusion coefficients, assess practical identifiability, derive confidence intervals, and investigate the influence of molecular size and charge on transport. Comparison with synthetic data evaluates parameter recoverability under the experimental protocol. Our analysis shows partial practical identifiability, with confidence intervals dominated by measurement uncertainty and potential bias for highly charged molecules, indicating the need for experimental refinement and improved modelling of charge-dependent transport.

Speaker: Patricia Lamirande (Université de Montréal)

10:40 AM → 12:00 PM Modelling heterogeneity in infectious disease transmission and control

10:40 AM Mosquito biting heterogeneity and the community impact of targeted malaria interventions

Heterogeneity in mosquito biting rates is a key driver of malaria transmission dynamics and strongly influences the distribution of cases within a population. We develop a stochastic compartmental model describing malaria transmission between humans and mosquitoes, incorporating variation in biting exposure. We quantify the level of biting heterogeneity required to generate different Pareto fractions in malaria case distributions, from relatively homogeneous transmission to scenarios where a small proportion of individuals account for a large proportion of cases. We then investigate the impact of targeted control strategies that prioritise individuals based on biting exposure. Our results show that targeting highly bitten individuals can substantially reduce overall transmission. However, protecting specific individuals may initially lead to temporary increases in cases among non-targeted individuals due to shifts in transmission dynamics. Over longer time horizons, targeted interventions generally reduce transmission across the entire community, including those not directly receiving control measures. These findings highlight the importance of accounting for exposure heterogeneity when designing malaria control strategies and demonstrate the potential long-term community-wide benefits of targeted interventions.

Speaker: Emma Fairbanks (University of Manchester)

11:00 AM Simulating Mosquito Flight Paths with a Random Walk Model

Many animal species have been shown to use search patterns described by Lévy flight instead of particle-like Brownian motion (\cite{Humphries2012}, \cite{Reynolds2007}, \cite{Sims2008}). To investigate which type of random walk describes the search pattern of mosquitoes, we analyse flight tracks obtained by infrared recordings of Anopheles mosquitoes in a screened cage by looking at the distribution of their step lengths. On the other hand, we set up and simulate different types of random walk models to extract those step lengths. To determine which random walk model fits the flight behaviour of mosquitoes and to build a final model, we compare the distributions of the step lengths yielded by the simulations to the distribution of the step lengths given by the recorded flight path data.
In a next step, we include stimuli into the simulations and scale up the model to the size of a village. The flight path simulation builds the foundation to model the dispersal of mosquitoes and hence helps to estimate the effect of interventions targeting the mosquito population to fight disease transmission, for example releasing mosquitoes infected with Wolbachia bacteria or genetically modified mosquitoes, or distributing tools such as spatial emanators, odour-baited traps for adult mosquitoes, attractive targeted sugar baits (ATSB), or oviposition traps to assess their impact. The goal is to use the model to suggest the optimal placement of interventions.

Speaker: Luzia Nora Felber (Swiss TPH)

11:20 AM Immunity-driven biases in malaria incidence: a study for Senegal and The Gambia

Pronounced demographic heterogeneity in immunity is a defining feature of malaria; slowly acquired through repeated and sustained exposure, yet vanishing when this ceases. While compartmental models offer computational efficiency and may capture population-level trends, they often simplify the complex, cumulative nature of acquired immunity against the disease. Furthermore, varying levels of acquired immunity may differentially modify the sensitivity of the disease to climate, thus creating systematic spatially-dependent biases unaccounted for by population-average modelling approaches. We present VECTRI-ABM, a novel grid-based mechanistic framework where the climate-sensitive vector ecology model, VECTRI, is integrated with an agent-based model (ABM) of human health, replacing its original compartmental SEIR module to explicitly resolve individual-level demographic and immunity traits.

We applied this framework to Senegal and The Gambia - a region characterized by a pronounced north-south rainfall gradient, with diverse transmission intensity regimes. Through counterfactual experiments, we quantify the systematic biases in modelled incidence that arise when individual exposure history is neglected. We show how these biases shift as a function of the rainfall regime and host age, identifying the demographic and climatic thresholds where population-level averages fail to capture malaria dynamics. Finally, we discuss how identifying these systematic biases supports the design of more effective, targeted interventions for malaria prevention and elimination programs.

Speaker: Miguel Garrido Zornoza (Abdus Salam International Centre for Theoretical Physics)

11:40 AM Identifying robust triggers for controlling epidemic waves in real-time

Effectively assessing outbreak control strategies in real-time remains a substantial public health challenge. During the COVID-19 pandemic, public health and social measures (PHSMs) were often implemented and relaxed under a "tiered" system to balance the benefits and costs associated with broad societal measures. To guide decision making, modelling studies designed frameworks for tiered PHSMs which typically assumed the movement between tiers was triggered by an incidence or prevalence metric (for example, the number of COVID-19 patients occupying beds in hospital). However, the epidemiological delay from transmission events to clinical outcomes leads to a substantial epidemic peak overshoot upon imposing "lockdown", which is difficult to infer from measurements of current incidence or prevalence alone. We therefore introduce a framework that combines scenario modelling of tiered PHSMs with explicit short-term forecasts to estimate the epidemic peak in real-time. As we show, optimal hospital occupancy thresholds for imposing lockdown can be inferred using this framework, accounting for a range of sources of uncertainty. We demonstrate that metrics characterising the epidemic speed (in particular, the growth rate and the serial interval) are crucial for imposing a timely and effective lockdown to prevent healthcare systems from becoming overwhelmed.

Speaker: Nathan Doyle (University of Warwick)

10:40 AM → 12:00 PM PDE aspects of neural assemblies

10:40 AM Qualitative properties for certain PDEs derived from neuroscience

In recent years, the qualitative study of models derived from neuroscience has experienced significant progresses, particularly within the communities of probabilist and PDE specialists. The aim is to use certain models to understand the emergence of complex dynamics observed within interacting neural networks.
In this regard, numerous PDE models have been proposed, presenting structures, and therefore mathematical difficulties, that vary greatly depending on the modeling choices made. We will begin with an overview of the main issues and existing results for PDE models derived from neuroscience that are now relatively well understood, in both linear and non-linear regimes. We will then focus on a particular framework where modeling involves equations with degenerate diffusion, for which, even in the simplest (linear) case, several questions remain open.

Speaker: Delphine Salort (Laboratoire Jacques Louis Lions)

11:00 AM Disentangling pulse-coupled oscillators in the mean-field regime through the pseudo-inverse in a dilated timescale

Systems of pulse-coupled oscillators model synchronization through singular interactions occurring at discrete times, when particles reach a specific firing phase. They have numerous applications in physics, biology and engineering, for example to cardiac cells, neurons and fireflies. They could also represent a stepping stone for the understanding of networks of voltage-conductance neurons at the mesoscopic scale. In the mean-field limit, the probability density in phase of the population of oscillators satisfies a singular continuity equation prone to finite-time blow-up, for which very few theoretical results are available. With José A. Carrillo, Xu'an Dou and Zhennan Zhou
\cite{CDRZ}, we have introduced a reformulation of the mean-field system based on the inverse distribution function seen in a dilated timescale. It allows to show a hidden contraction/expansion mechanism and to propose simple and rigorous proofs of the long-time behaviour, the existence of steady states, the rates of convergence and the occurence of finite time blow-up for a large class of monotone phase response functions.

Speaker: Pierre Roux (Centrale Lyon)

11:20 AM Navigational-enabling settings of a PDE modelling noisy grid cell activity

Grid cells, with their striking hexagonal firing patterns, are neurons which play a key role in the internal navigational system of mammals. This talk will concern a nonlocal Fokker--Planck-like PDE which emerged in a pursuit to better understand the effects of noise on grid cell activity. When this model produces hexagonal network activity which persists when translated in accordance with the mammal's movement in physical space, the model is in a setting which enables the mammal's ability to orientate itself. Through aspects concerning the existence and stability of particular solutions to the PDE, we explore for which parameter settings such activity could emerge.

Based on collaborations with:
José Antonio Carrillo, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
Maren Brathen Kristoffersen, Department of Mathematics, Norwegian University of Life Sciences, 1433 As, Norway
Pierre Roux, Institut Camille Jordan, Ecole Centrale de Lyon, 69134 Ecully, France

Speaker: Suzanne Solem (Norwegian University of Life Sciences)

11:40 AM Resolving the Blow-Up: A Time-Dilated Numerical Framework for Multiple Firing Events in Mean-Field Neuronal Networks

In large-scale excitatory neuronal networks, rapid synchronization manifests as multiple firing events (MFEs), mathematically characterized by a finite-time blow-up of the neuronal firing rate in the mean-field Fokker-Planck equation. Standard numerical methods struggle to resolve this singularity due to the divergent boundary flux and the instantaneous nature of the population voltage reset. In this work, we propose a robust {multiscale numerical framework based on time dilation}. By transforming the governing equation into a dilated timescale proportional to the firing activity, we desingularize the blow-up, effectively stretching the instantaneous synchronization event into a resolved mesoscopic process. This approach is shown to be physically consistent with the {microscopic cascade mechanism} underlying MFEs and the system's inherent fragility. To implement this numerically, we develop a hybrid scheme that utilizes a {mesh-independent flux criterion} to switch between timescales and a semi-analytical ``moving Gaussian'' method to accurately evolve the post-blowup Dirac mass. Numerical benchmarks demonstrate that our solver not only captures steady states with high accuracy but also efficiently reproduces periodic MFEs, matching Monte Carlo simulations without the severe time-step restrictions associated with particle cascades.

Co-authors:
Xu'an Dou, Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China,
Louis Tao, Center for Bioinformatics and Center for Quantitative Biology, Peking University, Beijing 100871, China,
Zhe Xue and Zhennan Zhou, Institute for Theoretical Sciences, Westlake University, Hangzhou 310030, China.

Speaker: Zhennan Zhou (Westlake university)

10:40 AM → 12:00 PM MBI Community Gathering: Emerging Methods and Mathematical Models Arising from Biology

10:40 AM Entropy-Based Information Sharing for Uncertainty Quantification in Multi-Layer Complex Systems

We propose an entropy-based framework for uncertainty quantification in settings involving multiple, heterogeneous data sources. The central idea is to represent each empirical layer through an entropy-induced probability measure, allowing information to be shared and propagated across layers in a principled and consistent manner. This approach provides a natural mechanism for reconciling uncertainty arising from observational, experimental, and model-based components, while enabling interpretable variance–covariance decompositions analogous to ANOVA.

As an illustrative example, we reference recent work on random-measure-based sensitivity analysis in randomized controlled trials (Bastian, Rabitz, and Rempala, 2025), where entropy-consistent measures are used to quantify and decompose uncertainty across treatment and outcome spaces. While arising in a clinical context, this example highlights the broader applicability of entropy-driven information sharing for uncertainty quantification in complex, multi-layer systems.

Speaker: Grzegorz Rempala (Ohio State)

11:00 AM Algebraic, Geometric, and Combinatorial Approaches to Modeling Gene Regulatory Networks

The challenge of developing predictive models for gene regulatory networks has motivated a multitude of approaches, ranging from the discrete to the continuous, the deterministic to the probabilistic. In many settings, however, available experimental data do not determine a unique model: time series or input-output data typically admit multiple network structures or dynamical rules that are equally consistent with the observations and are computationally indistinguishable. This ambiguity raises a fundamental question at the interface of biology and mathematics: how can one design experiments that more effectively discriminate among competing models?

In this talk, I will highlight algebraic, geometric, and combinatorial methods for modeling gene regulatory networks and focus on reducing model uncertainty through improved experimental design. The central idea is to use structural properties of model classes to identify data that are maximally informative for model selection. This perspective has led to new questions and results involving identifiability, algebraic characterization of candidate models, and the geometry of data.

Speaker: Brandilyn Stigler (Southern Methodist University)

11:20 AM Chemical Reaction Networks with Stochastic Switching Behavior and Machine Learning Applications

In this talk, we examine switching behavior in stochastic reaction networks, where molecular copy numbers fluctuate between multiple distinct states. Such switching occurs when intrinsic noise drives transitions between multiple stable or quasi-stable states, rather than through deterministic oscillations. Stochastic switching has been observed in various biological phenomena, including gene expression, cell fate decisions, and biochemical oscillators with noise-induced transitions.
We focus on two models exhibiting this behavior, emphasizing that while both display state switching, their underlying mechanisms differ significantly. Using stochastic simulations, we analyze and compare the dynamics of the two models, tuning parameters so that their trajectories appear similar. From these oscillatory time series, we extract key features and apply several measures and classification techniques to determine whether the models can be distinguished.
Additional preliminary results, including extensions to other network architectures and parameter regimes, will also be discussed. This work is conducted jointly with Dongli Deng at UMBC.

Speaker: Hye-Won Kang (University of Maryland, Baltimore County)

11:40 AM From Blackboard to Bedside: Translating Mathematical Sleep Models into Samsung Galaxy Watch

Standard recommendations of 7–9 hours of sleep do not reliably guarantee daytime alertness. Using wearable-derived sleep-wake data, we infer two latent physiological states—homeostatic sleep pressure and circadian phase—via a mathematical model, and generate personalized sleep-wake schedules aligned with each individual's circadian rhythm. In two prospective clinical trials, adherence to model-based schedules significantly improved alertness, with circadian alignment proving a far stronger predictor than total sleep time alone. These findings led to deployment of our algorithm across all Samsung Galaxy Watch devices—the first mathematical biology model adopted by a major tech company. Extending this framework, we show that mathematically derived circadian features from sleep-wake data accurately predict mood episodes in bipolar disorder, outperforming models that rely on richer but more invasive data. Finally, we introduce HADES-NN, a neural network method for optimizing circadian models under real-world discontinuous light signals, enabling future model personalization at scale.

Speaker: Jae Kim (KAIST)

10:40 AM → 12:00 PM Phenotypic Plasticity in Tumor Progression

10:40 AM Dynamical modeling of phenotypic plasticity in melanoma reveals strategies of drug-induced adaptation

Phenotypic heterogeneity of melanoma cells contributes to drug tolerance, increased metastasis, and immune evasion in patients with progressive disease. However, the dynamics of the co-existence and interconversion among these different phenotypes remains unclear. Here, we integrate dynamical systems modeling with transcriptomic data analysis at bulk and single-cell levels to investigate underlying mechanisms behind phenotypic plasticity in melanoma and its impact on adaptation to different therapies. We construct a minimal core gene regulatory network involving the transcription factors implicated in this process and identify the multiple 'attractors' in phenotypic landscape enabled by this network. The emergent dynamics of this regulatory network comprising MITF, SOX10, SOX9, JUN and ZEB1 can recapitulate experimental observations about the co-existence of diverse phenotypes and reversible cell-state transitions among them, including in response to targeted therapy and immune checkpoint inhibitors. Our model predictions about changes in proliferative to invasive transition and PD-L1 levels as melanoma cells evade targeted therapy and immune checkpoint inhibitors were also validated in multiple RNA-seq data sets from in vitro and in vivo experiments. Our calibrated dynamical model offers a platform to test combinatorial therapies against phenotypic plasticity and provide rational avenues for treating melanoma.

Speaker: Mohit Kumar Jolly (Indian Institute of Science)

11:00 AM Modeling Epigenetic Reprogramming and Phenotypic Plasticity in AML with State‑Transition Models

Acute myeloid leukemia (AML) progression reflects a stochastic and adaptive process driven by cellular plasticity and the continual reshaping of epigenetic regulatory programs. To capture these dynamics, we develop a stochastic modeling framework in which a Langevin equation describes noise‑driven fluctuations underlying shifts in differentiation potential, chromatin state, and lineage identity in mouse models of AML. These evolving processes are embedded within a state‑space that maps observed molecular and phenotypic changes onto latent variables summarizing disease evolution and therapeutic response. The associated Fokker–Planck equation characterizes how probability densities propagate across epigenetically regulated cellular states, enabling quantitative prediction of phenotype switching, treatment adaptation, and the emergence of resistant cell populations. By linking measurements of epigenetic reprogramming and lineage plasticity with a stochastic dynamical system, this framework provides a quantitative platform for forecasting AML behavior under treatment. In this talk, I will highlight how mouse models, public datasets, and mathematical modeling provide insight into plasticity in AML evolution and outline our efforts to translate the predictive models into clinical trials at City of Hope.

Speaker: Russell Rockne (Professor & Chair, Department of Computational and Quantitative Medicine Beckman Research Institute, City of Hope.)

11:20 AM Uncovering underlying physical principles and driving forces of cancer from single-cell transcriptomics

Cancer has been a serious disease for human health. Genetic mutations have often been thought to be mainly responsible for the cancer formation. More evidences have been accumulated that cancer emergence is not just caused by individual gene perturbation but also from the whole network or state of the system. This shift of thinking demands global quantification and physical understanding of the underlying mechanisms for cancer formation. Here, we develop cancer models from the underlying gene regulatory networks either based on the available low throughput or the recent high throughput sequence experimental studies \cite{Zhu2024AdvSci, Zhu2024PNAS, ZhuWangSubmitted}. Cancer landscape can be quantified and cancer can be revealed as attractors representing cancer states. The landscape barrier and switching time become the measures of how difficult to transform from normal to cancer state. Furthermore, the cancer formation process can be quantified by the optimal paths between the normal state and cancer state. Due to the presence of the curl flux as the nonequilibrium driving force, the forward path and backward paths for cancer formation and normal state restoration are distinctly different. The global sensitivity analysis based on the landscape topography and nonequilibrium driving forces identify key genes and regulations responsible for the cancer formation. We further identify the nonequilibrium indicators through the curl flux, entropy production and time irreversibility as the early warning signals for the cancer formation. This helps to design practical strategy for cancer prevention and treatment.

Speaker: Jin Wang (Department of Chemistry, Stony Brook University.)

11:40 AM Phase-space geometry as a determinant of phenotypic plasticity in breast cancer

Phenotypic plasticity in breast cancer can be viewed as stochastic switching between stable gene-expression states associated with clinically distinct subtypes. Building on our previously published NF-κB-centered regulatory network model for breast cancer heterogeneity \cite{Lopes2025}, I will present recent results showing that, in non-conservative gene regulatory systems, in which potential functions are generally not uniquely defined, geometric features of phase space offer a well-defined framework for describing transition probabilities and timescales. In particular, the distance between stable and unstable stationary states, together with the bifurcation structure organizing multistability, emerges as a robust determinant of transition accessibility, transition times, and variability. The analysis reveals a marked asymmetry between phenotypic regimes: the HER2+ attractor is comparatively robust to intrinsic parameter variation, whereas the TNBC regime strongly amplifies such variation, offering a dynamical interpretation for the pronounced heterogeneity observed in triple-negative breast cancer. More broadly, the results support a geometric framework for phenotypic transitions in gene regulatory networks operating far from equilibrium \cite{Caldas2026}.

Speaker: Francisco Lopes (Universidade Federal do Rio de Janeiro)

10:40 AM → 12:00 PM Meta-Perspectives on Mathematical Biology

10:40 AM Developing a handbook of mathematical modelling of infectious diseases for decision-making

Decision-making during public health crises, such as pandemics or epidemics, often relies on evidence from mathematical models produced by public health authorities. In such crises, e.g. the recent COVID-19 pandemic, government and public health authorities in many countries were assisted by academic researchers. However, the practices of modelling for decision-making are different from that of academia, and this clash of cultures hampered the contributions made by academic modellers. In order to improve on this situation and increase preparedness for future crises we have composed a document titled “Handbook of mathematical modelling of infectious diseases for decision-making”. The handbook describes the process of modelling infectious diseases in a chronological order going from preparatory work, implementation, to communication of model results and lastly management of models. The target audience are academic modellers and junior public health officials, and we believe that this handbook has the potential to strengthen collaboration between government authorities and academia, ultimately leading to improved preparedness.

Speaker: Philip Gerlee (Chalmers University of Technology, Sweden)

11:00 AM Interactive education and interdisciplinary communication via VisualPDE

Partial differential equations (PDEs) underpin mathematical models across science and engineering, yet their complexity presents a significant barrier to students and researchers outside mathematics. In this talk, I will present VisualPDE (a free, open-source, browser-based platform for real-time interactive simulation of PDE systems) and discuss its role as both a pedagogical tool and a medium for interdisciplinary communication.

VisualPDE requires no installation or coding knowledge and runs instantly in any web browser. Simulations can be shared via a URL, making them trivially embeddable in lecture notes, papers, and outreach materials. This immediacy transforms the teaching of abstract concepts, rather than presenting bifurcations and instabilities as static equations, students can explore them by direct manipulation, such as by tuning parameters, painting initial conditions, and probing boundary effects in real time.

Beyond the classroom, VisualPDE serves as a communication bridge between mathematical modellers and domain scientists. Shareable, interactive simulations allow collaborators in biology, ecology, and beyond to build genuine intuition about model behaviour without engaging directly with the underlying mathematics. In an era of open science, we hope that interactive simulations like these can be first-class outputs of mathematical research designed to broaden impact and deepen understanding.

Speakers: Adam K. Townsend, Andrew L. Krause, Benjamin Walker (University College London, UK)

11:20 AM Using bibliometrics to analyse trends in mathematical biology

Quantitatively understanding a research field is important for funding allocation, teaching and curriculum development, research organisation, and scientific communication. One way to achieve this understanding is through bibliometric analysis, which involves using statistical methods to examine patterns in scientific publication metadata and citation networks. We present two case studies that use bibliometric analysis. First, we obtain a comprehensive overview of mathematical oncology as a research field. Our analysis shows that since the 1960s, mathematical oncology has become more globally connected, and more interactive with external disciplines, with larger research teams and evolving research topics \citep{pugh2025bibliometric}. Moreover, our results quantitatively demonstrate that mathematical oncology benefits both mathematics and the life sciences. Second, we investigate the cross-disciplinary exchange in biological agent-based modelling. Our findings suggest limited cross-talk between disciplines, with citations largely self-contained. We discuss the potential advantages and disadvantages of research fields being isolated versus those that are more interconnected.

Speaker: Kira Pugh (Uppsala University, Sweden)

11:40 AM A Sensational Approach to Inclusive STEM outreach

“Science is not finished until it is communicated”. This quote attributed to Sir Mark Walport, the UKs Chief Scientist in 2013, has become a rallying cry for the science communication (SciComm) community and those involved in informal STEM education, to encourage researchers to communicate their science beyond the academe.
While there are no precise numbers, it is clear that more scientists, physicians, journalists and educators are choosing to get involved in engaging non-expert audiences with STEM subjects. This is reflected in the increasing number of communities dedicated to supporting SciComm, greater avenues for professional development, presence on social media platforms, and even in the requirements for funding bodies such as the NSF, to discuss the “Broader Impacts” of research beyond scientific advancement.
Science outreach connects research to communities, inspires future scientists, and strengthens public trust in evidence-based decision-making. However, outreach that overlooks inclusion, limits who benefits and who participates in STEM. This talk uses the example of a sensory-friendly science festival to argue that inclusive outreach — designed to reach diverse learners — is essential for equitable opportunity, improved innovation, and more resilient scientific systems.

Speaker: Parmvir Kaur Bahia (Artha Science Media)

10:40 AM → 12:00 PM Multiscale Modeling of Stochastic Reaction–Diffusion Systems in Biology

10:40 AM Field theories and quantum methods for multiscale complex systems

Many real-world complex systems — from biochemical networks and ecological dynamics to epidemics and socioeconomic models — share a common mathematical structure: agents or particles that move, interact, and change in number. Stochastic reaction-diffusion processes provide a natural and unifying framework to model this broad class of systems, yet their standard probabilistic formulations become unwieldy due to combinatorial complexity arising from nonlinear interactions and varying particle numbers. In this talk, I will show how quantum-inspired methods — second quantization, Fock space, creation and annihilation operators, and path integrals — offer an elegant and powerful alternative. Originally developed for quantum field theory, these tools can be brought into the classical domain of stochastic systems, where they handle combinatorial bookkeeping automatically and enable systematic derivations of emergent behavior at multiple scales. I will present a unifying field theory representation that encompasses previous formulations (Doi, Doi-Peliti, RDME) as special cases, and demonstrate how it yields consistent multiscale numerical schemes and parameter relations across scales. Crucially, while the framework is grounded in reaction-diffusion systems, its structure is sufficiently general to extend to a wide range of complex systems — including population dynamics, neuroscience, and social systems — wherever agents interact and change in number, opening new avenues for multiscale modeling across disciplines.

Speaker: Mauricio del Razo (Free University of Berlin)

11:00 AM Multi-resolution simulations of intracellular processes

All-atom and coarse-grained molecular dynamics~\cite{ref1}, Langevin dynamics~\cite{ref2}, Brownian dynamics~\cite{ref3,ref4}, and compartment-based stochastic reaction–diffusion models~\cite{ref4,ref5} are computational methodologies that have been applied to the spatio-temporal modelling of numerous intracellular processes. They differ in the level of biological detail they can capture and in the computational intensity of the resulting simulations. In some cases, it is possible to establish rigorous connections between these modelling frameworks by deriving a macroscopic (coarse-grained) description from the detailed one. I will discuss these connections, with a focus on the development, analysis, and applications of multi-resolution methods, which combine detailed (high-resolution) simulations in localized regions of particular interest (where accuracy and microscopic detail are crucial) with a coarser stochastic model in other regions where accuracy may be traded for computational efficiency. I will illustrate applications of multi-resolution methodologies to modelling intracellular calcium dynamics, actin dynamics, and DNA dynamics.

Speaker: Radek Erban (Oxford University)

11:20 AM Adding Drift to Stochastic Reaction-Diffusion Processes

Particle-based stochastic reaction-diffusion processes are widely used in modeling biological processes. There is now a well-developed set of results detailing their basic properties, how they rigorously relate to macroscopic reaction-diffusion PDE models, and a variety of numerical simulation methods for their accurate and efficient approximation. In contrast, adding drift to these models introduces a number of open questions.
In this talk, I will describe our recent work on particle-based stochastic reaction-drift-diffusion models in which drift arises from one- and two-body interactions. I will first introduce the physical formulation of these models, illustrating how satisfying detailed balance of reaction fluxes at equilibrium constrains reactive interaction functions for reversible reactions. I will then summarize our work proving the rigorous mean-field large-population limit of such particle models, and outline which types of reaction-drift-diffusion PDEs arise in this limit.

Speaker: Samuel Isaacson (Boston University)

11:40 AM Coarse-Grained Modeling of Particle Clustering Dynamics

Particle-based models with pairwise interactions provide a natural framework to describe clustering phenomena in biological systems, but their simulation and analysis become computationally demanding at large scales. In this talk, I will present two complementary approaches for efficient coarse-grained modeling of particle clustering dynamics. First, I will show that stochastic partial differential equations (SPDEs) can accurately reproduce spatiotemporal clustering behavior, including cluster formation and merging, beyond the reach of deterministic mean-field models~\cite{wehlitz2025approximating}. Second, I will introduce a data-driven reduction of transfer operators, yielding low-dimensional Markov models that capture metastable cluster configurations and transition pathways~\cite{wehlitz2026data}. Together, these approaches provide interpretable and computationally efficient descriptions of clustering dynamics, enabling the analysis of large systems and long time scales.

Speaker: Stefanie Winkelmann (Zuse Institute Berlin)

10:40 AM → 12:00 PM Mathematical models of vector-borne diseases

10:40 AM A Stage-Structured Seasonal Model for the Spread of Flavescence Dorée in Vineyards

Flavescence dorée is one of the most severe phytoplasma diseases affecting grapevines, posing an increasing threat to vineyards worldwide. The bacterial agent causing the disease is spread by the American grapevine leafhopper. We present a compartmental model for the spread of flavescence dorée incorporating stage structure in the vectors. To account for seasonal weather variations and the behaviour of the vectors, we consider periodic transmission, birth and death rates. We calculate the basic reproduction number as the spectral radius of a linear operator and show that it serves as a threshold parameter for disease persistence. Finally, we provide numerical simulations to assess the effect of varying key model parameters.

Speakers: Attila Denes (University of Szeged), Nigussie Nigussie Abeye Shifera (Bolyai Institute, University of Szege), Ábel Ábel Garab (Bolyai Institute, University of Szeged)

AD.pdf

11:00 AM On Multiscale Modeling of Vector-Borne Diseases

The transmission of infectious diseases involves complex interactions across multiple biological scales, from within-host immunological processes to between-host transmission dynamics. We develop a multiscale epidemic model linking host--vector population-level transmission dynamics to within-host and within-vector pathogen dynamics. Our model captures key features of within-vector viral progression and allows bidirectional coupling between within-host and between-host processes. Our results underscore the importance of carefully selecting coupling functions and provide guidance on when multiscale modeling is essential for understanding and managing vector-borne diseases.

Speaker: Jorge Velasco (UNAM)

JV.pdf

11:20 AM Underlying Complexity in Dengue Reinfection Dynamics: Backward Bifurcation and Serotype Invasion in a Multi-Serotype Model

Reinfection plays a central role in dengue dynamics, as secondary infection with a different serotype may lead to severe forms such as Dengue Hemorrhagic Fever (DHF) through Antibody-Dependent Enhancement (ADE). We propose a multi-scale nested immuno-epidemiological model coupling within-host immune dynamics and between-host transmission. The model accounts for primary and secondary infections, capturing the interplay between immunity and epidemiological spread \cite{Adimy2026Dengue}. We show the occurrence of backward bifurcation, implying that the basic reproduction number alone does not ensure disease eradication. We also derive an invasion reproduction number characterizing the ability of a new serotype to invade a population where another is endemic. These results highlight the underlying complexity of dengue reinfection dynamics and the role of ADE in shaping transmission and disease severity.

Speakers: Charlotte Dugourd-Camus (INRIA, Centre Lyon - France), Mostafa Adimy (INRIA), Ruben Taieb (INRIA, Centre Lyon - France)

MA.pdf

11:40 AM Dengue Fever Drivers and Mosquito Population Dynamics

In this talk, we discuss the relationship between mosquito population dynamics and dengue fever case counts. Drawing on data from a specific city in Brazil, we analyze the primary drivers of dengue outbreaks and demonstrate that mosquito population dynamics alone are not a reliable predictor of outbreaks. Instead, climatic factors and the immunological status of the population appear to be the main factors explaining the variability in yearly occurrences. To reach these conclusions, we employ techniques from machine learning and attractor reconstruction in dynamical systems.

Speaker: Roberto Kraenkel (UNESP)

10:40 AM → 12:00 PM Past, Present, and Future of Reaction Networks Theory

10:40 AM Bifurcations of Equilibria in Mass-action Systems

Multistability and oscillations are ubiquitous in nature, appearing in contexts ranging from biochemical reaction networks and cellular regulation to ecological and chemical processes. These phenomena are often associated with qualitative changes in system dynamics as parameters vary, making bifurcation analysis a fundamental tool for understanding the mechanisms that generate such behaviors.

In this talk, we give an overview of the recent developments in the systematic study of local bifurcations of equilibria of small mass-action systems, including fold, cusp, Andronov-Hopf, Bautin, and Bogdanov-Takens bifurcations. The intensive study of nontrivial dynamical properties in small reaction networks is justified and motivated by recent advances in inheritance theory, a mathematical tool that allows us to lift nondegenerate behaviors from smaller networks to larger, more realistic ones.

Joint work with Murad Banaji (Lancaster University, United Kingdom) and Josef Hofbauer (University of Vienna, Austria).

Speaker: Balázs Boros (University of Szeged)

11:00 AM QSDs and Reaction Networks

This talk is concerned with quasi-stationary distributions (QSDs) of continuous-time Markov chains (CTMCs) with extinction in a setting that embraces reaction networks. QSDs describe the long-term behavior of such stochastic systems conditioned not to go extinct.

QSDs have a long history in probability theory, and this talk draws from this rich history. The focus is on CTMCs on the non-negative integers with a local jump structure. This local jump structure enforces (among other things) a recursive characterization of QSDs, the existence of an extremal QSD, and the existence of a sequence of Karlin-McGregor-type polynomials of increasing degree that characterizes Kingman’s parameter. The local jump structure is naturally implied by the structure of reaction networks. Some of these results and their importance will be explained in a (presumably) non-technical way.

Furthermore, the results will be illustrated by examples from reaction network theory, and the intuition of the audience will be tested, and why our intuition might fail, will be discussed.

Speaker: Carsten Wiuf (University of Copenhagen)

11:20 AM Stochastic Reaction Networks: Definition, Classical Scaling and Long-Term Behavior

Stochastic reaction networks, modelled as continuous-time Markov chains, provide a principled framework for capturing the inherent randomness in biochemical and population systems. In this overview, I will introduce them and present the classical scaling limit, which establishes convergence to the deterministic reaction network model on compact time intervals as the system size grows. A natural question then arises: does this approximation persist over long-time horizons? The study of limit distributions is motivated both by the analysis of biological models over long-time intervals and by multiscale models, where fast subsystems are approximated by their stationary regime. I will discuss notable connections and discrepancies between the stochastic and deterministic long-term dynamics, highlighting the case of complex-balanced models. Time permitting, I will close with some related open problems.

Speaker: Daniele Cappelletti (Politecnico di Torino)

11:40 AM Utilizing Structure in Monte Carlo Methods for Stochastic Reaction Networks

Monte Carlo methods are among the most flexible tools for studying stochastic reaction networks, but they can be computationally expensive when exact simulation is used naively. In this talk, I will describe a general philosophy for improving such methods: exploit the structure inherent in the stochastic model itself. For reaction networks, that structure is often encoded through Poisson-process representations, such as Kurtz's random time change representation and related space-time Poisson constructions, which naturally suggest useful couplings between paths.

I will describe several simple but powerful coupling strategies, including the use of common Poisson processes, split couplings based on shared parts of reaction intensities, and shared space-time Poisson constructions. These couplings lead to efficient algorithms in a variety of settings, including parametric sensitivity analysis, multilevel Monte Carlo for expectations, and simulation of models with time-dependent intensities. The overall goal of the talk is introductory: to show how simple structural ideas can lead to substantial gains in efficiency across several Monte Carlo problems for stochastic reaction networks.

Speaker: David Anderson (University of Wisconsin-Madison)

10:40 AM → 12:00 PM Mathematical Modelling for Alzheimer's Disease

10:40 AM Deciphering Alzheimer’s Disease Dynamics: Modelling Protein Pathology, Inflammation, and Therapeutic Strategies

By 2030, an estimated 78 million people will be living with Alzheimer’s disease (AD). Despite decades of research, clinical trials continue to face failure rates exceeding $95\%$, highlighting the need for improved mechanistic understanding of disease progression and therapeutic response. Mathematical modelling provides a framework to integrate biological processes across scales and enable safe, cost-effective in silico experimentation.

AD is characterised by the aggregation of proteins into toxic species that propagate through the brain in a prion-like manner. These processes interact with biological pathways, including clearance mechanisms and neuroinflammatory responses, ultimately driving neurodegeneration.

In this talk, I present a mathematical framework for the spatiotemporal dynamics of AD that integrates protein aggregation, network-mediated transport, clearance, and therapeutic interventions. Reaction–diffusion models on human brain networks describe the propagation of protein pathology together with clearance and inflammation. Complementing this approach, models of aggregation are formulated as spatially extended nucleation–elongation–fragmentation systems. These models are integrated with quantitative systems pharmacology frameworks describing drug–target interactions and biomarker responses, allowing therapeutic interventions to be incorporated directly into disease dynamics. Calibrated to human and clinical data, this multiscale framework can reveal mechanistic links between clearance, protein propagation, and neurodegeneration. Analytical and computational results aim to provide a quantitative basis for identifying mechanisms whose modulation may slow AD progression.

Speaker: Georgia Brennan (Oxford–GSK Institute of Molecular and Computational Medicine, University of Oxford; Mathematical Institute, University of Oxford)

11:00 AM Spreading of pathological proteins through brain networks

Mathematical models can be used to verify medical hypotheses and quantify the mechanisms of the progression of neurological pathologies like Alzheimer's disease. In this work, we are interested in elucidating the spread of misfolded tau protein, a critical hallmark of Alzheimer's disease, alongside amyloid $\beta$ protein, while taking the synergistic interaction between the two proteins into account \cite{Bianchi2024MCA}. We analyze a model consisting of a set of ordinary differential equations defined on brain networks derived from human connectomes, where brain regions are connected by edges representing fiber tracts. In particular, we consider several modeling choices, all employing network frameworks for protein evolution, differentiated by the network architecture and diffusion operators employed. By carefully comparing the model results against clinical tau concentration data \cite{Petersen2010N}, gathered through advanced multimodal analysis techniques, we can identify values for the parameters of the mathematical model such that it can reproduce the disease progression. Moreover, we show that certain models better replicate the protein's dynamics and that the mathematical setting must be chosen with great care if the comparison with clinical data is considered decisive \cite{Landi2026MBE}.

Speaker: Samira Breitling (University of Bologna)

11:20 AM A mathematical model for tau aggregation and diffusion: An approach via two-scale homogenization of the Smoluchowski equation with transmission boundary conditions

Pathological accumulations of hyperphosphorylated tau protein aggregates, known as neurofibrillary tangles, are detected in several neurodegenerative tauopathies, including Alzheimer's disease \cite{GS:2017}. Tau is a highly soluble, natively unfolded protein which is predominantly located in the axons of neurons of the central nervous system. Here, its physiological function is to support assembly and stabilization of axonal microtubules. Under pathological conditions, tau can assume abnormal conformations. In particular, hyperphosphorylation has a negative impact on the biological function of tau proteins, since it inhibits the binding to microtubules, compromising their stabilization and axonal transport, and promotes self-aggregation. Recent evidences have demonstrated that the progression of tau pathology reflects cell-to-cell propagation of the disease, achieved through the release of tau into the extracellular space and the uptake by surrounding healthy neurons \cite{YAM:2017}. In this work, we prove a two-scale homogenization result for a set of diffusion-coagulation Smoluchowski-type equations with transmission boundary conditions. This system is meant to describe the aggregation and diffusion of pathological tau proteins inside the axons and in the extracellular space. We prove the existence, uniqueness, positivity and boundedness of solutions to the model equations derived at the microscale (that is, the scale of single neurons). Then, we study the convergence of the homogenization process to the solution of a macro-model asymptotically consistent with the microscopic one \cite{FL:2024}.

Speaker: Silvia Lorenzani (Politecnico di Milano)

11:40 AM Linking Astrocyte Morphology to Metabolic Dysfunction in Alzheimer’s Disease: A Multiscale Modelling Approach

Astrocytes are glial cells essential for brain homeostasis, acting as metabolic mediators that couple cerebral blood flow and nutrient uptake to neuronal energy demands. In Alzheimer’s disease (AD), progressive neurodegeneration is accompanied by profound alterations in astrocyte morphology and metabolism. Reactive transformation leads to significant structural remodeling and metabolic changes~\cite{esc}, yet how these morphological alterations contribute to astrocytic metabolic dysfunction remains unclear. Here, we investigate the relationship between AD-related morphological changes and metabolic function using a multiscale mathematical modelling framework ~\cite{far2021, far2023, pap}. The model integrates intracellular energy metabolism with realistic three-dimensional astrocyte morphologies reconstructed from post-mortem human AD and age-matched control. By coupling spatially resolved metabolic pathway dynamics with cellular geometry, we systematically analyse how disease-associated alterations affect energy production, intracellular distribution, and neuronal support capacity. Simulations show that AD-related metabolic dysfunction reduces energetic output and compromises astrocytic support to neurons. Energy deficits arise from the cumulative impairment of multiple pathways rather than a single defect. Notably, morphological remodeling appears to partially compensate for metabolic deficits, suggesting a potential protective response in AD.

Speaker: Sofia Farina (University of Bern)

10:40 AM → 12:00 PM Newtonian and non-Newtonian Biofluidmechanics: Integrating Theory, Experiments, Modeling, and Simulations

10:40 AM Geometry, pattern, and mechanics of notochords

Chordocytes, in early zebrafish, pack in a small number of stereotyped patterns. Disruptions of the WT pattern are associated with developmental defects, including scoliosis. The dominant WT "staircase" pattern is the only regular pattern with transverse eccentricity. Morphometry and pattern analysis have established a length ratio governing which patterns will be observed. Physical models of cell packing in the notochord have established some relationships between geometric and mechanical ratios. Since a major function of the early notochord is to act as both a column and a beam, we aim to understand the overall resistance to compression and bending in terms of these mesoscale cell/tissue properties. To frame these relationships, we developed a model of the notochord as an elastic closed-cell foam, packed in either “staircase” or “bamboo” pattern. We determine the tension ratio between different surfaces in the notochord in terms of the relative stiffnesses and internal pressure. We determine the flexural rigidity of the model notochords in terms of relative stiffnesses and pressure. We find that the staircase pattern is more than twice as stiff as the bamboo pattern. The staircase pattern is also more than twice as stiff in lateral bending as in dorsoventral bending. This biomechanical difference may provide a specific developmental advantage to regulating the cell packing pattern in early-stage notochords.

Speaker: Sharon Lubkin (North Carolina State University)

11:00 AM Riding the Wave: Emergent Metachronal Paddling and Swimming in 3D FSI Model of a Gossamer Worm

Metachrony is often found throughout nature in many locomotory and fluid transport systems. Gossamer worms, also known tomopterids, are a soft-bodied, pelagic polychaete that employ metachronal paddling, with flexible parabodia on both sides of their body that navigate the midwater ecosystem which they inhabit. In the following study, we introduce a three-dimensional, computational, fluid-structure interaction model of a tomopterid, using a stadium (i.e. a rectangle with two half circles) with flexible parapodia appendages. The motion of the flexible parapodia will emerge from the interplay of passive body elasticity, active tension, and hydro-dynamic forces, and metachrony will result from differences in phase between the parapodia. The body is freely swimming as a result motion of the parapodia and the metachronal waves formed on both sides of the body. The model is used to explore how variations in phase across the body affect the resulting swimming performance and stability.

Speaker: Alexander Hoover (Cleveland State University)

11:20 AM Mixing and transport in the Drosophila melanogaster oocyte

In the oocyte of the common fruit fly, large scale cytoplasmic flows appear in the mid-to-late stages of oogenesis. Proteins, synthesized in adjoining nurse cells, and yolk, endocytosed through the cell cortex, are transported and mixed throughout the oocyte, presumably accelerated by the cytoplasmic flows. While a biophysical mechanism has been proposed which explains the onset of cytoplasmic streaming flows [1,2], the flows thereby produced are poor at mixing and typically orient themselves orthogonal to the required transport direction [3]. In this talk, we explore further mechanisms which accelerate cytoplasmic mixing and transport.

[1] David B. Stein, Gabriele De Canio, Eric Lauga, Michael J. Shelley, and Raymond E. Goldstein. Swirling instability of the microtubule cytoskeleton. Physical Review Letters, 126(2):028103, 2021.
[2] Sayantan Dutta, Reza Farhadifar, Wen Lu, Gokberk Kabacaoglu, Robert Blackwell, David B. Stein, Margot Lakonishok, Vladimir I. Gelfand, Stanislav Y. Shvartsman, and Michael J. Shelley. Self-organized intracellular twisters. Nature Physics, 20(4):666-674, 2024.
[3] Olenka Jain, Brato Chakrabarti, Reza Farhadifar, Elizabeth R. Gavis, Michael J. Shelley, and Stanislav Y. Shvartsman. Geometric effects in large scale intracellular flows. PRX Life, 3(2):023007, 2025.

Speaker: David Stein (Flat Iron Institute)

11:40 AM Locomotion, collective dynamics and chemotaxis of micro-swimmers in Brinkman flow

Micro-swimmer dynamics in heterogeneous media is receiving increased interest in fluid dynamics and biological physics due to the pervasiveness of microorganisms in complex environments [1]. We present a model for a microswimmer moving in a porous medium. One such a porous medium consisting of with impurities immersed in fluid, is the Brinkman fluid which approximates a sparse matrix of stationary sphere obstacles via a linear resistance term added to the viscous fluid momentum equation. We present theoretical derivations and numerical simulations of the motion of dumb-bell micro-swimmers in Brinkman flow as well as their dynamics near no-slip and no-stress planes [2]. Next, we present continuum models, linear analysis and nonlinear simulations examining the collective dynamics and chemotactic aggregation of many such micro-swimmers in Brinkman flow, together with phase diagrams specifying parameter spaces for the predicted dynamics [3, 4]. Lastly, we discuss how such a medium affects the spread of a bacterial accumulation and compare to experiments [5]. The results provide new analytical tools for understanding locomotion in complex fluids and offer new insights on the collective behavior of active suspensions within porous or structured environments.

[1] Saverio E. Spagnolie and Patrick T. Underhill, Swimming in Complex Fluids. Annual Review of Condensed Matter Physics 14:381, 2023.
[2] Francisca Guzman-Lastra and Enkeleida Lushi, Microswimmer locomotion and hydrodynamics in Brinkman flows. Physical Review E 112(5):055110, 2025.
[3] Yasser Almoteri and Enkeleida Lushi. Microswimmer collective dynamics in Brinkman flows. Physical Review Fluids 10 (8):083102, 2025.
[4] Yasser Almoteri and Enkeleida Lushi. Chemotactic aggregation dynamics of micro-swimmers in Brinkman flows. arXiv:2504.20925, 2025.
[5] Yasser Almoteri, Bacterial motion and spread in porous environments. Ph.D. thesis, New Jersey Institute of Technology, 2023.

Speaker: Enkeleida Lushi (Soft Active Matter Lab)

10:40 AM → 12:00 PM Spatial plasticity and heterogeneity in cancer: from niches to therapy

10:40 AM Spatial immune-tumor ecology in the multiple myeloma bone niche: an agent-based modeling approach

Cancer progression can be understood as the disruption of tissue homeostasis by tumor cells that co-opt their microenvironment\cite{BasantaAnderson2017}. In multiple myeloma (MM), this disruption unfolds within the bone marrow, where stromal cells, osteoclasts, osteoblasts, and immune populations form spatially heterogeneous niches. We have previously shown that integrated computational models of the bone ecosystem can capture how spatial microenvironmental structure shapes cancer-bone interactions\cite{Araujo2014} and how environment-mediated drug resistance (EMDR) in stroma-proximal niches facilitates relapse and clonal heterogeneity\cite{Bishop2024}. Separately, our work on stromal protection in breast cancer demonstrated that stroma-augmented proliferation indirectly drives chemoresistance by accelerating tumor recovery between treatment cycles\cite{Miroshnychenko2023}. Here, we extend our MM bone ecosystem ABM by introducing cytotoxic T-cell and regulatory T-cell (Treg) agents whose activity depends on local microenvironmental conditions. We investigate how spatial niche structure shapes effective anti-myeloma immunity, how Treg-mediated suppression generates local immunosuppressive refugia, and how these dynamics influence evolutionary trajectories under therapy. Our results suggest that spatially homogeneous assumptions about immune function can substantially mischaracterize treatment response, underscoring that niche-specific immune ecology is critical for understanding resistance in MM.

Speaker: David Basanta (Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA)

11:00 AM Integrating longitudinal MRI and clinical data into a biomechanistic tumor growth model for spatial forecasting of prostate cancer aggressiveness

The Gleason score (GS) is a key predictor of prostate cancer (PCa) aggressiveness and survival, yet treatment decisions rely on biopsies that incompletely sample highly heterogeneous tumors. As a result, clinically relevant spatial variations in tumor aggressiveness may remain undetected. To address this clinically unresolved issue, I present a personalized modelling framework for pointwise prediction of PCa aggressiveness across the 3D tumor domain that is informed by routine clinical and imaging data. The approach combines physics-based and data-driven components in a three-step pipeline. First, a biomechanistic model of PCa growth is personalized using longitudinal MRI and serum PSA data. Second, the model generates spatial maps of mechanistic biomarkers (e.g., reflecting tumor proliferation activity, cell density, and growth dynamics). Third, machine-learning classifiers use these spatial features to infer local tumor aggressiveness across the 3D tumor geometry. Preliminary results using a reaction-diffusion biomechanistic model in a cohort of n=16 PCa cases in active surveillance show that a logistic classifier based on tumor proliferation activity and density achieved an AUC under the ROC curve of 0.96, with sensitivity of 86.4% and specificity of 90.7% for prediction of GS. Of note, model-based predictions anticipated the emergence of higher-risk disease more than one year earlier than standard monitoring, thereby showing promise for guiding clinical decision-making.

Speaker: Guillermo Lorenzo (Department of Mathematics, University of A Coruña, Spain)

11:20 AM How evolvability dynamics affect tumor growth and treatment response

Drug resistance is an ongoing problem for maintaining a treatment response in advanced cancers, which are often more heterogeneous and evolvable. Evolvability may be beneficial if lesions can easily respond to large shifts in the microenvironment by modifying their traits to survive, like how metastases can survive a new environment and even thrive despite treatment applications. However, evolvability may also be a detriment. With too much deviation from the parental phenotype, cells lose important functions necessary to survive. So, is there an optimal rate of evolvability for tumors to grow and survive treatment that can be exploited therapeutically?

We use an off-lattice agent-based model to investigate how the rate of change through proliferation-migration phenotype space affects tumor growth and response to treatment. During growth, both proliferation and migration are advantageous traits. Increasing migration allows cells to distribute spatially, which allows more proliferation by lessening the spatial competition, and increasing proliferation allows for faster turnover and more mutation. More evolvability leads to more heterogeneity and faster recurrence under treatment. But when evolvability is costly, tumor survival depends on the rate and jump size of heritable changes to transiently lose proliferation fitness selected for during growth and gain resistance for survival. We consider how to design treatment strategies based on a tumor’s evolvability dynamics.

Speaker: Jill Gallaher (Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL)

11:40 AM Quantifying Tissue Architecture in the Tumour Microenvironment with Multi-Parameter Persistent Homology

Spatial transcriptomics has revolutionised our ability to measure gene expression while preserving tissue architecture. Yet extracting meaningful patterns from the complex interaction of spatial organisation and molecular profiles remains challenging, particularly in the heterogeneous tumour microenvironment (TME). Here we apply Multi-Parameter Persistent Homology (MPH), a topological data analysis framework that can simultaneously track cellular organisation patterns across spatial proximity and gene expression levels, to reveal disease-relevant tissue architecture in cancer that may be invisible to conventional methods.

MPH constructs two-parameter filtrations combining spatial distance with gene expression gradients, enabling quantitative characterisation of topological features as they emerge and persist across both parameters. This approach captures how cells organise relative to both their neighbours and their molecular states, which provides a unified signature of tissue structure well suited to characterise the spatial and molecular heterogeneity central to tumour plasticity.

We demonstrate MPH's capabilities in a cancer cell line derived from colorectal cancer tumour, revealing spatial immune and stromal compartmentalisation patterns relevant to understanding TME organisation. Notably, we find differences in topological signatures across fibroblast populations that are not observed in macrophage populations, suggesting that stromal heterogeneity in the TME may have structure beyond purely spatial organisation. We are currently extending this framework to additional human cancer datasets, with ongoing data collection and methods development aimed at broadening its applicability to clinical contexts.

MPH's quantitative characterisation of tissue architecture offers potential for identifying pathology-specific spatial patterns that may inform treatment outcome prediction and disease progression monitoring. Topological approaches like MPH provide a bridge between molecular measurements and the architectural context essential for understanding tumour plasticity, stromal remodelling, and therapeutic response.

Speaker: Kylie Savoye (1) School of Mathematics, College of Engineering and Physical Sciences, University of Birmingham, Birmingham, UK; 2) School of Physics and Astronomy, College of Engineering and Physical Sciences, University of Birmingham, Birmingham, UK)

10:40 AM → 12:00 PM Mathematical Modelling and Automatic Treatment of the HPT Complex and Thyroid Diseases

10:40 AM Data-Based Calibration and Fast–Slow Decomposition of a Patient-Specific Hypothalamus–Pituitary–Thyroid Axis Model

The hypothalamic-pituitary-thyroid (HPT) axis regulates endocrine feedback mechanisms essential for metabolic homeostasis. Mathematical models based on ordinary differential equations provide a framework for studying hormonal regulations. Nevertheless, the integration of physiological models with patient-specific clinical data continues to present significant challenges.

In this study, a dynamic model of the HPT axis\cite{pandi} for the simulation of hypothyroidism is calibrated using clinical hormone measurements and analyzed with respect to its intrinsic fast–slow structure\cite{Kuehn}. The estimation of model parameters is achieved through the utilization of multiple objective functions, whose outcomes are subsequently compared to align simulated hormone dynamics with clinical data from the General Hospital of Vienna.

The calibrated system is studied using methods from singular perturbation theory\cite{wechsel}. The separation of physiological time scales can be exploited through the implementation of a fast-slow decomposition, which results in a reduced model. We examine whether this reduced formulation preserves the essential regulatory dynamics consistent with the Tikhonov–Fenichel theory\cite{tik}.

The reduced model reveals the dynamical organization of endocrine feedback mechanisms and thereby facilitates the analysis of stability and long-term behavior. Future work includes bifurcation analysis within the parameter ranges obtained from the data-driven calibration.

Speaker: Clara Horvath (TU Wien)

11:00 AM Mathematical modelling of thyroid response to incidental radiotherapy exposure

The thyroid gland is an organ at risk (OAR) during head-and-neck radiotherapy (RT) due to its proximity to the treatment field. Ionising radiation can damage thyroid tissue, disrupt hormonal regulation by the hypothalamus-pituitary-thyroid (HPT) axis, and lead to endocrine dysfunction. Clinical studies report that 40-50% of patients develop hypothyroidism as a late RT-induced toxicity \cite{rooney2023}. In nasopharyngeal carcinoma (NPC) patients, hypothyroidism peaks ~24 months post-RT, coinciding with a reduction of ~40% in thyroid volume that subsequently stabilises \cite{lin2018}.

This work presents a mechanistic model of ordinary differential equations (ODEs) to simulate RT-induced changes in thyroid volume and T4-TSH dynamics. Thyroid volume reduction is modelled as a dose-dependent fraction of the initial volume derived from the radiobiological linear-quadratic (LQ) formalism. The HPT feedback loop is described using Michaelis-Menten kinetics, with T4 production expressed as a function of thyroid volume \cite{pandiyan2014}. Model parameters were calibrated using longitudinal clinical data from NPC patients \cite{lin2018}.

The model reproduces observed thyroid volume reduction and long-term T4-TSH clinical levels. It provides a baseline for developing a predictive tool to estimate patient-specific risk of RT-induced hypothyroidism. Future work will focus on validating the model and evaluating its predictive performance using individualised patient data.

Speaker: Isabel Gonzalez Crespo (TU Wien)

11:20 AM Hormone level estimation in the pituitary-thyroid axis with infrequent sampling

Control techniques that rely on a known model of the hypothalamic-pituitary-thyroid axis, such as model predictive control, have recently been explored for systematically recommending medication dosages to treat thyroid diseases like hypo- and hyperthyroidism \cite{A,B,C}. When implemented based on a high-fidelity model, they require knowledge of internal hormone concentrations of thyroid stimulating hormone, thyroxine, and triiodothyronine inside the pituitary and thyroid glands \cite{A,C}. However, only peripheral concentrations can be measured from blood tests, often at irregular and sparse sampling times, preventing the direct use of these techniques. We address this by implementing a sample-based moving horizon estimation scheme for the HPT axis based on \cite{D}, that estimates the internal concentrations from irregular measurements of peripheral concentrations. Robust stability of the estimator is demonstrated across multiple sampling schemes in simulation. Frequent sampling allows the tracking of intraday behavior and hence better estimation performance, but less-frequent sampling still captures slower behavior which is clinically relevant.

Speaker: Seth Siriya (Leibniz University Hannover)

11:40 AM Human-Readable Tabular Reinforcement Learning for Dosing Decisions in Graves’ Disease

Graves' disease is an autoimmune thyroid disorder causing hyperthyroidism, with a lifetime risk of 3% in women and 0.5% in men, see \cite{A}. It is commonly treated with antithyroid drugs where current dosing guidelines still provide limited support for optimal dose selection as it is reported e.g. in \cite{B,C}. Strong inter-individual variability poses a major challenge for conventional computer-based dosing approaches. Among machine learning paradigms, reinforcement learning is particularly well suited for managing sequential treatment decisions (see e.g. \cite{D}) as required in Graves' disease. We developed a reinforcement learning based agent, which approximates its policy using a neural network. It was evaluated on a validated simulation platform and outperformed existing algorithmic approaches as well as experienced endocrinologists. Since the decisions of neural network-based agents are opaque to clinicians, we additionally developed fully human-readable, inherently interpretable tabular reinforcement learning agents. Contrary to common expectations, these transparent agents performed better than the neural network–based approach. This result suggests that transparent, tabular reinforcement learning may be applicable to a broader class of cyclic treatment settings in which drug doses are iteratively adjusted based on measurable physiological parameters, as it is the case in Graves' disease.

Speaker: Thomas Benninger (Graz University of Technology)

10:40 AM → 12:00 PM Uncovering life’s equations: hybrid AI for biological dynamics learning

10:40 AM Data-Driven Modelling of Cell Cycle Regulation

Understanding how local crowding regulates progression through the cell cycle is central to explaining tissue growth and contact inhibition. We develop a novel model of density-dependent cell-cycle progression using Universal Differential Equations (UDEs), in which transition rates between stages of the cell-cycle are represented by neural networks. This approach preserves key mechanistic features, including the Brownian motion of individual cells and conservation of mass between successive cell-cycle phases, while allowing experimental data of expanding epithelial monolayers to determine how local crowding influences progression through the cell cycle.

Speaker: Luke De Bretton-Gordon (University of Oxford)

11:00 AM Using inference to obtain models for biological systems

I will discuss how to use Bayesian inference approaches to obtain models for biological data in different contexts. In particular, I will discuss two examples: First, I will describe how we can use inference approaches to obtain the underlying differential equations that govern a specific biological process and apply it to the case of bacterial growth. Second, I will describe how we can use inference to develop a statistical generative model for neural connectomes of a developing animal using C. elegans as an example.

Speaker: Prof. Marta Sales Pardo (Universitat Rovira i Virgili)

11:20 AM Making PINNs ready for parameter inference from noisy data

A common inverse problem in systems biology, biophysics and related disciplines is the inference of model parameters from limited measured data. For cases where the underlying dynamics follow a set of known (or assumed) differential equations, Physics-Informed Neural Networks (PINNs) have been put forward as decent approximators of the inverse equations, offering an alternative way to estimate parameters to classical methods. However, naive application of PINNs for parameter inference suffers from uncontrolled overfitting and convergence problems when the available data is noisy. Here we show that these problems stem from inadequate loss function design and training. We introduce PINNverse, a recently proposed reinterpretation of the PINN training paradigm as a constrained optimization problem, which overcomes these limitations. PINNverse combines the advantages of PINNs with the Modified Differential Method of Multipliers and enables convergence to any point on the Pareto front. Based on a few classical ODE and PDE problems, we demonstrate that PINNverse accurately infers model parameters even under high levels of noise in sparse data. Finally, some potential future applications are discussed.

Speaker: Dr Roman Vetter (ETH Zurich)

11:40 AM Towards Inferring Biological Mechanisms with Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have developed into a flexible framework for embedding mechanistic knowledge within data-driven models. Our work provides two complementary studies using PC9 lung cancer cell microscopy data.
First, we apply a Biologically-Informed Neural Network (BINN) to spatiotemporal (2D+t) data under a reaction–diffusion model, where diffusion and growth are treated as unknown functions of cell density. We augment this architecture with symbolic regression (SR) to recover interpretable analytical expressions for the diffusion and growth functions.
Second, we explore Bayesian PINNs for inverse problems with noisy, sparse biological data. We use an ordinary differential equation model of population dynamics and compare fully Bayesian inference using Hamiltonian Monte Carlo with approximate Bayesian approaches. We further examine the universal PINN (UPINN) framework, highlighting trade-offs between flexibility and mechanistic constraints, and propose an iterative UPINN–SR strategy to infer governing structure when prior knowledge is limited.
Together, these contributions offer practical, interpretable, and user-friendly workflows for applying physics-informed learning to biological systems.

Speaker: William Lavery (Uppsala University)

10:40 AM → 12:00 PM Mathematical modeling to propose optimized immunotherapies for chronic disease

10:40 AM Predicting outcomes of combination treatment of Tuberculosis using a multi-scale quantitative systems pharmacology model

Understanding how to safely shorten antibiotic treatment for tuberculosis (TB), caused by infection with Mycobacterium tuberculosis (Mtb), is a critical step towards eradicating the world's leading cause of death by single infectious pathogen. Many patients need three months of antibiotic treatment or less, though shortening the recommended treatment duration is dangerous as we cannot predict who will have recurrent TB. The first confounding factor is the substantial heterogeneity exhibited during TB, both between and within patients. Second is data paucity, as our understanding must reconcile the limited-resolution human datasets and corresponding experimental murine and non-human primate animal models. To synthesize our knowledge toward more principled predictions of TB treatment outcomes we extended HostSim, our recent whole-host model of Mtb infection and treatment. HostSim bridges datasets for antibiotic treatment of TB and the potential for post-treatment relapse via a detailed representation of within-host pharmacokinetics, pharmacodynamics, and host-immune interactions. We have now added the ability to track in silico recreations of diagnostic tests that clinically and experimentally establish disease states. Our simulations reproduce the relative efficacy of multiple TB treatments, predict regimen-specific rates of misdiagnosed cure, and articulate how experimental and clinical study design may subtly vary what mechanisms underpin post-treatment relapse.

Speaker: Christian Michael (University of Michigan)

11:00 AM A mathematical model of TCR-T cell therapy

Engineered T cell receptor T cells (TCR-T) are intended to drive strong anti-tumor responses upon recognition of the specific cancer antigen, resulting in rapid expansion in the number of TCR-T cells and enhanced cytotoxic functions, causing cancer cell death. Although TCR-T cell therapy against cancers has shown promising results, it remains difficult to predict which patients will benefit from such therapy. We develop a mathematical model to identify mechanisms associated with an insufficient response in a mouse cancer model. Using mathematical modeling, we show that certain parameters, such as increasing the cytotoxicity of effector TCR-T cells and modifying the number of TCR-T cells, play important roles in determining outcomes. This is a joint work with Zuping Wang, Heyrim Cho, Noriko Sato, and Peter Choyke.

Speaker: Doron Levy (University of Maryland)

11:20 AM Illuminating antigen presentation dynamics in the pancreatic cancer microenvironment with omics-informed agent-based modeling

By coupling omics‑derived cell states to ABMs of PDAC ecosystems, this work develops a new in silico framework that can systematically investigate the implication of candidate antigen presentation and T cell activation mechanisms in the microenvironment from PDAC spatial multi-omics data, allowing us to better understand the interplay of pro-activation and pro-tolerance signals experienced by T cells in the PDAC microenvironment. This framework supports in silico identification of microenvironmental features that favor control over progression, and allows us to forecast putative outcomes of rational combination therapy strategies in PDAC on a per-tissue basis. In the context of PDAC, this will pave the way for prevention studies in future work adapting this framework to pancreatic precancer and to understanding the sequential microenvironment transformations that enable lesion progression. Moreover, the modeling framework and TME cell types selected here are generic to be used for cell behavior and therapy modeling across tumor atlases, providing a pipeline for modeling antigen presentation and immune recognition in any solid tumor microenvironment.

Speaker: Jeanette Johnson (University of Maryland)

11:40 AM Towards Optimization of Monoclonal Antibody Therapeutics Using a 3D Model of Cancer-Immune Interaction

T cell exhaustion is a dysfunctional state that develops after prolonged antigen exposure, in which T cells progressively lose effector function. Exhaustion is marked by the sustained expression of inhibitory receptors which transmit suppressive signals that limit immune activity. Recent studies indicate that the 24 hour period after initial antigen exposure is a critical window in the determination of T cell fate. Monoclonal therapeutic antibodies that target inhibitory receptors boost immune function by disrupting suppressive signaling pathways and have been shown to aid in the recovery of cytotoxic function. In this project, we explore trajectories of early phase T cell exhaustion and the impact of immune checkpoint intervention within the first 24 hours of antigen exposure by constructing a multiscale, off-lattice 3D model of the tumor microenvironment. We couple an agent-based model of cell–cell interactions with a reaction–diffusion model for antibody transport and track exhausting interactions between cancer and effector T cells. We assess parameter sensitivity by computing first-order and total-order Sobol indices. We highlight key factors that influence T cell migration and progression into an exhaustive state. Our analysis provides insights into how microenvironmental and therapeutic parameters influence T cell function and may inform future modeling strategies for immunotherapy optimization.

Speaker: Jordana O'Brien (University at Buffalo)

2:00 PM → 2:50 PM Self-organisation in mouse development

Embryo patterning coordinates cell differentiation, tissue growth and morphogenesis. Understanding how precision is achieved despite the inherent developmental variabilities remains a challenge. Using early mammalian embryos as a model system, we aim to understand the design principle of multi-cellular organisms. Our studies show that feedbacks between cell fate, polarity and cell/tissue mechanics underlie the robustness in development. I will discuss our recent works.

Speaker: Prof. Takashi Hiiragi (Hubrecht Institute, Royal Netherlands Academy of Arts and Sciences (KNAW))

3:00 PM → 4:20 PM Immune attack on the nervous system: mathematical models of multiple sclerosis

3:00 PM Computational Approaches to Multiple Sclerosis: Immune Dynamics and Data-Driven Lesion Modeling

Multiple Sclerosis (MS) is a chronic autoimmune disease affecting approximately 1.8 million people worldwide and demands improved tools for diagnosis and disease understanding. This talk presents two complementary computational models addressing distinct challenges in MS research and care. The first focuses on medical imaging and builds upon an MS lesion segmentation dataset [1]. To address data scarcity, we investigate generative deep learning for artificial data augmentation. A two-stage pipeline is employed: a Variational Autoencoder (VAE) generates synthetic lesion masks, followed by a Conditional Generative Adversarial Network (cGAN) that synthesizes realistic brain textures conditioned on these masks. We evaluate the impact of augmented data on MRI lesion segmentation performance. The second model targets disease mechanisms through an in silico representation of Experimental Autoimmune Encephalomyelitis (EAE) [2]. The model captures key immunological dynamics of EAE progression, enabling simulation of disease evolution and therapeutic strategies while reducing costs and ethical constraints of animal experimentation. Together, these approaches demonstrate how computational modeling advances both clinical applications and mechanistic understanding of MS.

Speakers: Barbara Quintela (Universidade Federal de Juiz de Fora), Gustavo G Silva (Federal University of Juiz de Fora (UFJF)), Luan C Silva (Federal University of Juiz de Fora (UFJF)), Marcelo Lobosco (Federal University of Juiz de Fora (UFJF)), Philippe Neumann (Federal University of Juiz de Fora (UFJF))

3:20 PM From Mechanistic Simulation to Regulatory-Grade Evidence: Agent-Based Modelling of Multiple Sclerosis with UISS-MS

Multiple sclerosis (MS) is a complex, multifactorial disease arising from the interplay between immune dysregulation, environmental triggers, and neurodegenerative processes. Traditional mathematical models based on ordinary and partial differential equations have provided important system-level insights, but often face limitations in capturing stochasticity, heterogeneity, and multi-scale dynamics inherent to MS pathogenesis.

Agent-based modelling offers a complementary framework to address these challenges. In this context, the Universal Immune System Simulator for Multiple Sclerosis (UISS-MS) has been developed as a mechanistic platform to reproduce immune system dynamics underlying disease onset, relapse, and progression. The model integrates cellular interactions, antigen recognition processes, molecular mimicry mechanisms, and environmental triggers, including Epstein–Barr virus (EBV) reactivation, within a unified stochastic simulation environment.

UISS-MS enables the generation of virtual patient cohorts, supporting the in silico exploration of disease trajectories and treatment responses, including immune reconstitution therapies such as cladribine. The framework has demonstrated the ability to reproduce clinically observed relapse patterns and inter-patient variability. Ongoing efforts focus on robustness analysis, credibility assessment, and alignment with emerging regulatory expectations for mechanistic models.

These results highlight the potential of agent-based approaches to bridge theoretical immunology and translational application, supporting the development of digital twins and regulatory-grade in silico trials in multiple sclerosis.

Speakers: Francesco Pappalardo (University of Catania), Giulia Russo (University of Catania)

3:40 PM Mass-conserving boundary motion in a model of invasion and recession

In multiple sclerosis patients, immune cells attack myelinated nerve axons, creating demyelinated regions called lesions. MRI observations show that individual lesions can grow or shrink over time. These lesion dynamics provide important insights into disease progression, as well as the efficacy of treatment. We develop a moving boundary model to represent lesion boundaries as sharp interfaces that can advance or recede. Existing moving boundary extensions of reaction–diffusion equations, such as the Fisher–KPP equation, typically use a Stefan-like condition in which boundary motion is determined by the flux of cells. Instead, we model the boundary velocity as a function of local cell density, allowing us to represent biological processes where cells degrade or deposit material to move a boundary without being consumed. We observe a variety of behaviours depending on the parameterisation of the boundary velocity function, including regimes supporting multiple invading and receding travelling waves, unstable travelling waves, and receding solutions with population blow-up.

Speakers: Adrianne Jenner (Queensland University of Technology), Georgia Weatherley (Queensland University of Technology), Michael Dallaston (Queensland University of Technology)

4:00 PM In silico trials of anti-EBV therapies in MS

Ordinary differential equation (ODE) models of the pathogenesis of multiple sclerosis (MS) were made to study the role of EBV infection on MS dynamics. Modeling allows in silico testing of several hypotheses regarding the role of EBV on MS pathogenesis and the efficacy of anti-viral therapies and anti-EBV vaccines.

Two ODE models were made, one of the immune system, and the other of CNS damage. The immune system model assumes that dysregulation caused by EBV infection causes spikes in the population of T-effector cells. The populations of T-effector, Active B, and Infected B cells from the immune system model are consolidated into the CNS model, representing inflammation that causes axon damage.

In order to test various hypotheses of the mechanism by which EBV causes MS, various parameters were manipulated to see the effects on the levels of the T-eff population. The hypotheses that were tested were molecular mimicry, mistaken self, bystander damage, insufficient killing of infected B-cells by Natural Killer cells, and EBV induced B cell migration to CNS.

Furthermore, antiviral therapies, vaccines, and existing MS therapies were incorporated to test the effects on T-effector and B-cell populations. The existing MS therapies were used to further constrain the models, as well as to predict the effects of combinations of therapies. These models show that there are multiple mechanisms that can manifest in the inflammation that causes MS symptoms.

Speakers: Jordi García Ojalvo (Pompeu Fabra University, Hospital del Mar Research Institute), Keith Kennedy (Pompeu Fabra University, Hospital del Mar Research Institute), Pablo Villoslada (Pompeu Fabra University, Hospital del Mar Research Institute)

3:00 PM → 4:20 PM Bridging Structure and Dynamics in Biological Networks

3:00 PM A Research Program on Modularity in Biological Systems

This talk will outline a research program aimed to develop a formal foundation
for research on the concept of modularity that links structure and function of networks.
The program is based on an April 2026 workshop on this topic at the
National Institute for Theoretical and Mathematical Biology.

Speaker: Reinhard Laubenbacher (University of Florida)

3:40 PM Design principles of complex cellular decision-making networks in cancer

Elucidating the design principles of regulatory networks driving cellular decision-making is of fundamental importance in mapping and controlling cellular behaviour. Despite their size and complexity, large biological regulatory networks often lead to a limited number of cell-states/phenotypes. How this canalization is achieved remains largely elusive. Here, we investigated multiple different networks governing cell-state transition during cancer metastasis, and identified a latent design principle in their topology that limits their phenotypic repertoire – the presence of two "teams" of nodes engaging in a mutually inhibitory feedback loop. These "teams" are specific to these networks and directly shape the phenotypic landscape and consequently the cell-fate trajectories. Our analysis reveals that network topology alone can contain information about phenotypic distributions it can lead to, thus obviating the need to simulate them. We present experimental evidence of such "teams" in transcriptomic datasets across many contexts (cancer cell plasticity in breast cancer, melanoma, lung cancer etc.). Overall, we propose these "teams" as a network design principle that drive cell-fate canalization in diverse decision-making processes, and drastically reduce the dimensionality of the phenotypic space.

Speaker: Mohit Kumar Jolly (Indian Institute of Science)

4:00 PM Biconnected components and structural robustness in directed networks

Strongly connected components (SCCs) are essential for identifying modular structures in directed networks. However, they are inherently fragile, as the removal of even a single node can fragment the component and compromise its functionality. To address this limitation and better capture structural stability, we study strongly bi-connected components (SBCs), subgraphs where every pair of nodes is linked by at least two vertex-independent directed paths in both directions. Using a generating function formalism, we develop an analytical framework to estimate the size of the largest SBC in directed random graphs. Our analysis reveals that while the largest SBC emerges at the same threshold as SCC, they grow more gradually due to stricter connectivity requirements. These findings suggest that SBCs offer a more robust framework for modularity, with implications for failure-tolerant design and biological network dynamics.

Speaker: Byungjoon Min (Chunbbuk National University)

3:00 PM → 4:20 PM Advanced Progresses in Population Models Driven by Natural and/or Artificial Intelligence

3:00 PM Integrating Machine Learning Techniques in Mathematical Models of Dengue Transmission Dynamics

About half of the world's population, about 4 billion people, live in areas with a risk of dengue infection. Recent evolutionary adaptations of dengue-transmitting mosquitoes to colder regions, such as the Himalayas of Nepal, have raised severe public health concerns about dengue pandemics. In this talk, I will demonstrate how machine-learning techniques and mathematical models can be combined to develop valuable tools for describing dengue transmission dynamics. Using dengue and climate data from Nepal and Taiwan, I will present methods for computing dengue-virus transmission reproduction numbers using mathematical models integrated with machine learning. Our methods provide a valuable approach to combining mathematical models and real-time data in a machine-learning framework to identify effective strategies for preventing dengue outbreaks.

Speaker: Naveen Vaidya (San Diego State University)

3:20 PM A dimension-reduction technique for modelling evolution in structured populations

Natural populations exhibit complex class structures that shape evolutionary trajectories. While evolutionary demography provides a formal framework to predict adaptation using invasion fitness, the high mathematical dimensionality of these models often precludes interpretable analytical solutions. We introduce two complementary tools to simplify complex life cycles. First, we formulate the 'invasion determinant,' an algebraic method that yields a direct scalar condition for mutant invasion. Second, we develop the Projected Next-Generation Matrix (PNGM), which structurally compresses life-cycle graphs by eliminating secondary classes. We demonstrate that this reduction is mathematically equivalent to separating dynamical timescales, explicitly preserving Fisher's reproductive values for the retained focal classes. We will illustrate with diverse ecological examples.

Joint work with Ryosuke Iritani.

Speaker: Troy Day (Queen's University)

3:40 PM Modeling the invasion of novel SARS-CoV-2 variants and their co-existence with or replacement of ancestral variants in the United States

To better understand SARS-CoV-2 variant succession during the COVD-19 pandemic, we developed multi-variant transmission models, derived conditions for novel variants to invade and coexist with or replace ancestral ones, and explored phenomena that might explain observed patterns. To invade, novel variants require reproduction numbers greater than unity when ancestral ones are at their endemic equilibria. Replacement occurs when one variant can invade at another’s endemic equilibrium, but not vice versa, and coexistence occurs when both variants can invade at the other’s endemic equilibrium. As transitions among successive Omicron variants almost certainly involved immune escape, we explored three hypotheses for the transitions from Alpha to Beta and Beta to Omicron, greater reproduction numbers, shorter generation times, and immune escape. We found that, while greater reproduction numbers always are advantageous, Beta may also have had a shorter generation time than Alpha by virtue of infecting cells in the upper versus lower respiratory tract. But neither was advantageous while the vaccination of healthcare and other essential workers reduced transmission, nor was immune escape advantageous until susceptible hosts were limiting. Consequently, whether replacement of Beta by Omicron was caused or facilitated by immune escape is unclear. Developing, evaluating, and improving these models increased our understanding of phenomena affecting transitions among SARS-CoV-2 variants.

Joint work with Troy Day (Queens University) and John W Glasser (Emory University).

Speaker: Zhilan Feng (National Science Foundation)

4:00 PM Waning immunity and the critical vaccination threshold

Measles is currently affecting many countries globally. In recent studies we have shown that measles vaccine induced immunity can wane over time. In this talk we will determine the control reproduction number and the critical vaccination threshold under these conditions. We will then present a case study for measles infection in Ontario, Canada and determine the effective size of the population of the outbreak.

Speaker: Jane Heffernan (York University)

3:00 PM → 4:20 PM Mathematical Endocrinology: Models of Regulation, Disease and Dynamics

3:00 PM A harmful cycle: understanding the roles of inflammation, serotonin and the blood brain barrier in neurological development through mathematical models.

Experimental results have highlighted the role of serotonin in fetal brain development, and have indicated that inflammation can cause a cyclical disruption to the blood-brain barrier permeability, leading to long-term neurological disorders. In this talk I will present a mathematical model of the tryptophan-serotonin pathway in the placenta that includes modulation by maternal inflammation. In particular, we explore the hypothesis that blood brain barrier disruption due to gestational maternal immune activation can initiate a cycling of immune activation and BBB dysfunction that persists into adulthood. The model has the potential to help us understand a possible mechanism for the development of mental disorders.

Speaker: Ami Radunskaya (Pomona College)

3:20 PM Mathematical Modeling of the Gut-Brain Axis

In this talk I will present a mathematical model that describes the interaction of gut and brain through the presence of serotonin and tryptophan. The neurotransmitter serotonin is produced in the brain and the gut from the amino acid tryptophan via an enzymatic reaction. However, tryptophan is not produced by the body, but is obtained from food. While serotonin cannot cross the blood-brain barrier, tryptophan can, and does. Since serotonin regulates digestion, mood, sleep, and other physical processes in response to stress, we build a model that describes the kinetics of its production and absorption. Because both tryptophan and serotonin are present in the gut and the brain, the tryptophan-serotonin pathway is a major communication route between the gut and the brain. This model extends previous models of serotonin and tryptophan focused in the brain. This work is a collaboration with Noah Avery Hughes, Harsh Jain, Steven R Lippold, Ami Radunskaya, Susmita Sadhu, and Sundar Tamang.

Speaker: Cornelia Mihaila (St Michael’s College)

3:40 PM The Four Ds of Ovulation: Dynamics, Dysfunction, Disparities, and Dosing

Endocrine physiology is a complex system of crosstalk between hormones in various tissues. Tight regulation of reproductive hormones is essential for ovulatory function, but dysregulation can lead to infertility and may be exacerbated by other endocrine--especially metabolic--abnormalities and/or racial and ethnic disparities. Further, inter-individual differences may alter clinical outcomes under both physiological and pathological circumstances. Here we discuss a series of mathematical models describing ovulatory dynamics with applications to polycystic ovary syndrome, endometriosis, metabolism, and oral contraceptives.

Speaker: Erica Graham (Bryn Mawr College)

4:00 PM A mathematical model of melatonin synthesis and interactions with the circadian clock

Circadian rhythms play an important role in human health and disease. In mammals, many cells in the central nervous system and periphery have circadian clocks; these cellular clocks are synchronized hierarchically, with the synchronized cells of the suprachiasmatic nucleus (SCN) acting as the master clock. For the pineal gland, an indirect neural projection from the SCN conveys this timing information, resulting in pineal melatonin release into both the blood and the cerebrospinal fluid. The hormone melatonin thus becomes a whole-body messenger of the current state of the clock. Melatonin, in turn, affects the SCN and is involved in phase resetting of the master clock. In this talk, I will present a mathematical model of the molecular synthesis of melatonin and its interactions with a mechanistic model of the circadian clock. The model predicts the primary mechanisms of melatonin’s phase resetting effects; current work uses the model to study observed sex differences in melatonin signaling and their health consequences.

Speaker: Janet Best (The Ohio State University)

3:00 PM → 4:20 PM Multiscale modeling in bioelectromagnetics

3:00 PM Multiscale mathematical modeling of pulsed field cardiac ablation

Cardiac ablation is a key procedure for treating arrhythmias, one of the leading causes of death worldwide. While radiofrequency ablation (RFA), based on thermal injury, has long been the clinical standard, pulsed field ablation (PFA) has recently emerged as a promising non-thermal alternative. PFA relies on irreversible electroporation, a microscopic phenomenon in which strong electric fields disrupt the cell membrane, leading to cell death.

Modeling PFA is essential to understand how these microscopic effects translate to the tissue scale and to improve clinical guidance. In this talk, we present a physiologically relevant model specific to cardiac tissue, going beyond the classical Poisson framework with nonlinear conductivity. Our approach is based on the periodic homogenization of a nonlinear microscopic bidomain model, where electroporation is described as a voltage-dependent increase in membrane conductance. The associated two-scale expansion is derived and rigorously justified.

From its leading terms, we obtain an effective macroscopic model and introduce relevant quantities to identify ablated regions. We then investigate clinically relevant scenarios, highlighting the impact of fiber orientation and pulse repetition, and propose an extension accounting for conductivity memory effects between pulses.

Speaker: Annabelle Collin (Nantes Université)

3:40 PM Computational assessment of wireless powering of a pulmonary artery intravascular sensor via volume conduction

Remote monitoring of heart failure patients using intravascular implants may enable early detection of disease worsening and reduce hospitalizations \cite{Mohebali_Kittleson_2021}. Within the FORESEE project, a multiparametric pulmonary artery sensor is being developed for wireless powering and communication through volume conduction \cite{Becerra-Fajardo_Minguillon_Krob_Rodrigues_González-Sánchez_Megía-García_Galán_Henares_Comerma_del-Ama_et al._2024}, \cite{García-Moreno_Comerma-Montells_Tudela-Pi_Minguillon_Becerra-Fajardo_Ivorra_2022}. In this approach, harmless high-frequency current bursts ($6.78$ MHz) are applied across the torso using textile electrodes, and the implant is powered through two pick-up electrodes located at its ends.
The feasibility of this powering strategy was assessed by means of computational modeling. A three-dimensional adult human torso model, including the pulmonary artery, was used for electromagnetic simulations (COMSOL Multiphysics). The influence of implant electrode exposed area, implant length, and implant position was analyzed while ensuring compliance with electrical safety criteria (SAR $\le 10$ W/kg). Additional simulations considered physiological variability, different respiratory cycle states and adipose tissue thickness.
The results showed that more than 5 mW can be safely delivered to the implant, sufficient to power the sensor electronics. Although adipose tissue thickness and implant alignment were identified as critical factors, the study supports the feasibility of safely powering a pulmonary artery intravascular sensor using volume conduction.

Speaker: Mar Gadea Saez (Universitat Pompeu Fabra)

4:00 PM Pulsed Field Ablation: electroporation based cardiac ablation

Pulsed field ablation (PFA) – an electroporation-based ablation - is being rapidly adopted as a safer and more efficient alternative to conventional thermal ablation methods for the treatment of cardiac arrhythmias, particularly atrial fibrillation. Although electroporation is a phenomenon occurring on the cell membrane level, its effects require modeling on several levels. The basic biophysics of PFA, focusing on electroporation at the membrane, cellular, and tissue levels will be presented providing mechanistic explanations for the observed clinical outcomes and potential adverse events. Drawing on decades of electroporation research in other biomedical fields, modeling attempts/efforts will challenge current understanding of PFA. Cell membrane electroporation is based on long standing “pore formation” theory leading to transient membrane permeabilization \cite{Kotnik_Rems_Tarek_Miklavcic_2019}. Although non-thermal, when applied in vivo, high electric currents increase temperature, which can be significant \cite{Cornelis_Cindric_Kos_Fujimori_Petre_Miklavcic_Solomon_Srimathveeravalli_2020}. Cell membrane electroporation is usually related to membrane electroporation which depends on local electric field. Electric field distribution in the tissue depends on tissue conductivity, which is inhomogeneous and anisotropic, and further increases locally with cell membrane electroporation and temperature increase. Mass transport, electrochemistry and cellular and tissue effects like cell death \cite{Batista Napotnik_Polajzer_Miklavcic_2021}, interstitial fluid pressure \cite{Pusenjak_Miklavcic_2000} and effects on blood perfusion \cite{Jarm_Cemazar_Miklavcic_Sersa_2010} are only sparsely addressed although they may be critical in predicting treatment outcome.

Speaker: Damijan Miklavčič (University of Ljubljana)

3:00 PM → 4:20 PM Advances in Modeling Human Behavior and Infectious Disease Spread: A cross-disciplinary perspective

3:00 PM The role of human behavior in shaping infectious disease dynamics

Demography and social structures shape many aspects of an infectious disease outbreak in a population – from host susceptibility and exposure to transmission and health outcomes. However, the social forces that shape human behavior are difficult to quantify and often omitted from mathematical epidemiological models. In this talk, I will discuss some recent work using data from surveys to parameterize infectious disease models to capture heterogeneities in disease outcomes.

Speaker: Ayesha Mahmud (University of California, Berkeley)

3:20 PM Social Dilemma of Disease Control

This talk will focus on the social dilemma aspects of disease control, and in particular on the "hysteresis” effect in bottom-up public health behavior dynamics that is responsible for resistance to top-down public health recommendations, ranging from mask hysteria, distancing disobedience, and vaccine hesitancy. Synergistic integration of top-down and bottom-up perspectives is required to increase the awareness and preparedness of epidemics of disease.

Speaker: Feng Fu (Dartmouth College)

3:40 PM Behavioral Adaptation to Novel Pandemics: Learning to Move from Mobility Restrictions to Less Costly Measures

During the COVID-19 pandemic, individuals initially responded to epidemic risk through high-cost interventions such as mobility reduction. However, empirical data reveal that mobility reductions became less pronounced in later waves despite persistent death rates. This declining responsiveness likely reflects economic constraints, psychological fatigue, and learning about disease risk that shift individuals toward alternative cost-effective protective measures (e.g., mask wearing). Existing aggregate behavioral feedback models fail to capture this reallocation of protective behavior across interventions. In this study, we formalize this micro-level behavioral adaptation by incorporating an explicit learning mechanism, driven by accumulated pandemic experience, that shifts individuals from high-cost interventions (such as mobility reduction) toward lower-cost measures (such as mask wearing) within a risk-responsive epidemic model.

Speaker: Binod Pant (Northeastern University)

4:00 PM MS173-4

3:00 PM → 4:20 PM Recent perspectives on mathematical-biology education

3:00 PM Universal design for learning applied to the development of a new a second-year undergraduate statistics course

Universal Design for Learning (UDL) is an educational framework that provides students with avenues for access to course material. The core principles of UDL are to provide learners with multiple means of engagement, representation and action and expression. In the context of the design of a new second-year undergraduate statistics course, we have developed course materials, including assessment, that prioritise accessibility and agency for students. In this talk I will discuss what are the ‘low hanging fruit’ that you may be able to apply to your context, as well as the more challenging aspects of applying UDL.

CAST (2024). CAST Universal Design for Learning Guidelines version 3.0.link here

Speaker: Adriana Zanca (The University of Melbourne)

3:20 PM Mentoring First-Year STEM Students Through Collaborative Research in the Haynes Scholars Program

The Haynes Scholars Program at James Madison University is an academic residential learning community for a cohort of first-year STEM majors that emphasizes early research and fostering a sense of belonging. Over the past year, we co-taught the program's sequence of two research courses, where small groups of first-year students worked on accessible projects in mathematical biology with a unified application theme of white-nose syndrome in bats. Our aim was to introduce them to the process of doing applied mathematical and statistical research: reading the literature, asking questions, exploring models, and presenting their results. We will share how we structured the experience, including scaffolding the background material and pacing the research steps, while also giving the students ownership of their projects. We'll also reflect on what worked well, what was challenging, and how this kind of early research experience helps build confidence and community for students just beginning their STEM journey.

Speaker: Alex Capaldi (James Madison University)

3:40 PM Structured Onboarding of Undergraduate Researchers in Mathematical Biology

The Ford Versypt Lab uses mathematical biology methods to study tissues, treatments, and toxicology. We introduce new undergraduate students to a suite of techniques for these topics in mathematical systems biology. To onboard students in a semester or summer research experience, we use a structured approach with two phases: the training phase and the research phase. We have crafted a series of computational notebooks (MATLAB and Python) arranged as assignments that introduce applying conservation balances to populations of cells and amounts of chemical species in living organisms and numerically solving systems of ODEs. Then we provide guidance for an open exploration period for the students to investigate topics of their interest that use the techniques and computational notebooks for the remainder of the academic term. They receive guidance on searching the literature. They are tasked with finding two mathematical biology papers that involve ODE models with different equations for the selected biomedical topics. By the end of the term, they must use MATLAB or Python to replicate the two models, write a report detailing their progress and their topic, and present their work. By using MATLAB or Python templates provided by the lab, students focus on the learning goals related to the research concepts instead of being hindered by programming or analytical mathematics proficiency or deficiency. Senior students also appreciate that the templates enable them to quickly make progress towards using advanced techniques. This approach has been used with one high school student and dozens of college undergraduate students across all levels and majors including applied mathematics, chemical engineering, biomedical engineering, and biology.

Speaker: Ashley Ford Versypt (University of Buffalo)

4:00 PM Putting Math Bio in its Place

Place-based mathematics pedagogy can increase student engagement and persistence in the classroom, at a time when maintaining student attention is increasingly difficult. By focusing on relevance, this pedagogical framework enables students to connect their lived experiences to mathematics, thereby supporting engagement and persistence in the classroom. Mathematical biologists often focus on topics of particular interest to students of this generation, such as public health, sustainability, and environmental change. Mathematical biology, therefore, has the unique potential to bring “place” into the classroom in a way that other areas of theoretical and applied mathematics cannot. In this talk, I will share my experience working to integrate place-based pedagogy, mathematical biology, and culturally relevant teaching practices with educators in Hawaiʻi. I will discuss practical ways of incorporating place-based practices into your own math classrooms.

Speaker: Kyle Dahlin (Virginia Tech)

3:00 PM → 4:20 PM MBI Community Gathering: Emerging Methods and Mathematical Models Arising from Biology

3:00 PM Asthma-mediated control of optic glioma growth via T cell-microglia interactions.

Optic glioma, a slow-growing tumor, is associated with Neurofibromatosis type 1 (NF1) mutations and increased midkine (MDK) production. A connection between asthma and optic glioma has previously been observed, but the mechanisms are unclear. To elucidate the role of asthma in the regulation of glioma formation, we investigated the role of T cells and the subsequent pathways in the regulation of microglia, a key player in the glioma tumor microenvironment (TME). While asthma is often linked to chronic inflammation, our mathematical analysis and experimental evidence suggest that inflammation can play a key role in suppressing the proliferation of optic glioma cells via immune reprogramming of T cells and the delicate control of signaling networks in microglia. Through a mathematical model, we investigate the complex interactions between tumor and immune cells in optic glioma. Our results indicate that asthma-induced T cell reprogramming inhibits tumor growth by promoting the release of decorin and a subsequent suppression of CCR8 and the intercellular binding kinetics in microglia, followed by blocking of CCL5 production in TME via suppression of NFκB. We also developed anti-cancer strategies by leveraging this asthma-induced immune regulation. Midkine intracellular dynamics also suggest a critical link between stromal cells and glioma cells. Our study based on hybrid multi-scale models suggests that the critical role of asthma control can perturb TME near optic glioma, leading to a critical cue on development of multi-organ anti-cancer therapeutics in optic glioma.

Speaker: Yangjin Kim (Konkuk University)

3:20 PM Generative models for particle tracking microscopy

I will discuss the use of diffusion models for particle tracking microscopy images. The goal is to have a fully integrated generative model that connects stochastic models of particle motion to microscopy image data. Unfortunately, the observation likelihood function is too complex to explicitly model, and we do not know this function. Learning the likelihood function from a suitably large image set is the primary purpose of so-called diffusion models. We discuss the application of these neural network models for evaluating the log likelihood of image sets given particle positions.

Speaker: Jay Newby (University of Alberta)

3:40 PM Toward Predictive Digital Twins for Precision Oncology: A QSP Modeling Approach

In this talk, I present a computational approach to precision oncology that combines mechanistic modeling with modern machine learning to build predictive digital twins; patient- and subgroup-specific models that forecast tumor progression and response to therapy. Our foundation is quantitative systems pharmacology (QSP) modeling, where tumor–immune dynamics are represented as systems of differential equations. We parameterize these models using patient observations and introduce a clustered inference strategy that stratifies individuals by immune profiles and estimates mechanistic parameters within each cluster. This reduces heterogeneity, improves identifiability, and yields interpretable subgroup phenotypes that link immune state to dynamical behavior. A distinguishing aspect of our evaluation is out-of-treatment generalization: we calibrate tumor growth and immune dynamics without fitting treatment response data, then use the resulting mechanistic parameters to predict outcomes under therapy. This design sharpens the scientific test of the model and targets the real-world challenge of predicting under new regimens. I then describe a digital twin platform that operationalizes this pipeline.

Speaker: Leili Shahriyari (UMASS Amherst)

4:00 PM Exploration of structure learning in pediatric sickle cell data

Pain episodes are a defining feature of sickle cell disease and can lead to reduced quality of life. Statistical analyses by Valrie et al. (2021) examined interactions between physiological (like pain severity and sleep quality) and psychosocial variables (like positive and negative affect) in pediatric sickle cell patients. Clinical datasets can present challenges for continuous dynamical systems modeling as there may be a mix of continuous data and categorical data (for instance, whether a patient took a nap, disease genotype, or the type of medication taken) recorded within the dataset, and there may not be obvious biophysical relationships to guide modeling the variables. In this work-in-progress talk, we consider probabilistic graphical models (or Bayesian networks) which are flexible enough to address the mix of categorical and continuous data types present in a clinical dataset. We will explore the learned model structures between variables for subpopulations of patients defined by age.

Speaker: Reginald Haverford College (McGee)

3:00 PM → 4:20 PM Novel Tools and Methodologies for Epidemiological Models

3:00 PM The impact of sojourn distribution assumptions on malaria parasite transmission dynamics: a flexible within-host modeling framework to accommodate empirically driven distributions

Many compartmental infectious disease models assume that sojourn times (the time spent in each state) are exponentially distributed; that is, the probability of exiting a particular state at an instant in time is independent of time already spent in that state. While this simplifying assumption may be sufficient in certain contexts, for complex diseases like malaria where control and elimination efforts are hindered by drug resistance, relaxing this assumption to enhance biological realism and better facilitate multi-scale modeling is particularly advantageous. In this talk, we present a flexible PDE model framework of within-host malaria parasite dynamics that allows for non-exponential distributions for the sojourn times for each red blood cell and parasite life cycle stage. We discuss how our framework accommodates empirically driven distributions and demonstrate that different distribution assumptions can substantially impact malaria transmission probability estimates.

Speaker: Jordan Pellett (Grand Valley State University)

3:20 PM Forecasting Malaria using test positivity and reported case rates

Parameters are fundamental components of biological models and play a critical role in determining model behavior. While some parameters can be estimated directly from experimental or observational data, many remain difficult to measure or infer. This work investigates the role of parameters in a malaria transmission model when the available data consist only of the number of malaria tests performed, the number of positive test results, and the population size. We examine parameter identifiability by analyzing the relationship between model parameters and observable quantities, both in the presence and absence of measurement noise. To assess the influence of parameters on model outputs, we compute Sobol sensitivity indices, which quantify how variations in parameter values contribute to changes in the model predictions. Finally, we apply data assimilation techniques to perform forward prediction and to estimate parameters that cannot be determined from experimental data alone.

Speaker: Katie Gurski (Howard University)

3:40 PM Modeling Insecticide Resistance and Management of Malaria Mosquitoes

With over 1 million deaths annually across the globe due to mosquito-borne diseases, insecticide resistance is a major public health concern. Insecticide-resistant mosquitoes experience both positive and negative selective forces, depending on the resistance genotype, the type and dosage of insecticide applied, and the fitness costs associated with the resistance mutations they carry. Understanding how these forces interact with each other is critical in determining optimal resistance management strategies. We develop and analyze an ODE-based model to examine the impact of resistance management strategies on the evolution of insecticide resistance in mosquito populations and explore optimal control options.

Speaker: Lihong Zhao (Kennesaw University)

4:00 PM Likelihood-Free Confidence Regions for Stochastic Epidemic Models via CTMC Simulation and Neural Networks

Estimating confidence regions for parameters in stochastic epidemic models is challenging when the likelihood is intractable. In continuous-time Markov chain (CTMC) formulations of compartmental models such as SIR, the likelihood cannot be evaluated directly due to the intractability of the Kolmogorov forward equations. Existing approaches rely on simplifying assumptions, such as Gaussian approximations or ad hoc noise models, which can lead to inaccurate inference.
We develop a fully frequentist framework for constructing confidence regions without explicit likelihood evaluation. Our method uses empirical moments from CTMC simulations and Monte Carlo approximations of a Mahalanobis-type test statistic, producing confidence sets with nominal coverage. However, the computational burden of Monte Carlo simulation limits dense exploration of the parameter space. To address this, we introduce a neural network–based pipeline that learns the mapping from parameters to the mean and covariance of the CTMC and estimates key quantiles (0.68, 0.80, 0.90, 0.95) using coverage-based stopping criteria.
We apply our method to SIR and SEIR models and additionally test the models on the English boarding school influenza dataset. Results show that our approach yields narrow, well-calibrated confidence regions when data are modeled as stochastic realizations of CTMC dynamics rather than observations with additive noise.

Speaker: Madison Pratt (University of Tennessee, Knoxville)

3:00 PM → 4:20 PM Progresses in Mathematical and Computational Immunobiology and Infections

3:00 PM Revealing the influence of cell motility on immune processes within complex tissue environments

Cell motility represents an important hallmark of immune processes governing cell interactions, communication and function. Determining how external factors, such as chemokine gradients and structural elements, influence immune cell motility is therefore of critical importance to understand the development of immune responses and their impact on pathological changes within complex tissue environments. Here, by combining individual cell-based models using the cellular Potts modelling (CPM) framework with theoretical analyses, we could reveal how the mode of cell motility is shaped by porous environments, as represented by extracellular matrices (ECM). Geometrical properties of these structures define characteristic cell motility regimes, with spatial heterogeneities in tissue environments effectively guiding cell movement and leading to nonhomogeneous cell distributions that can determine cellular interactions. By developing computationally efficient graph-based modelling approaches, we are able to combine them with time-lapse microscopy data on cell dynamics to infer and predict how host-pathogen interactions are shaped by complex tissue environments. Our analyses, as well as analyses of experimental data, illustrate the necessity to account for spatial interactions when aiming to determine the key processes governing disease progression and tissue pathology.

Speaker: Frederik Graw (Department of Medicine 5, Hematology and Oncology, University Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg)

3:20 PM Beyond MIC: Defining a Minimum Inhibitory Dose (``MID") for Periodic Antibiotic Treatments

Rising antimicrobial resistance drives the search for dosing strategies that maximize bacterial eradication while minimizing unnecessary drug exposure. Standard indices, such as the minimum inhibitory concentration (MIC) or the time spent above MIC ($\%T_{>MIC}$), are static snapshots that often fail to capture the time-varying nature of periodic dosing. To address this gap, we introduce the minimum inhibitory dose (MID), a dynamic MIC analogue defined as a threshold dose size, above which bacterial populations show net negative growth from one dose to the next. Using Floquet theory on a coupled bacterial-growth and antibiotic pharmacokinetic/pharmacodynamic (PK/PD) model, we calculate the MID as a function of the dose schedule and PK/PD properties. Our framework recapitulates established clinical guidelines: minimizing the dose period-normalized MID identifies frequent dosing as optimal for time-dependent antibiotics such as ampicillin and infrequent dosing for concentration-dependent antibiotics such as rifampin. Applying this framework to N. gonorrhoeae treated with ceftriaxone, the MID accurately predicts historical dose size adjustments driven by shifts in MIC and fitness costs. These results position the MID as a unifying, mechanism aware metric to guide future rational antibiotic dosing strategies.

Speaker: Jessica Conway (Penn State, USA)

3:40 PM MS31-3 (Talk confirmed)

Awaiting abstract.

Speaker: Leor Weinberger (University of Miami)

4:00 PM Uncovering the T cell differentiation pathway

Adoptive T cell therapy is a promising immunotherapy for treating cancer, leveraging the T cell’s natural ability to kill cancer cells. A crucial step in this therapy involves the expansion of T cells ex vivo, however, it can be difficult to balance the desired amounts of memory, effector and dysfunctional T cell subtypes. Mathematical modelling of T cell expansion is a powerful tool that can be used to optimise expansion, assuming that the differentiation (to memory and effector) and dysfunction pathways are well-understood. Unfortunately, there is a large amount of uncertainty and disagreement in the literature describing the ways in which T cells differentiate to memory and effector cells, or become dysfunctional. I present one of the first large-scale mathematical investigations that aims to answer fundamental questions regarding T cell differentiation and dysfunction. Using observations from biological literature, we constructed a list of potential model features which inform the structure of an ordinary differential equation model. We compare all possible models (7,280 unique pathways) to data describing the ex vivo expansion of T cell subtypes, and we determine the most plausible features of the T cell differentiation and dysfunction pathways. This framework allows for a deeper understanding of T cell behaviour during immune responses which may be exploited to improve the administration of adoptive cell therapy.

Speaker: Mason Lacy (Queensland University of Technology)

3:00 PM → 4:20 PM Methods in applied population dynamics

3:00 PM Bifurcation Structures in Low-Dimensional Models of Ant–Coffee Berry Borer Dynamic

Ant communities play a key role in the natural regulation of agricultural pests, acting through collective behavior and non-linear feedback at the ecosystem level. In coffee agroecosystems, interactions between ant populations and the Coffee Berry Borer (CBB) provide a paradigmatic example of biologically mediated pest suppression driven by low-dimensional dynamics rather than large-scale complexity. In this talk, we present a class of minimal dynamical systems that describe ant–CBB interactions, focusing on the qualitative structure of the models. Using piecewise-smooth systems of ordinary differential equations, we analyze equilibrium configurations, stability properties, and bifurcation structures in response to changes in key ecological parameters. Our results reveal multiple dynamical regimes, including pest persistence, effective biological control, and bistability between controlled and outbreak states. Transitions between these regimes are governed by bifurcations that provide a mechanistic explanation for changes in pest pressure observed in managed coffee systems. The analysis highlights how collective ant behavior can induce nonlinear threshold effects leading to robust pest suppression. This work illustrates how low-dimensional dynamical models can capture essential features of complex agroecosystems and provides a theoretical framework for understanding biologically driven control strategies from a mathematical biology perspective \cite{Abaraya2023,DiBernardo2008B,Dufour2008,Trujillo2023,Trujillo2024}.

Speakers: Carlos Andrés Trujillo-Salazar (Universidad del Quindío, Colombia), Deissy Milena Sotelo-Castelblanco (Universidad Nacional de Colombia), Gerard Olivar-Tost (UCM)

GO.pdf

3:20 PM A Matrix-Based Framework for Structured Inheritance in Population Dynamics: Bilinear Forms for One- and Two-Sex Models

Anticipating the outcomes of genetic interventions requires combining population dynamics, genetics, and control theory. In this talk, we discuss a unified formulation that uses bilinear forms for inheritance matrices to model mating combinations in offspring, explicitly capturing complex mating systems such as polygyny and polyandry. We illustrate this approach through three models. First, we use a single-sex Mendelian inheritance model to analyse insecticide resistance. Next, we present a unified model of Mendelian and maternal inheritance simulating simultaneous resistance evolution and Wolbachia introgression in a mosquito population. Finally, a two-sex model incorporates sex-specific inheritance matrices to evaluate seasonal Wolbachia suppression and replacement strategies. The stability analysis and simulations demonstrate how this matrix-based approach rigorously supports the synthesis of effective vector control. We acknowledge the support by ARASY ESTR01-23 \cite{estigarribia2021modelling,perez2020class,vian2026multi}.

Speakers: Christian E. Schaerer (UNA), Pastor Pérez-Estigarribia (UNA)

PEPE.pdf

3:40 PM About the Combination of Control Tools Against the Oriental Fruit Fly Using a Metapopulation Approach

The oriental fruit fly, \textit{Bactrocera dorsalis}, is a major invasive pest and classified as a quarantine pest by the European Union. First recorded in La Réunion in April 2017, it is now established and causes serious damage, particularly in mango orchards. Due to the high biodiversity of La Réunion, chemical control is highly restricted, so only non-chemical tools can be used, such as the Male Annihilation Technique (using Methyl-eugenol traps) and soil entomopathogen fungi applied via irrigation systems to target the pupal and adult stages. Additionally, the Sterile Insect Technique (SIT) has been under investigation since 2020. It consists of mass rearing, irradiation, and release of sterilized insects to compete with wild populations, reducing reproduction rates.

All these control approaches have been studied using mathematical models \cite{bliman2025feasibility,bliman2025sterile,dumont2025}. The aim of this talk is to present new mathematical results, illustrated with simulations, where the combination of these control tools is analyzed to derive optimal strategies in space and time.

Speaker: Yves Dumont (CIRAD)

YD.pdf

4:00 PM Modelling Movement and Stage-Specific Habitat Preferences of a Polyphagous Insect Pest

The feeding preferences of \textit{Diabrotica speciosa} (Coleoptera: Chrysomelidae) generate a parent-offspring conflict, as selecting the optimal host for offspring development can negatively affect adult survival and fecundity. Understanding this conflict is essential for developing effective pest-management strategies. We investigated the foraging behavior of \textit{D. speciosa} using an individual-based model in two scenarios. In an intercropping scenario, we simulated parent-offspring conflict with adults exploiting two crops (corn and soybean) providing distinct nutritional advantages for each life stage. Three adult dispersal strategies were compared under continuous oviposition: simple diffusion, attraction to a fixed host, and alternating between hosts with a foraging period $\tau$ per crop. Two behavioral principles were explored: “mother knows best” (adults foraging on corn during oviposition) and “optimal bad motherhood” (adults foraging on soybean to maximize their own fitness), including pre-oviposition effects. In a landscape scenario, population dynamics were simulated across four crop plots with temporal changes. Results indicated that crop-alternating dispersal near an optimal $\tau$ maximized population performance, and the “mother knows best” strategy supported higher population growth than “optimal bad motherhood.” Landscape heterogeneity, fallow periods, and reduced soybean monocultures lowered insect density. Our findings suggest that alternating crop foraging enhances population fitness, while spatial and temporal crop management can effectively mitigate \textit{D. speciosa} infestations \cite{Ferreira2020}.

Speaker: claudia ferreira (UNESP)

CPF.pdf

3:00 PM → 4:20 PM Insights into cell-tissue interactions via mathematical modelling and computational simulations

3:00 PM Spatial organization of adhesion-deficient cells governs multiscale rigidity transitions in epithelial tissues

Epithelial tissues maintain structural integrity through a balance between cell-cell adhesion and cortical contractility. Disruption of E-cadherin-mediated adhesion is a hallmark of metastatic progression, yet the physical mechanisms by which local molecular defects escalate into global tissue destabilization remain poorly understood. Traditional theoretical studies have focused on the density of defective cells, while largely neglecting their spatial organization—a critical factor in clonal expansion.We employ a 2D stochastic vertex model to investigate how the spatial arrangement of adhesion-deficient cells dictates tissue-scale rigidity transitions. By comparing random and clustered distributions, we identify a distinct mechanical response across scales. Our results show that while isolated defects are rapidly eliminated via $T_2$ extrusion events with minimal impact on tissue architecture, clustered defects significantly delay extrusion kinetics. This "shielding effect" fosters the emergence of local fluidization zones characterized by a high cellular shape index ($q > 3.81$). Furthermore, we demonstrate that clustered defects leave a "topological scar" in the wild-type matrix, lowering the global threshold for the unjamming transition. By linking local molecular dysfunction to macroscopic fluidization, our framework provides new insights into how clonal clustering facilitates tissue invasion and metastasis.

Speaker: Pilar Guerrero (Universidad Carlos III de Madrid)

3:20 PM Modelling single and collective cell migration through confined non-isotropic environments using geometric surface PDEs

In this talk, I will introduce a modelling approach for single and collective cell migration through confined non-isotropic environments using geometric surface partial differential equations. By assuming that cell migration is driven by cell surface biochemical processes and surface mechanics, the evolution law of the cell and nuclear envelope is modelled through a force balance equation posed at each surface material point in the normal direction. The force balance equation naturally encodes most of the biophysical properties of energetic closed surfaces such as surface tension, bending energy, surface area/volume constraint/conservation as well as taking into account intra- and extra-cellular forces, cell-to-cell interactions, cell-to-environment interactions, and so forth. This modelling approach leads to 4th-order geometric surface partial differential equations which are solved efficiently by employing an operator-splitting approach within an evolving surface finite element method. Numerical simulations demonstrate the generality, applicability and predictive power of this modelling approach; it offers a new and robust modelling formalism that bridges the gap between experiments and theory of single and collective cell migration through biologically relevant non-isotropic and confined environments.

Speaker: Anotida Madzamuse

3:40 PM Mathematical Models for the Mechanics of Soft Tissues: From Linear Elasticity to Morpho-Visco-Poroelasticity

Biological tissues are often subjected to forces. In many cases, such as tumor growth or skin contraction, it is crucially important to model the state of tissues that are exposed to forces in order to improve or optimize therapies for different pathologies. The simplest models use linear elasticity as a constitutive law. This linearity enables the use of the superposition principle and the use of fundamental solutions to analyze the influence of multiple points of action of forces. A clear illustration of this principle is the immersed interface method \cite{roy2020immersed}. In this presentation, we discuss this principle in terms of convergence properties using the singularity removal principle \cite{Gjerde_2019}.

However, in real-life tissues, the use of linear elasticity is too restrictive due to the presence of moisture and the porous structure of biological tissues. Furthermore, in various biomedical cases, the microstructure of the tissue changes due to cellular activity. For this reason, we construct and use a model that consists of elasticity, porosity and microstructural changes. The mathematical framework is referred to as morpho-visco-poroelasticity \cite{Hall_2008}. This framework is original and for this reason, we analyze this framework in terms of stability around equilibria \cite{Sabia2025}. Since numerical solutions can be characterized by spurious oscillations, we provide conditions for monotonicity by mathematical analysis. Furthermore, we propose a numerical stabilization method to avoid spurious oscillations on forehand.

Speaker: Sabia Asghar (Hasselt University)

4:00 PM Contact guidance and ECM architecture jointly regulate cancer invasion

Cancer invasion emerges from coupled interactions between tumour cells and the extracellular matrix (ECM), where fibre architecture, remodelling, and microenvironmental cues jointly regulate migration and growth. Building on our earlier PhysiCell framework for collagen-density-dependent spheroid invasion, we present a hybrid discrete-continuous model that incorporates fibre orientation, anisotropy, contact guidance, chemotaxis, cell-front ECM sensing, matrix displacement/degradation, and proliferation regulated by oxygen and mechanical pressure. Simulations show that invasion is enhanced when ECM fibres provide coherent directional cues: perpendicular or radial organisation promotes outward invasion, whereas parallel or tangential organisation suppresses it. Crucially, fibre anisotropy determines whether aligned architectures are effectively translated into directed motion. We further show that ECM remodelling has context-dependent effects: increasing reorientation can rescue invasion in initially restrictive matrices, but diminish invasion when the initial architecture is already favourable. The model reproduces experimentally motivated qualitative trends and yields mechanistic predictions on how tumour cells reshape and exploit ECM structure during collective invasion. These results provide a computational framework for dissecting tumour--ECM feedbacks and for designing experiments on matrix-guided invasion.

Speaker: Fabian Spill

3:00 PM → 4:20 PM Dynamical Analysis of Biochemical Reaction Networks

3:00 PM Structural classification of chemical reaction networks via visual and algebraic decompositions and its implications to steady state analysis

Biochemical and environmental modeling utilizes reaction networks to represent complex transformations, yet the standard Linkage Class Decomposition (LCD), which is based purely on visual connectivity, frequently fails to capture the algebraic properties that govern long-term system dynamics. This work introduces a structural classification based on the finest decompositions of chemical reaction networks, which bridges this gap by mapping the hierarchical relationships between the LCD and two critical algebraic structures: the Finest Independent Decomposition (FID) and the Finest Incidence-Independent Decomposition (FIID). They act as the fundamental building blocks for characterizing general and complex-balanced equilibria, respectively. By the partial order of "coarsens to," between such decompositions, we categorize reaction networks into six distinct classes, three subclasses of Independent Linkage Classes (ILC) and three subclasses of Dependent Linkage Classes (DLC). To facilitate this classification, we introduce two discriminants: the Deficiency Difference, measuring the variance between total and subnetwork deficiencies, and Common Complexes Cardinality. We further establish the properties of these subclasses and provide illustrative examples. By separating ILC and DLC networks, the framework reveals alignment between structural connectivity and kinetic attributes that could offer insights in the steady state analysis of biochemical and environmental systems.

Speaker: Bryan Hernandez (University of the Philippines Diliman)

3:20 PM The polyhedral structure of the disguised toric locus

Polynomial dynamical systems arise in many applications (e.g., biochemistry, population dynamics) but are hard to analyze because they can display multistability, oscillations, and chaos. Mass-action systems, and in particular complex-balanced (toric) systems, are remarkably stable: they admit a unique attracting equilibrium and rule out oscillations and chaos. We study the set of rate constants for which a mass-action system is dynamically equivalent to a complex-balanced system, the disguised toric locus, and introduce a flux-based toolkit for its analysis and computation. We prove the disguised toric locus is homeomorphic to a prism over the disguised toric flux locus, a polyhedral cone with rich combinatorial structure. This leads to new theoretical results on the geometry of the disguised toric locus: that is a contractible manifold with boundary. This prism/flux viewpoint also brings practical consequences: an explicit computational strategy that, for the first time, computes the full disguised toric locus for many networks of interest. Based on joint work with Boros, Craciun, Jin, and Henriksson (2510.03621)

Speaker: Diego Rojas La Luz (University of Wisconsin–Madison)

3:40 PM A bimolecular reaction network with chaotic dynamics

I plan to give a rigorous proof that the Willamowski-Roessler reaction network $$X \leftrightarrow  2X, \quad X+Y \leftrightarrow 2Y, \quad Y \leftrightarrow 0, \quad X+Z \leftrightarrow 0, \quad  Z \leftrightarrow  2Z$$ has chaotic dynamics.

Speaker: Josef Hofbauer (University Vienna)

4:00 PM Stability and Robustness in Biochemical Networks with Bifunctional Enzymes

Recent work has revealed that biochemical networks with bifunctional enzymes can display remarkably rich dynamics, including ultrasensitivity, switch-like responses, concentration robustness, and even species exhaustion. This talk presents a dynamical systems analysis of such networks, shedding light on the subtle architectural differences that produce these vast differences in functional behavior. We outline and employ the next-generation matrix method—only recently adapted to biochemical reaction networks—to characterize previously incomputable thresholds for the stability of boundary steady states. These thresholds are critical for determining when a mechanism will proceed or shut down. Using bifurcation analysis, we further establish conditions for multistationarity, showing how multiple positive steady states can arise within a single stoichiometric compatibility class—a property theorized to underlie toggle-switch behavior in genetic networks. Finally, we consider the capacity of such networks for absolute concentration robustness (ACR)—an essential feature of metabolic regulation—and explore the interplay between robustness and boundary stability.

Speaker: Matthew Johnston (Lawrence Technological University)

3:00 PM → 4:20 PM Universal Differential Equations in Mathematical Biology

3:00 PM Sensitivity analysis for biological differential equation models with many parameters

Mathematical models of biology commonly use differential equation formulations. Certain application areas, such as signal transduction modeling or scientific machine learning, involve models that contain many parameters. Efficient training of these models requires sensitivity analysis that scales well as the number of parameters grows. Hence, adjoint sensitivity analysis (ASA) is typically employed, instead of forward sensitivity analysis (FSA).

In this work, we derive a new sensitivity analysis method that has similar scaling properties to ASA but, unlike ASA, can be solved in the forward direction. This provides some computational efficiency gains in terms of memory and complexity, especially for the stiff systems that are common when modeling biology. Furthermore, higher-order sensitivities are cheaper to compute with the new method. A drawback is that, when the parameter size is small or the state size is large, then the FSA or ASA methods, respectively, can naïvely outperform the new method.

Speaker: Dilan Pathirana (University of Bonn)

3:20 PM Elucidating Regional and Global Epidemiological Trends Using Neural Network Model-form Error Corrections

The field of scientific machine learning (SciML) seeks to fuse traditional mathematical modeling with advances in machine learning to balance mechanist equations with data-driven inference, resulting in computational models that preserve scientific knowledge while readily adapting to the unknown through data-driven discovery. These advancements are setting the foundation for which SciML surrogates provide novel diagnostics that decompose global and local behavior inherent to high fidelity stochastic models and real-world data. This presentation will introduce neural network (NN) function approximations of model-form error to close the gap between ordinary differential equations (ODE) to an epidemiological agent-based model (ABM). This universal differential equations approximation to the ABM allows us to preserve the foundational ODE that represents the global disease dynamics and couples it with the NN for function approximations of nonlinear state transition dynamics. Equipped with an approximation to the ABM, we further our investigation to account for variability in contact patterns in real-world data by analyzing county level disease dynamics within the state of New Mexico U.S. and compare the result to trends observed in aggregation for the total state dynamics. Ultimately, we will introduce a novel diagnostic to elucidate the regional and global epidemiological trends to fundamentally understanding the impact of regional versus global trends on disease transmission.

Speaker: Erin Acquesta (Sandia National Laboratories)

3:40 PM Universal Differential Equations Trained on Remotely Sensed Datasets Can Identify Tipping Points in Large-Scale Ecosystems

Identifying tipping points in spatially distributed ecosystems is critical for conservation but remains challenging due to the complexity of nonlinear dynamics, spatial connectivity, and limited observational data. We present a framework combining Universal Differential Equations (UDEs) with a novel dynamic gradient matching algorithm to learn ecosystem dynamics from large-scale remotely sensed time series. Dynamic gradient matching extends existing gradient matching approaches by simultaneously fitting linear spline smoothing functions and UDE parameters via a joint loss function, eliminating the need for ODE solvers during training while accounting for both process and observation error. This enables efficient scaling to datasets with many state variables. We evaluate four UDE model formulations on simulated spatially distributed kelp forest dynamics with emergent Allee effects, testing their ability to detect and quantify tipping points. The models achieve low false positive rates (0.5–6.2%) and moderate to high true positive rates (58.5–91.5%) for threshold detection, with performance depending on the proximity of the system to the tipping point and spatial correlation of environmental forcing. We further demonstrate the approach on satellite-derived kelp abundance data from central California using the Kelp Watch database, incorporating sea surface temperature as a covariate and estimating dispersal kernels. Results highlight the potential of UDE-based approaches for data-driven identification of critical transitions in spatially extended ecosystems.

Speaker: Jack Buckner (Oregon State University)

4:00 PM Theme and Variations: Conditional Universal Differential Equations for Biological Heterogeneity

Biological data often exhibit substantial heterogeneity between individuals. While part of this variability reflects random biological variation, systematic differences may arise from physiological diversity or disease. To reflect this diversity in mechanistic models, we often use the same mathematical equations, while individuals differ in parameter values that govern system dynamics. Capturing this structure, without disregarding the relevant physiological variability remains challenging for regular universal differential equations (UDEs).

In regular UDEs, mechanistic ordinary differential equations are combined with neural networks to learn a single population-level relationship, and therefore struggle to represent systematic heterogeneity between individuals. To address this limitation, we propose conditional universal differential equations (cUDEs). Instead of learning a single function, cUDEs learn a parameterized family of functions conditioned on a latent variable, allowing the model to capture individual differences while preserving a shared mechanistic structure.

We demonstrate this approach by modelling postprandial C-peptide production in a mixed population of healthy individuals and individuals with type 2 diabetes. Combining cUDEs with symbolic regression enables recovery of interpretable mechanistic relationships while accounting for population heterogeneity.

Speaker: Max de Rooij (Eindhoven University of Technology)

3:00 PM → 4:20 PM State of the art methods in modeling for cell and developmental biology

3:00 PM The role of transient crosslinks in the chromatin search response to DNA damage

Homology search is a means through which DNA double-strand breaks (DSBs) explore the genome for sequences of lossless repair. As this search process is fundamental to the relationship between DNA damage and disease, a better understanding the underlying mechanisms is crucial. In this work, we use an effective entropic bead-spring polymer chain model to simulate the spatiotemporal dynamics of the yeast genome during interphase. Through a combination of mathematical modeling and experimental work, we explore the effects of inducing damage within a chromosome segment that, previous to the damage event, occupies a cross-linked region organized by transient structural maintenance of chromosome (SMC) complexes. Using novel computational and visualization techniques, we investigate the particular role of these transient crosslinks in driving local chromatin dynamics, repair mechanisms, and substructure.

Speaker: Caitlin Hult (Gettysburg College)

3:20 PM Harnessing Discrete, Multiscale Modeling and Topological Data Analysis to Forecast Stem Cell Behavior

Pluripotent stem cells have the capacity to differentiate into all the primary germ layers represented in embryos. Individual cells process information from their environment through biophysical and biochemical cues in order to determine their cell fate (i.e., the germ layer into which they will differentiate). However, cell autonomous decision-making does not fully account for the organizational features associated with developmental patterning. In this work, we investigated the role of intercellular/intracellular signaling and morphogen-based chemotaxis in the context of cell fate decisions. Along with in vitro experiments, we developed an ensemble of multiscale, agent-based models which represent key mechanisms (e.g., signaling and cell division) using discrete mathematical models (e.g., Boolean networks and Markov chains, respectively). The goal of this type of modeling is to connect the local interactions with the population-level patterning that we observed in microscopy images. We also used persistent homology to generate multiscale, topological descriptors (i.e., persistence landscapes) from both microscopy images and model simulations. By comparing descriptors from in vitro and in silico experiments, we were able to perform model selection and to improve model predictions of emergent organization under a variety of differentiation conditions.

Speaker: Daniel Cruz (California Polytechnic State University, San Luis Obispo)

3:40 PM Learning collective multicellular dynamics with an interacting mean field neural SDE model

The advent of temporal single-cell RNA sequencing (scRNA-seq) data has enabled in-depth investigation of dynamic processes in heterogeneous multicellular systems. Despite remarkable advancements in computational methods for modeling cellular dynamics, integrating cell-cell interactions (CCIs) into these models remains a major challenge. This is particularly true when dealing with high-dimensional gene expression profiles from large populations of interacting cells, where the intricate interplay between cells can be obscured by data complexity.
In this talk, I will present scIMF, a deep generative Interacting Mean Field model that learns collective multicellular dynamics directly from temporal scRNA-seq data. Built on the McKean-Vlasov stochastic differential equation (MV-SDE) framework , scIMF models each cell's dynamics as a function of both its own gene expression state and the empirical distribution of the entire cell population. A cell-wise Transformer attention mechanism parameterizes the interaction term, enabling efficient inference of nonlocal and asymmetric CCIs.
Benchmarked against state-of-the-art methods across zebrafish embryogenesis, mouse fibroblast reprogramming, and pancreatic β-cell differentiation datasets , scIMF achieves superior gene expression reconstruction at unobserved time points and more accurate cellular velocity inference. Furthermore, scIMF uncovers biologically interpretable, non-reciprocal interaction patterns of cells, providing a principled framework for studying complex, particularly non-equilibrium biological systems.

Speaker: Lin Wan (Chinese Academy of Sciences)

4:00 PM Multi-scale regulation of organ growth through a gene-regulatory network that drives a transient proliferative signal

Organ growth during development is orchestrated by a combination of patterning, cell
proliferation, and morphogenesis, but the extent in which these contributions are
integrated into a multi-scale process is largely unknown. The developing wing of the fruit
fly, Drosophila melanogaster, offers an excellent experimental model to address this
question because there is a broad knowledge of the molecular players that drive
patterning and growth. Previous work has revealed that the gene regulatory network that
drives the expansion of the gene that determines cell fate, also involves the nuclear
translocation of the Hippo effector, Yorkie (Yki), which has been extensively reported as
a source of driving an excess of cell proliferation in overexpression conditions. However,
it is unclear if wild-type Yki levels participate in normal developmental growth. We
found that nuclear Yki levels moderately and transiently increase prior to wing cell
differentiation. We then used mathematical modelling to show that this result is
consistent with the gene network of the system and built a multi-scale molecular/tissue
model to investigate the possible role of this transient nuclear Yki as a mechanism that
transiently contribute to organ growth. This modelling-driven hypotheses-generation
approach uncovers a key role of transient effects that are often neglected when averaging
over space and time in classical developmental studies.emphasized text

Speaker: Marcos Nahmad (Centre for Research and Advanced Studies (Cinvestav))

3:00 PM → 4:20 PM Newtonian and non-Newtonian Biofluidmechanics: Integrating Theory, Experiments, Modeling, and Simulations

3:00 PM From Langevin Functions to Macro Closures: Multiscale Modeling of Viscoelastic Biofluids

Viscoelastic behavior in biological fluid arises from the stretching of polymeric structures. Capturing finite extensibility is essential for predicting phenomena like strain hardening and elastic instabilities. This work develops a multiscale framework linking the statistical mechanics of freely jointed chains, expressed through the inverse Langevin function (ILF), to stochastic microscale simulations and continuum constitutive models.

Using the Brownian Configuration Field approach [1], we compare stochastic dumbbell dynamics across three ILF approximations: the classical FENE model and the more accurate Pade-based approximations of Cohen and Rickaby–Scott (RS). While models coincide in weak and fully stretched limits, significant differences emerge in the moderate extension regime critical to biofluids. FENE consistently underestimates chain stretch and stress. Linear stability analysis shows that the ILF choice influences eigenvalue growth, impacting numerical stiffness.

To enable large-scale simulations, we derive corresponding macroscopic closures—FENE-P, FENE-CR, and new Cohen/RS-based variants—which preserve Pade-based accuracy while maintaining computational efficiency. Validation against stochastic data demonstrates enhanced prediction of strain hardening, oscillatory responses, and thinning dynamics.

[1] M. A. Hulsen, A. P. G. Van Heel, and B. H. A. A. Van Den Brule. Simulation of viscoelastic flow using Brownian configuration fields. Journal of Non-Newtonian Fluid Mechanics, 70(1):79–101, 1997.

Speaker: Paula Vasquez (University of South Carolina)

3:20 PM Dynamic deformation and positioning of nucleus

We investigate the coupled dynamics of centrosomes and the cell nucleus under microtubule-mediated pulling within a viscous cytoplasmic environment. A coarse-grained, stoichiometric framework [1] is developed to capture the interactions between microtubules and force generators (FGs) distributed on the nuclear envelope and cortex. The model integrates hydrodynamic coupling, nuclear envelope elasticity, FG transport along the nuclear envelope, and FG binding kinetics, enabling quantitative predictions of force balance and shape evolution. Using a boundary-integral formulation benchmarked against analytical limits, we examine how envelope stiffness, permeability, and FG mobility control the stability and positioning of the centrosome nucleus complex. Simulations in spherical and spheroidal geometries reveal that enhanced FG mobility or weakened envelope stiffness amplifies nuclear deformation and destabilizes centrosomal organization conditions reminiscent of pathological nuclear softening. Parameter sweeps across FG number and mechanical moduli delineate the transition from stable to misaligned configurations. This framework establishes a unified mechanical description linking molecular-scale force transduction to mesoscale nuclear morphology, providing mechanistic insight into how cytoskeletal dysregulation and envelope integrity jointly govern centrosome nucleus coupling.

[1] Yuan-Nan Young, Vicente Gomez Herrera, Huan Zhang, Reza Farhadifar, and Michael J. Shelley. Geometric model for dynamics of motor-driven centrosomal asters. Phys. Rev. Research, 7: 013004, 2025.

Speaker: Yuan-Nan Young (New Jersey Institute of Technology)

3:40 PM Monte Carlo simulations of membrane microfiltration for water purification

Microfiltration is a water purification method used by municipal facilities to produce potable water that relies primarily on a size-exclusion mechanism. When a contaminated solvent passes through a membrane filter, unwanted contaminants with diameter larger than that of the membranes pores, such as suspended solids, large bacteria, and proteins, are retained on the membrane. This foulant build-up occludes the area open for fluid flow, impairing the efficiency of filtration operations by decreasing the flux through the membrane over time. Backwashing is a strategy to restore filtration wherein clean water is processed backward through the membrane to dislodge attached foulants. The overarching goal of this work is to determine the optimal backwashing parameters (duration, frequency, and flux) to ensure sufficient membrane recovery without sacrificing more clean water than is needed.

We developed a 2D Monte Carlo model to simulate forward filtration and backwashing through constant pressure, dead-end, at-sheet membranes, and benchmarked it against lab-scale experiments [1]. Then, we extended our model to approximate the more complicated hollow-fiber membrane geometry and were able to qualitatively capture constant-flux filtration operations in such systems. Our next step aims to incorporate long-term fouling mechanisms into our model to capture foulant build-up during cake filtration which can lead to biofilm formation. This research is funded by NSF CBET-2211001.

[1] Abigail R. Drumm and Francesca Bernardi. Monte Carlo simulations of two-dimensional at-sheet membrane lters for constant-pressure water puri cation. Physical Review E, 112(5):055501, 2025.

Speaker: Francesca Bernardi (Worcester Polytechnic Institute)

4:00 PM A spheroidal squirmer model for euglenids

Euglenids are flagellated microorganisms whose elongated, flexible bodies enable rich swimming dynamics in confined environments. Focusing on their flagellated mode of locomotion rather than body shape deformations, we construct a simplified hydrodynamic model in which the euglenid is represented as a rigid prolate spheroid and surface slip velocities are imposed over a portion of the body to model the action of the flagellum at one pole. Using a boundary element method, we numerically compute the flow field and resulting swimmer dynamics driven by the squirming activity. We investigate the behavior of these swimmers in both straight and wavy channels, focusing on how confinement and channel geometry influence trajectories, orientations, and migration patterns. Systematic variations of swimmer aspect ratio, the active fraction of the body length, and channel parameters allow us to identify key geometric and hydrodynamic mechanisms governing swimmer–channel interactions. Our results highlight the strong coupling between swimmer geometry and environmental structure, demonstrating that the body shape and flagellar activity can be tuned to promote transport through particular structures. This framework provides a physically grounded and computationally efficient model for euglenid motility and offers insights relevant to microorganism transport in complex microfluidic and biological environments.

Speaker: Henry Shum (University of Waterloo, Canada)

3:00 PM → 4:20 PM Personalized forecasting in oncology informed by multiscale multimodal data

3:00 PM From patient vascular data to radiotherapy outcome prediction: a multiscale mechanistic framework

Radiotherapy (RT) efficacy in solid tumours is critically shaped by the microvascular environment (MVE); hypoxic niches confer radioresistance, while RT-induced phenotypic selection enriches residual tumours in cancer stem cells (CSCs), driving recurrence. We present a multiscale computational framework integrating three components: (i) a phenotype-structured PDE model for tumour cell dynamics with oxygen-dependent proliferation, necrosis, plasticity, and radiobiological response \cite{celora_spatio-temporal_2023}; (ii) a 3D–1D coupled model for microvascular oxygen transport \cite{possenti_mesoscale_2021}; and (iii) patient-specific vascular networks generated from capillary density data of head and neck cancer cohort \cite{materne_patient-specific_2025}, subjected to vessel damage to simulate RT-induced MVE degradation. A reduced order model based on proper orthogonal decomposition and mesh-informed neural networks enables real-time oxygen field evaluation \vite{vitullo_nonlinear_2024}. Simulating fractionated (FRT) and ultrahypofractionated (UHFRT) protocols on healthy and 50%-pruned networks reveals that vascular architecture—not dose alone—is the primary determinant of outcome. Although hypoxia-induced dedifferentiation shifts the residual tumor composition to radioresistant stem-like states, vascular geometry compromises the efficacy of RT, rendering dose escalation essentially pointless. UHFRT outperforms FRT in well-perfused settings, but both fail under severe MVE damage. These patient-informed results provide mechanistic insights to guide RT planning, paving the way for patient-specific digital twins.

Speaker: Cristina Macaluso (Politecnico di Milano, Italy)

3:20 PM NHOC: A PET imaging biomarker for survival forecasting in oncology

Human cancers are biologically and morphologically heterogeneous, exhibiting complex spatiotemporal dynamics during tumor growth. Imaging with positron emission tomography (PET) enables visualization of metabolic activity and its intratumor heterogeneity.
Using continuous and discrete mathematical models of tumor growth, we showed that the location of the metabolic activity hotspot drifts from the tumor center toward the periphery. This observation led to the definition of NHOC, the normalized distance from the PET hotspot to the tumor centroid.
We applied this metric to cohorts of patients with breast cancer and non–small-cell lung cancer (NSCLC). In these datasets NHOC was shown to be a strong predictor of survival \cite{jim21}.
NHOC is therefore a biomarker inspired by mechanistic modeling that enables personalized forecasting in patients.
Since the publication of the original study, this concept has gained significant traction in the medical community. NHOC has been applied and extended by nuclear medicine groups and validated in independent cohorts \cite{hov24,chen25}.
Moreover, we have recently extended its application to a cohort of high-grade gliomas, where it continues to demonstrate prognostic value \cite{bos26}. These results highlight the generalizability of the biomarker across tumor types.
In this talk, I will review the mathematical foundations of this metric, its application as an imaging biomarker, and its impact on enabling personalized forecasting.

Speaker: Jesús J. Bosque (Universidad Politécnica de Madrid, Mathematical Oncology Laboratory (MOLAB))

3:40 PM From measurement to decision: a tissue-aware digital-twin platform for CAR T cell dosimetry

Chimeric antigen receptor (CAR) T cell therapy has transformed the treatment of certain haematological malignancies, yet relapse and primary resistance remain common. Although CAR T cells circulate systemically, their ability to activate, persist and eliminate target cells varies across tissues, suggesting that microenvironmental context plays a key role in therapeutic outcome.
Understanding these dynamics requires integrating experimental observations with mechanistic modelling across biological scales. Experimental systems provide essential measurements of CAR T behaviour, but many mechanistic hypotheses and treatment strategies cannot be directly tested in vivo. Agent-based models (ABMs) offer a complementary approach by representing cell-level interactions and emergent population dynamics, enabling controlled exploration of tissue contexts, dosing strategies and treatment schedules while supporting the principles of the 3Rs (Replace, Reduce, Refine).
Here I present an integrative framework linking multiscale experiments with mechanistic modelling to study CAR T dynamics across anatomical sites. Central to this effort is the development of an organ-to-organ atlas capturing tissue-specific CAR T behaviour across multiple organs. Integrated with an ABM as a mechanistic engine, these data enable calibration of tissue-aware virtual experiments and lay the groundwork for patient-specific digital twins capable of forecasting treatment responses in silico.

Speaker: Luciana Luque (CRUK Scotland Institute)

4:00 PM Modelling phenotypic plasticity and adaptation to hypoxia and treatment in glioblastoma

Glioblastoma (GBM) is the most common and lethal brain cancer. It has a dismal prognosis with a 5-year survival rate of 6.8% \cite{stankovic2021vitro}. It remains one of the most challenging malignancies due to its high intratumoral heterogeneity and the ability of cancer cells to adapt to harsh microenvironmental conditions. This adaptive response is primarily driven by hypoxia, which triggers a metabolic and behavioral shift that enables cells to transition towards more aggressive stem-like phenotypes, increasing GBM resilience \cite{uribe2022adapt}. Phenotypic plasticity is also a key driver of treatment failure, fostering resistance to current therapies such as radiotherapy and chemotherapy with temozolomide \cte{amirmahani2025epigenetic}.
In this work, we present a continuum modeling framework designed to simulate the phenotypic plasticity and adaptation of GBM cells in response to hypoxia and therapeutic pressure. The proposed model describes cellular evolution through a set of internal variables that represent the phenotypic state of the cell population as a function of microenvironmental cues \cite{perez2023modelling}.
The framework was validated using both in vitro and in vivo longitudinal datasets that capture the dynamic evolution of glioblastoma under different oxygen \cite{perez2023modelling} and treatment conditions \cite{perez2024modelling}, demonstrating the model’s ability to provide not only predictions of tumor progression but also a mechanistic explainability of the underlying phenotypic shifts.

Speaker: Marina Pérez-Aliacar (Universidad de Zaragoza, Spain)

3:00 PM → 4:20 PM Clinically Focused, Translational Modeling of Cancer

3:00 PM Phase i trials in cancer: From board to bench to bedside and back again

Cancers are complex evolving systems that adapt to therapeutic intervention through a suite of resistance mechanisms, therefore whilst the maximum tolerated dose (MTD) therapies generally achieve impressive short-term responses, they unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during cancer treatment is becoming more widely accepted.  However, MTD treatment strategies continue to dominate precision oncology. Adaptive therapy is an evolutionary therapy that aims to slow down the emergence of drug resistance by controlling tumor burden through competition between drug sensitive and resistant cell populations. This approach was developed through mathematical model driven insights and has been shown to work in preclinical animal models (prostate, ovarian, melanoma, breast) and in pilot clinical trials (NCT02415621; NCT05189457; NCT03543969). In this talk we will discuss how mathematical models and machine learning can be used to optimize treatment strategies \cite{scibilia2025mathematical}, including adaptive therapy, and drive Phase i (imaginary) trials \cite{kim_phase_2016}. We will highlight how mathematical model driven digital twins can: (i) Integrate patient variability; (ii) Bridge between bench and bedside; (iii) Be calibrated from historic clinical data; (iv) Drive Phase i trials; (v) Stratify and optimize treatment; (vi) Predict novel trial outcomes.

Speaker: Alexander Anderson (Moffitt Cancer Center)

3:20 PM Personalized predictions of Glioblastoma infiltration

Glioblastoma (GBM) is a highly invasive brain tumor, whose cells infiltrate surrounding normal brain tissue beyond the lesion outlines visible in the current medical scans. Predicting GBM infiltration is critical for designing radiotherapy treatment plans because GBM recurrence is largely driven by diffuse tumor infiltration. However, standard radiotherapy, the mainstay for treating this diffuse infiltration, relies on uniform expansions that neglect patient specific biological and anatomical factors. Mathematical models can complement the data by predicting spatial distributions of tumor cells beyond the visible margins. This requires estimating patient specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. Here, we discuss biophysical growth models and methods for solving the inverse problem, including new scientific machine-learning methods PINN-GBM and BiLO \cite{zhang_personalized_2025, ZHANG2026114679} that use physically-informed neural networks and GLIODIL \cite{balcerak_individualizing_2025}, which integrates traditional numerical methods with data driven paradigms. Using a newly developed open-source platform (PREDICT-GBM) that integrates a curated, longitudinal dataset of 255 patients with a unified evaluation pipeline \cite{noauthor_brainlesion/predictgbm_2026,zimmer2026predictgbmmulticenterplatformadvance}, we find that the biophysical models significantly outperform standard-of-care protocols in predicting future recurrence sites and demonstrate greater robustness compared to purely data-driven recurrence prediction methods.

Speaker: John Lowengrub (University of California, Irvine)

3:40 PM A Multiscale Physiologically Based Pharmacokinetic Model for mRNA-Encoded Therapeutics: Preclinical Predictions and Translational Perspectives

mRNA-encoded therapeutics are emerging as a promising strategy for cancer treatment, yet the quantitative link between lipid nanoparticle (LNP) delivery, intracellular mRNA processing, and systemic protein exposure remains poorly defined. We present a multiscale physiologically based pharmacokinetic (PBPK) model that integrates a parsimonious LNP–mRNA trafficking and translation layer with a mechanistic antibody PBPK framework based on \cite{S19}, including FcRn recycling and two-pore tissue exchange \cite{C25}.
The model was calibrated and validated in mice using five literature datasets covering multiple mRNA-encoded anticancer therapeutics with diverse molecular weights, Fc properties, and LNP-mRNA formulations. It accurately reproduced plasma concentration-time profiles across single- and multi-dose regimens, while structural identifiability analysis supported robust estimation of the mRNA-related parameters \cite{C11}.
These results support the use of the model as a general platform to compare mRNA-LNP systems, investigate delivery and expression kinetics, and optimize dose scheduling for mRNA-encoded therapeutics.
The talk will present the model, its validation across diverse case studies, and will address the opportunities and current limitations of extending this parsimonious preclinical framework to non-human primates and humans, toward predictive tools for optimizing therapeutic kinetics and supporting individualized mRNA treatment strategies \cite{M09}.

Speaker: Elio Campanile (University of Trento)

4:00 PM Identifying population interactions in multiple myeloma immunotherapy with SINDy

Introduction:
Multiple myeloma (MM) is managed with complex multi-agent immunotherapy, including
daratumumab (dara), a CD38 antibody, and BCMA-targeted CAR-T cell therapy for
relapse. As the treatment landscape for MM is broad, it is important to identify
prognostic biomarkers to help personalize treatment for individuals. To investigate
immune interactions and response to immunotherapy, we used sparse identification of
nonlinear dynamics (SINDy).
Methods:
Patient’s immune populations were measured longitudinally via cytometry in two City of
Hope trials: (1) dara maintenance post-stem cell transplant and (2) BCMA-targeted
CAR-T therapy. Cell type abundances were input into SINDy to identify patient-specific
interaction dynamics.
Results:
Under dara maintenance therapy, SINDy discovered multiple 1st order interaction terms
between immune populations which distinguished responders from non-responders,
including NK cell-mediated stimulation of CD4+ T cells (AUC=0.90), and CD8+ T-cell
mediated stimulation of NK cells (AUC=0.88). Further, the dynamic stability of the
identified system predicted response (AUC=0.89). In BCMA CAR-T treatment, CAR-T
cells contributed towards dynamic system stability. Interactions with CD8+ T-cells
(Spearman R=0.87, p<0.001) and B-cells (Spearman R=0.94, p<0.0001) were strongly
correlated with the individual’s immune system stability.
Conclusion:
SINDy reveals interpretable immune interaction structures that separate treatment
responders from non-responders and characterize system-level stability, offering a data-
driven framework for personalizing immunotherapy in multiple myeloma.

Speaker: Ryan Woodall (City of Hope)

3:00 PM → 4:20 PM Mathematical Foundations of Biochemical Computing

3:00 PM Reliable computing with reaction networks with unknown or variable rate constants

Recent advances in synthetic biology have made it possible to deploy chemical reactions that implement computation inside a cell. On the theoretical side, several algorithms have been proposed that optimize for accuracy, computational speed, and resource efficiency. Most of these algorithms, however, rely on two assumptions: (i) the parameters or reaction rate constants are perfectly known, and (ii) the rate constants are insensitive to fluctuating environmental conditions. Neither of these assumptions is realistic in practice, as rate constants are subject to physical, biochemical, and physiological variability, and difficult to measure accurately. We develop a novel repertoire of chemical reactions that perform arithmetic computations, including the operations of addition, rectified subtraction, multiplication, division and $n$th roots -- with the key property that the reaction network modules may contain rate constants that are unknown or environment-dependent. Furthermore, the modules may be used as building blocks to produce arbitrary composite computations while retaining rate-constant independence.

Speaker: Badal Joshi (California State University San Marcos)

3:20 PM Molecular Machines and the EM algorithm

The implementation of abstract dynamical systems with molecular systems has gained scientific interest. Automated theoretical schemes can compile formal reaction networks into DNA oligonucleotide sequences; thereby providing a potential molecular implementation of the dynamics of the formal reaction network. In this context, we propose a novel algorithm for learning parameters of Hidden Markov Model (HMM), a flexible statistical framework widely used in Bioinformatics, Machine Learning and Data Science to model an underlying hidden structure.

Our algorithm is specified by a network of chemical reactions, and mimics the Baum-Welch algorithm which is the standard learning algorithm for HMMs. The Baum-Welch algorithm is an iterative Expectation-Maximization (EM) algorithm where one step is performed at a time in a prescribed sequence. The reaction network scheme is divided into four subnetworks that correspond to the forward, backward, expectation, and maximization steps of the Baum-Welch algorithm. Each subnetwork describes a system of ordinary differential equations that might be run separately, exactly mimicking the steps of the Baum-Welch algorithm, or simultaneously, thereby obtaining a variant on the Baum-Welch algorithm.

Promising areas of application of this work come from cellular biology. In the future, a molecule-based HMM device might learn a molecular environment within an organism by sensing and interacting with the environment at the molecular level. It might take action according to the learning outcome, for example, choosing among different drug options, or a molecule-based HMM might be used as a building block in an artificial cell or population of cells, enabling cooperative behavior among cells or facilitating various tasks.

Speaker: Carsten Wiuf (University of Copenhagen)

3:40 PM Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed

Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting values of other chemical species. The broad goal of this nascent field is to develop systems that can operate in the niche of a (wet) cellular environment, rather than to directly compete with modern digital computers.

There have been numerous works that design reaction networks that carry out basic arithmetic. However, in general, these constructions have speeds of computation (i.e., rates of convergence) that depend intimately upon the inputs to the computation itself, sometimes making them unusably slow. In this talk, I will discuss how we designed a full suite of “elementary” chemical systems that carry out arithmetic computations (such as inversion, addition, roots, multiplication, rectified subtraction, absolute difference, etc.) over the real numbers, and that have speeds of computation that are independent of the inputs to the computations. Moreover, we proved that finite sequences of such elementary modules, running in parallel, can carry out composite arithmetic over real numbers, also at a rate that is independent of inputs. I will close with a number of open questions and directions for future work.

Speaker: David Anderson (University of Wisconsin-Madison)

4:00 PM Analog computation with transcriptional networks

Transcriptional networks represent one of the most extensively studied types of reaction networks in synthetic biology. While transcriptional networks typically rely on cooperativity and highly non-linear behavior of transcription factors to regulate production of proteins, they are often modeled with simple linear degradation terms. In contrast, general analog computation requires both non-linear positive as well as negative terms, seemingly necessitating control over not just transcriptional (i.e., production) regulation but also the degradation rates of transcription factors. Surprisingly, we prove that controlling transcription factor production (i.e., transcription rate) without explicitly controlling degradation is mathematically complete for analog computation, achieving equivalent capabilities to systems where both production and degradation are programmable. We demonstrate our approach on several examples including oscillatory and chaotic dynamics, analog sorting, memory, PID controller, and analog extremum seeking. Our results provide a systematic methodology for engineering novel analog dynamics using synthetic transcriptional networks without the added complexity of degradation control and informs our understanding of the capabilities of natural transcriptional networks.

Speaker: David Soloveichik (University of Texas at Austin)

5:00 PM → 6:20 PM Immune attack on the nervous system: mathematical models of multiple sclerosis

5:00 PM Exploring immune pathways and remyelination in Multiple Sclerosis

In this talk, I review a class of mathematical models for the early stages of Multiple Sclerosis (MS). A central immunological question concerns the trigger of the immune cascade initiating MS pathology. We compare two scenarios: one based on local microglia activation, recruitment of systemic immune responses, and oligodendrocyte apoptosis \cite{ BBGLPS16,GLRSS24,KhonCal,LBBGPS17}; the other on cytokine-mediated modulation of macrophage activation \cite{MF21}.
We focus on a reaction-diffusion-chemotaxis system for activated macrophages, cytokines, and oligodendrocytes. By varying the parameter governing the effect of cytokines on macrophage activation, the model captures both mechanisms within a unified framework.

Combining analytical results and numerical simulations, we show that the model generates a variety of demyelination patterns. For biologically realistic parameter values, its asymptotic states reproduce pathological features consistent with MRI observations.
Bifurcation analysis highlights marked differences between the two scenarios. The innate-immunity mechanism leads to highly aggressive pathology, with strong focal inflammation and rapid progression, whereas the cytokine-mediated mechanism yields milder inflammation and much slower disease evolution.

Finally, I discuss ongoing extensions including endogenous repair mechanisms active in acute inflammation, with the aim of describing remyelination processes observed in early MS and their failure in chronic lesions.

Speaker: Maria Carmela Lombardo (University of Palermo)

5:20 PM Derivation from kinetic theory of chemotaxis models for Multiple Sclerosis

We present the derivation of a class of reaction-diffusion models for Multiple Sclerosis starting from kinetic equations for the distribution functions of the cell populations involved in the biological processes underlying the evolution of the disease. The kinetic setting for the cell distributions is outlined, detailing interaction operators that account for conservative and non-conservative processes. Under suitable hypotheses of multiple scale processes, an asymptotic diffusive limit of kinetic equations is performed, leading to a system of reaction-diffusion equations for population densities, with general diffusivity and growth functions for some kinds of cells. The Turing instability analysis of such macroscopic system provides necessary conditions for the emergence of spatial patterns in a two-dimensional domain; the shape and stability of such patterns are discussed through a weakly nonlinear analysis, and some numerical simulations are presented in order to confirm theoretical results.

Speakers: Maria Groppi (University of Parma), Marzia Bisi (University of Parma), Romina Travaglini (University of Pavia)

5:40 PM A New Paradigm for the Mathematical Modelling of Multiple Sclerosis

The mathematical modelling of MS so far has focussed on a few aspects of the disease, but an overall modelling framework is missing. Here we propose a paradigm for the mathematical modelling of MS. Based on biological principles we propose six consecutive modelling levels. We develop models on Level 1,2, and 3, and test if these models can describe known effects related to MS. We first show that periodic disease outbreaks are possible in this framework. We show that presence of Epstein-Barr virus infections can initiate the disease, low levels of estrogen and vitamin D can alleviate it, mutations in the HLA-DR gene can promote MS, and we find that memory B-cells play a dominant role in the disease progression.

Speakers: Adrianne Jenner (Queensland University of Technology), Thomas Hillen (University of Alberta)

6:00 PM Instability and pattern selection in chemotactic models of multiple sclerosis

Multiple sclerosis is characterised by the formation of localised lesions in the white matter of the brain and spinal cord, resulting from immune-mediated damage to nervous tissue. Mathematical models that incorporate the chemotactic migration of immune cells provide a natural framework through which to investigate how such structures can emerge through self-organisation.

In this talk, I analyse a reaction-diffusion-chemotaxis model of multiple sclerosis. Building on previous work demonstrating the emergence of spatial patterns for biologically relevant parameter regimes, I focus on the mathematical mechanisms that govern pattern selection, stability and morphological transitions. In particular, I discuss the role of secondary instabilities, such as Eckhaus and zigzag instabilities. These are known as mechanisms of pattern selection and can account for the formation of defects frequently observed in real patterns. I also present a weakly nonlinear analysis of radially symmetric solutions to characterise the existence and stability of axisymmetric structures that resemble the concentric lesion patterns observed in Balo's sclerosis.

These results demonstrate how tools from pattern formation theory can shed light on the spatiotemporal evolution of immune-driven lesions and emphasise their wider applicability in analysing the emergence and stability of spatial structures within various modelling frameworks, including multiscale and phenotype-structured models.

Speakers: Eleonora Bilotta (University of Calabria), Francesco Gargano (University of Palermo), Marco Sammartino (University of Palermo), Pietro Pantano (University of Calabria), Valeria Giunta (Swansea University)

5:00 PM → 6:20 PM Mathematical Models of Tumour-Immune Interactions and Cancer Evolution

5:00 PM Spatial dynamic modelling to understand how dendritic cell clustering affects T cell activation

The coordination of the immune system is essential for maintaining health. Recent clinical studies show breast cancer patients with high dendritic cell (DC) clustering in tumour-draining lymph nodes have improved survival outcomes, when compared to those with a lower degree of DC clustering. However, the mechanistic basis for this spatial organization effect remains unclear.
We develop a spatially dynamic model of T cells interacting with Dendritic cells within the lymph node. We present a probabilistic agent-based model (ABM) of T cells, and use it to derive the deterministic, phenotypically structured partial differential equation (PS-PDE) of T cell activation and motion. Using the PS-PDE, we derive an analytic approximation of the expected level of T activation, based on the topology of a given Dendritic cell population. Our analytic approximation enables us to identify T cell characteristics that benefit most from Dendritic cell clustering, to result in an enhanced stimulation distribution. We perform a sensitivity analysis with our models, to identify T cell characteristics that result in desirable T cell activation.
Our key findings show that T cells with an intermediate level of stimulation uptake benefit most from higher levels of Dendritic cell clustering, activating with a comparable or greater abundance, and greater heterogeneity, when compared to T cells of a similar characteristic but with a lower level of Dendritic cell clustering.

Speaker: Domenic Germano (University of Melbourne)

5:20 PM TRAIL sensitivity: Decision boundaries in a continuous cell-state landscape with implications for NK-mediated cytotoxicity

Natural Killer (NK) cells mediate tumor cell killing through mechanisms such as granzyme–perforin release and death ligand–induced activation of the extrinsic apoptosis pathway \cite{Prager2019}. Among them, the TNF-related apoptosis-inducing ligand (TRAIL) plays a central role and has been widely explored as a therapeutic agent. However, its efficacy is consistently limited by fractional killing, whereby a subset of cells remains tolerant even at high doses\cite{roux2015fractional}. To investigate the origin of this heterogeneity, we develop a mechanistic model of the TRAIL-induced apoptosis pathway \cite{fiandaca2025drug}. By fitting the model to single-cell time resolved FRET trajectories monitoring apoptosis commitment across multiple doses, we infer latent, cell-specific protein abundances together with key kinetic parameters, recapitulating the full diversity of observed responses. These inferred parameters define a continuous state space describing each cell’s underlying biochemical configuration. By linking each trajectory to early signaling dynamics, we identify a dose-dependent decision boundary within this space that separates apoptotic from tolerant regions, indicating that cell fate is largely determined by a cell’s position in this state space at the time of treatment. Taken together, these results provide a quantitative basis for understanding heterogeneous sensitivity to TRAIL–induced apoptosis and suggests new strategies to modulate response in NK-based therapies.

Speaker: Giada Fiandaca (OMPutational pharmacology and clinical Oncology (COMPO) and Cancer Research Center of Marseille)

5:40 PM The co-evolution of a tumour’s genomic landscape and TCR repertoire

Cancer–immune co-evolution shapes tumour progression and immunotherapy
response, but quantitatively linking immune selection pressure to genomic intratumour heterogeneity and to the tumour-infiltrating T-cell receptor (TCR) repertoire remains challenging. Central to this challenge is recognising that immune selection drives a dynamic process in which the TCR repertoire both shapes and is shaped by the evolving tumour genomic landscape.

We set out to identify immune evasion signatures in one of the largest sets of TCR repertoires from non-small cell lung cancer (NSCLC). We performed bulk TCR sequencing on multi-region tumour samples from 265 NSCLC patients in the TRACERx 421 cohort, comprising 1.27 million unique TCRα and 2.5 million TCRβ chains.

A conceptual expectation of cancer–immune co-evolution predicts that the number of mutations is correlated with the number of expanded T-cell clones, previously shown in a smaller subset of the cohort \cite{joshi}. Using data analysis alongside an agent-based model of tumour–immune co-evolution, we investigate the contexts in which this relationship holds. The model links mutation accumulation to T-cell clonal expansion and allows us to explore how immune evasion mechanisms, such as MHC loss and checkpoint mediated immune suppression, perturb this relationship \cite{puttick,martinez-ruiz}. The analysis of the TRACERx 421 genomic, transcriptional and TCR repertoire data reveals foundational principles for the relationship between tumour evolution and host immune control.

Speaker: Isabella Sodi (University College London)

6:00 PM Optimizing combined oncolytic virotherapy and chemotherapy for neuroblastoma: a mathematical approach

Neuroblastoma is the most common extracranial solid tumor in children, where high-risk cases often face poor prognosis. We propose an ordinary differential equation model to investigate optimal combined dynamics between chemotherapy (Cyclophosphamide) \cite{Garaventa} and oncolytic virotherapy (Celyvir, mesenchymal stem cells carrying the adenovirus ICOVIR-5)\cite{Melen}, combining our previous works on chemotherapy \cite{Italia} and virotherapy \cite{Otero}.

The mechanistic model incorporates interactions between tumor, immune system, virus, and drug. Calibrated using published data, we perform mathematical analysis to identify threshold values for treatment administrations required to eliminate the tumor. Through sensitivity analysis, we determine key parameters driving treatment outcomes, serving as potential biomarkers.

We formulated an optimal control problem with a nonlinear objective functional aimed at minimizing tumor burden and treatment toxicity \cite{Pontrjagin}. We show that periodic bang-bang control regimes optimize the delivery of Celyvir, while singular control can characterizes the chemotherapy regimen. By conducting in silico trials on virtual patient cohorts, we assessed the effects of patient heterogeneities on optimal solutions. Our results demonstrate that personalized scheduling, informed by patient-specific data, can significantly optimize combined treatment outcomes, providing a mechanistic-based foundation for clinical decision support systems.

Speaker: Matteo Italia (University of Castilla-La Mancha)

5:00 PM → 6:20 PM Bridging Structure and Dynamics in Biological Networks

5:00 PM Attractors are less stable than their basins: Canalization creates a coherence gap in gene regulatory networks

Waddington’s epigenetic landscape has long served as a central metaphor for cellular differentiation, depicting mature cell types as stable valley floors. Boolean networks, introduced by Kauffman in 1969, provide a mathematical formalization in which attractors represent phenotypes and basins correspond to developmental valleys. Traditional stability measures assess robustness via perturbations of arbitrary states, although biological systems typically reside at attractors. Here we formalize and analyze attractor coherence – a stability measure Kauffman envisioned but never rigorously developed – which quantifies the likelihood that perturbations of attractor states induce phenotype switching. Across 122 curated biological Boolean models, we uncover a paradox: attractors representing mature cell types are consistently less stable than the trajectories leading to them. Simulations of random networks show that this coherence gap arises from canalization, where specific genes dominate regulation. While canalization increases overall stability, it disproportionately stabilizes transient states, placing attractors near basin boundaries. The gap is almost perfectly predicted by network bias, itself shaped by canalization. These results revise Waddington’s landscape: canalization creates robust developmental valleys while flattening ridges near attractors, enabling phenotypic plasticity.

Speaker: Claus Kadelka (Iowa State University)

5:20 PM Principles of dynamical modularity in biological regulatory networks

Biological systems are thought to be hierarchically modular, such that small semi-autonomous modules work together to create larger modules, each responsible for function at a different scale of organization. We thus expect that understanding each module in isolation and putting them together tells us how the whole works. When it comes to cellular regulation, however, a registry of biological modules and their behaviors do not appear to be not sufficient to decipher their coordinated response. Here we ask: are there are general rules by which cellular functions are coordinated in health and disease? We hypothesize that distinct phenotype-combinations are generated by interactions among several multistable regulatory switches, each in control of a discrete set of phenotypic outcomes. To test whether this organization sets apart regulatory networks from random ones, we define measures that quantify whether a) a Boolean network's dynamics can be accurately described via combinations of module-autonomous dynamics, b) modules preserve dynamical autonomy while coupled to others, and c) switches at all scales of the hierarchy show robustness in their phenotype-choice control. Comparing a modular mammalian cell cycle model to its randomized counterparts, we formulate three general principles that govern the way coupled switches coordinate their function. These principles can guide construction of large Boolean regulatory models that reproduce a broad range of observed cell behaviors.

Speaker: Erzsebet Regan (The College of Wooster)

5:40 PM Network dynamical stability analysis of age-related health

Nearly every physiological function declines with age, as risk of death, disability and chronic disease rises exponentially. Whereas many specific diseases have well-characterized biomarkers and diagnostic thresholds, age-related decline is difficult to quantify and often appears as small, ambiguous changes across many biomarkers. We hypothesized that these changes reflect collective, pathological behaviours that push health systems away from stability, i.e. homeostasis. We used linear order eigen-analysis to characterize these deviations in terms of stability and fixed point drift. We then analyzed associations with adverse outcomes including death and chronic disease – that we surmise occur after deviations reach a tipping point.

We used longitudinal health data from multiple species and datasets\cite{Pridham2023-pi,Pridham2024-ql,Pridham2024-in} to estimate interaction networks to linear order. Stability analysis using the eigen-decomposition consistently revealed that health biomarker data are stable, and demonstrate two characteristic behaviours. The position of the fixed point drifts with age, a phenomenon we call “mallostasis”, and variance accumulates along weakly-stable dimensions, a phenomenon we call “stochastic accumulation”. Each network has only a few such dimensions but they dominate risk of adverse outcomes. Analysis of these dimensions shows that each dimension shares similarities to a different medical syndrome. We discuss the dynamical behaviour and utility of eigen-states for characterizing overall health.

Speaker: Glen Pridham (Weizmann Institute of Science)

6:00 PM From self-sustained intracellular oscillations to whole-cell network organization in Physarum polycephalum

Across living systems, oscillations support coordination, information flow, and decision making, from neural rhythms to calcium signaling in single cells. The unicellular slime mold Physarum polycephalum is a striking example: despite lacking a nervous system, it exhibits decision-like behaviors including maze solving, network formation, and exploration–exploitation trade-offs. However, existing models focus either on large-scale network adaptation or local mechanochemical oscillations, leaving open how intracellular dynamics propagate through the organism to shape collective behavior.
We present a mechanistic model linking intracellular oscillations to network-scale dynamics by coupling self-sustained calcium oscillations to active pressure, fluid flow, and morphology. In one spatial dimension, reaction–diffusion dynamics drive pressure and tube radius changes, reproducing contraction waves and stimulus-induced symmetry breaking. We extend the model to two spatial dimensions using a phase-field formulation in which calcium-regulated tension drives cell deformation and migration.
The model reproduces key cell-level behaviors including exploration–exploitation trade-offs and efficient transport network formation. More broadly, the results show how feedback between oscillatory dynamics and evolving morphology constrains information flow in a living transport network, illustrating how network structure and nonlinear dynamics jointly generate complex behavior in biological systems.

Speaker: Linnéa Gyllingberg (University of California, Los Angeles (UCLA), USA)

5:00 PM → 6:20 PM Advanced Progresses in Population Models Driven by Natural and/or Artificial Intelligence

5:00 PM Spatial Pattern Formation and the Evolution of Cooperative Behavior

Social dilemmas featuring tension between the individual incentive to cheat and a collective goal to maintain cooperative behavior arise across a range of natural and social systems, from the origins of multicellular life to the sustainable manage of shared natural resources. Evolutionary game theory provides a helpful analytical framework for describing this conflict between individual and collective interests, exploring mechanisms that can help the emergence of cooperative behaviors. In this talk, we discuss several PDE models for evolutionary games featuring diffusion of individuals and directed motion towards either increasing payoff or improved environmental quality. We show that biased motion of cooperators can promote the formation of spatial patterns featuring regions with greater population density and increased average payoffs and environmental quality in regions in which cooperators have aggregated. However, by measuring the average payoff of the population or the average level of environmental quality across the population, we see that these pattern-forming mechanisms can actually decrease the overall success of the population, relative to the equilibrium outcome in the absence of spatial motion. This suggests that payoff-driven and environmental-driven motion can produce a kind of spatial social dilemma, in which biased motions towards more beneficial regions can produce emergent patterns featuring a worse overall environment for the population.

Speaker: Daniel Cooney (University of Illinois Urbana-Champaign)

5:20 PM Rotating waves driven by asymmetric cognitive map in nonlocal aggregation-diffusion model driven by spatial cognitive map

Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. A reaction-diffusion-aggregation system coupled with a separate dynamically updating map is proposed to describe the animal population movement. We show that when an asymmetric cognitive map influences instantaneously, a rotating movement pattern emerges.

Speaker: Junping Shi (College of William & Mary)

5:40 PM Are the mathematical biological models governed by nonlinear first order Caputo fractional differential equations solvable?

Consider the first order Caputo fractional differential equation (FDE)
$$(D^{1-\alpha}_{C,a^+}u)(x):= (I^\alpha_{a^+} u')(x)=f(x,u(x))\quad \mbox{for almost every } x\in [a,b],$$ where $\alpha\in(0,1)$, $I^\alpha_{a^+}$ is the Riemann-Liouville fractional integral, $u'$ is the traditional first-order derivative and $f: [a,b] \times [0,\infty) \to \mathbb{R}$ is a function. The Caputo FDE can be a single equation or a system of equations. It was claimed in some previous papers that if $f$ satisfies the locally Lipschitz condition in the second variable, then the Caputo FDE has a unique solution. However, the result would be incorrect, see the open question below. The above result has been widely used in the literature to obtain the existence and uniqueness of solutions of a variety of models such as disease models and predator-prey models published, for example in *Scientific Reports*, *PLoS One*, *Epidemics*, *Communications in Nonlinear Science and Numerical Simulation*. However, these previous results which applied the above claimed result to obtain the existence and uniqueness of solutions of the models would not be correct unless one can prove that the locally Lipschitz condition implies the necessary condition for the Caputo FDE to have solutions: $$Fu\in I^\alpha_{a^+}(L^1[a,b]) \quad \mbox{for all } u\in S,$$ where $S$ is a ball in $C_+[a, b]$ and $(F u)(x) = f (x, u(x))$ for almost every $x\in [a, b]$. The open question is under what conditions on the nonlinearity $f$ , does the above necessary condition hold? It is noted that if the nonlinearity $f$ satisfies the locally Lipschitz condition in the second variable or is infinitely differentiable, it is unknown whether $f$ satisfies the necessary condition.

Speaker: Kunquan Lan (Toronto Metropolitan University)

6:00 PM MS124-12

Speaker: Samares Pal (University of Kalyani)

5:00 PM → 6:20 PM Mathematical Endocrinology: Models of Regulation, Disease and Dynamics

5:00 PM Models of Regulation and Disease Dynamics in Ovarian Cancer Invasion

The ovarian tumor microenvironment is shaped by dynamic interactions among cancer, stromal, and immune cells, but the drivers of progression remain unclear. In ovarian cancer, we found that immune balance is more prognostic than absolute immune cell abundance: CD8/Treg and CD8/CD4 ratios were more strongly associated with survival than CD8+, CD4+, or Treg levels alone. Macrophage state was also critical. Tumors enriched in M2 macrophages were linked to vascular invasion, persistent disease, and worse survival, whereas higher M0 macrophage levels predicted better outcomes; M1 macrophages showed little prognostic value. Neutrophil infiltration, though less common, was likewise associated with poor survival. Unsupervised clustering identified four immune-defined subtypes, with the worst outcomes in tumors enriched for M2 macrophages and CD4+ T cells and depleted in M0 macrophages. To investigate the dynamics of some of these players mechanistically, we pair patient-derived observations with a three-dimensional tumoroid model of ovarian cancer invasion and a baseline ODE model describing the coupled dynamics of ovarian cancer cells, stromal cells, macrophages, and mesothelial invasion. This experimental–mathematical framework allows us to examine how these components interact and how those interactions may be leveraged to reduce tumor invasion.

Speaker: Leili Shahriyari (University of Massachusetts Amherst)

5:20 PM Modeling PSA Dynamics to Characterize Prostate Cancer Treatment Response

Prostate cancer (PCa) remains a major global health burden, with more than 1.5 million new cases diagnosed annually worldwide. In the United States alone, over 300,000 men are expected to be diagnosed in 2026, with more than 36,000 deaths. Prostate-specific antigen (PSA) is widely used as a surrogate marker of tumor burden, and its temporal dynamics are closely associated with disease progression.
Improving our understanding of patient-specific PSA kinetics and the underlying drivers of progression is critical for advancing PCa treatment. In this study, we developed and analyzed two simple kinetic pharmacodynamic models of PSA dynamics, a latent variable and transit compartment linking to PSA dynamics. We evaluated each model’s ability to describe longitudinal PSA data from 55 patients undergoing hormone therapy. Model performance was assessed using goodness-of-fit metrics, diagnostic plots, and predictive accuracy for patient-specific trajectories.
Both models were able to capture key features of PSA dynamics, describing both responsive and progressive patient dynamics. However, the transit model demonstrated superior predictive performance and greater stability in estimating patient-specific parameters. These findings highlight the potential of simple mechanistic models to characterize disease progression and support personalized treatment strategies in prostate cancer.

Speaker: Renee Brady-Nicholls (Moffitt Cancer Center)

5:40 PM Longitudinal Biomarkers and Alzheimer's Disease in Down Syndrome

Background: Down syndrome (Trisomy 21) includes triplication of the APP gene, leading to excess amyloid precursor protein and early amyloid plaque formation. Individuals with Down syndrome typically develop plaques in their 40s, and Alzheimer's disease is their leading cause of mortality. APP‑directed interventions may therefore provide substantial clinical benefit in Down syndrome. However, Down Syndrome also involves immunologic and metabolic comorbidities.
Methods: The Alzheimer's Disease Biomarkers-Down Syndrome (ABC-DS) consortium has recruited a population study of over 100 Down Syndrome patients. Participants undergo cognitive testing and multimodal biomarker profiling, including inflammatory, metabolic, and PET‑based amyloid measures.
Results: PET‑derived amyloid measures are the strongest predictors of cognitive decline. Observed accumulation rates indicate that trials with approximately 50 participants per arm should be powered. However, immunologic and metabolic comorbidities may introduce heterogeneity that complicates trials or reveals subgroups requiring additional interventions.
Discussion: Interventions targeting amyloid accumulation in Down Syndrome are urgently needed. In addition to reporting these results, we will also pose forward‑modeling challenges related to immunologic and metabolic dysfunction in Down syndrome.

Speaker: Samuel Handelman (Aerska)

6:00 PM Analyzing (Sub-phenotyping) the Longitudinal Progression to Type 2 Diabetes using Machine Learning and Physiological Simulations

Type 2 diabetes (T2D) diabetes disease progression is associated with genetic susceptibility coupled with risk factors like overweight/obesity and prior incidence of gestational diabetes. Impaired insulin sensitivity coupled with alpha and beta cell dysregulation is observed in the progression to T2D. What is unclear is why some individuals progress to T2D while others never transition. In our previous model of
disease progression~\cite{subramanian2025evaluating}, we showed that mild alpha cell dysregulation could be beneficial as it leads to robust compensatory insulin secretion in the milieu of impaired insulin sensitivity leading to long term glycemic stability. Here we analyze longitudinal data on at risk individuals from the DPP/DPPOS study~\cite{diabetes200910} using Machine Learning tools coupled with simulations of the previously developed physiological model. We generated fine-grained sub-phenotyping of individuals, based on the relative influence of the different underlying dysregulations in disease progression. We first performed multivariate dynamic time warping (DTW)-based hierarchical clustering of longitudinal trajectories using a composite dissimilarity measure that combined path-length-normalized dynamic time warping distance with penalties for differences in participants’ baseline levels at study entry and mean longitudinal levels over follow-up. The clustering revealed groups of individuals who showed not only long-term stability but also periods of improvement in glycemia. The simulations showed that mild alpha cell dysregulation is likely to develop and plateau in these individuals leading to this behavior. This work highlights the power of integrating physiological modeling with machine learning tools to deliver precision medicine.

Speaker: Vijaya Subramanian (Johns Hopkins University)

5:00 PM → 6:20 PM Multiscale modeling in bioelectromagnetics

5:00 PM A multiscale cardiac pulsed field ablation model: from cellular electroporation effects to lesion formation prediction

Cardiac pulsed field ablation (PFA) is an emerging non-thermal ablation modality that employs high-intensity, short-duration electric pulses to induce irreversible electroporation in cardiac cells. In contrast to conventional thermal techniques, PFA selectively disrupts cell membranes while largely preserving the extracellular matrix and surrounding critical structures, thereby reducing collateral damage. This selectivity, combined with rapid energy delivery, enabled the quick adoption PFA for the treatment of many types of cardiac arrhythmia.
In this work, we present a multiscale modeling framework that links cellular electroporation dynamics to tissue-level lesion formation in cardiac PFA. At the cell level, the model captures pore generation, membrane oxidation, and the resulting changes in cellular permeability and electrical conductivity in response to the evolution throughout the temporal progression of the electric pulses. At tissue level, these cellular responses are integrated into a bidomain formulation to predict lesion development. The proposed time-dependent multiscale framework accounts for physiological tissue responses during and after the delivery of the pulses, and is capable of simulating PFA-induced lesion formation along time.

Speaker: Argyrios Petras (Johann Radon Institute for Computational and Applied Mathematics)

5:20 PM Multiscale modelling, analysis and simulation of cancer invasion processes

Invasion, one of the hallmarks of cancer, is a complex process involving numerous interactions between cancer cells and the extracellular matrix, facilitated by matrix degrading enzymes (MDEs). It was demonstrated experimentally that there are two important types of MDEs, membrane-bound and diffusible metalloproteinases, involved in cancer invasion. To analyse the impact of those two types of MDEs on cancer invasion, we formulate a microscopic cell-scale model for the degradation of the extra-cellular matrix by matrix degrading enzymes produced by cancer cells. Using tools from the theory of homogenisation we propose a macroscopic tissue-level model for cancer cell invasion into the extra-cellular matrix mediated by bound and soluble MDEs. For the macroscopic model we prove the well-posedness result and propose a finite element method for the numerical approximation. Simulation results illustrate the role of the bound and soluble enzymes in cancer invasion processes.

Speaker: Mariya Ptashnyk (Heriot-Watt University, Edinburgh, Scotland, UK)

5:40 PM Homogenization of a phenomenological electropermeabilization model

In this work, we study the homogenization of the phenomenological electropermeabilization model introduced by Kavian et al (2014) in a periodic tissue subject to an applied electric field. We introduce a small parameter epsilon and derive the most relevant scaling of the equations in epsilon through dimension analysis. Asymptotic expansions yield a macroscopic model, where we are able to define an effective conductivity of the medium in terms of solutions to cell problems on the microscopic scale. The effective conductivity agrees qualitatively with experimental data from real tissue and depends non-linearly both on time and the applied electric field. Due to the non-linearities in the equations, the macroscopic and microscopic problems do not fully decouple, and the effective conductivity exhibits memory effects. Still, we are able to prove two-scale convergence of the solutions as epsilon tends to zero using monotonicity arguments. Our results therefore provide a rigorous mathematical coupling between cell-scale properties in the tissue and the observed macroscopic conductivity dynamics.
The talk will provide an overview of the above results. Some numerical results will also be shown, varying parameters including size and shape of the biological cells.

Speaker: Tobias Gebäck (Chalmers University of Technology and University of Gothenburg)

6:00 PM Multiscale Modeling of Electroporation Capturing Long-Term Membrane Permeability

We derive a tissue-scale model of electroporation through periodic asymptotic analysis, based on a cell-scale model introduced by Leguèbe et al. (2014). In the cell-scale model, electroporation is described by coupling the transmembrane voltage to phenomenological variables representing the degree of membrane poration and oxidative effects in the lipid bilayer. An important biological feature of electroporation is that cell membranes can remain permeable to molecules for minutes after the electric pulse has ceased, even after pore resealing. This effect is accounted for by an additional phenomenological variable governed by a reaction–diffusion equation posed on the cell membranes. Using periodic homogenization, we rigorously upscale the coupled system from the cellular level to an effective tissue-scale description. In the homogenization limit, the membrane reaction–diffusion dynamics persist and give rise to macroscopic equations with diffusion effects inherited from the microscale structure. This multiscale framework provides a basis for analyzing and optimizing pulse protocols in applications such as drug delivery and electrochemotherapy, where both immediate and long-term permeability effects are crucial.

Speaker: Emil Timlin (Chalmers University of Technology)

5:00 PM → 6:20 PM Advances in Modeling Human Behavior and Infectious Disease Spread: A cross-disciplinary perspective

5:00 PM Extending an SEIR behavioural model with structures for supply chain efficiency and vaccine allocation

A key challenge in infectious disease modelling is to extend beyond classical epidemiological structures to model the interplay between the spread of a disease and how people respond to an outbreak \cite{lejeune2025formulating}. Recent research highlights the potential of incorporating a human behaviour feedback loop into existing model structures as a promising way to advance disease forecasting, and provide better methods for decreasing the negative impact of disease countermeasures on society \cite{gozzi2025comparative,rahmandad2022enhancing}. This talk presents an age-cohort infectious disease spread model, and builds upon recent contributions for exploring pandemic response strategies in the context of limited resources \cite{andrade2024preparing} in three ways. First, the it incorporates a negative feedback structure to capture human behaviour which moderates disease spread; second, it adds a supply chain structure that determines the availability of countermeasures; and third, it implements allocation policies to allow for prioritisation of specific age cohorts for vaccine distribution. The scenario results are framed based on the overall aNack rate and hospitalisation rate, and the conventional scenario analysis is extended to encompass techniques from the discipline of statistical learning – namely explanatory model analysis \cite{biecek2021explanatory}, which can be deployed to highlight influential model parameters.

Speaker: James Duggan (University of Galway)

5:20 PM Not Everyone Panics Alike: When Heterogeneous Behavioral Responses Change Epidemic Outcomes

Compartmental epidemic models increasingly capture demographic and contact heterogeneities, yet behavioral responses are typically treated as uniform: as cases or deaths rise, an average person perceives greater risk and increases compliance with non-pharmaceutical interventions (e.g., masking), reducing transmission. But is treating societal behavior as a single average feedback loop a safe simplification? We first develop a two-group compartmental behavioral epidemic model in which groups differ in infection fatality ratio, susceptibility, and contact rates, generating distinct behavioral responses to the same epidemic signals. We show increased variation in mortality risk alters dynamics: homogeneous assumptions lead to underestimated prevalence and overestimated fatality. Heterogeneity in susceptibility alone reduces cumulative cases and deaths, and differences in mixing patterns amplify these effects. A counterintuitive result emerges: a lower-risk group responding weakly reaches herd immunity early, indirectly shielding a more cautious, higher-risk group. We further extend the model to eight age groups reflecting COVID-19 risk variation, examining how behavioral heterogeneity shapes outcomes at a finer scale. Together, these findings clarify when explicitly representing heterogeneous behavioral responses is essential for reliable epidemic modeling.

Speaker: Navid Ghaffarzadegan (Virginia Tech)

5:40 PM Optimizing infectious disease mitigation under dynamic conditions

Mitigation measures are essential for controlling the spread of infectious diseases during pandemics and epidemics, but they impose considerable societal, individual, and economic costs. We developed a general optimization framework to balance costs related to infection and to mitigation \cite{muller2025optimizing}. Optimizing the trade-off between mitigation and infection cost, we identify three key effects: First, assuming a constant reproduction number, the optimal response to an infectious disease requires either strict mitigation or none at all, depending on disease severity; an intermediate mitigation level is never optimal. Second, under seasonal variations, optimal mitigation is stricter during winter. Interestingly, a single wave of infections still arises in spring with 3 months delay to the seasonal peak of infectivity, replacing the autumn/winter waves known for classical influenza. Third, during steady vaccination campaigns, even optimal mitigation can result in transient infection waves. Finally, we quantify the cost of delayed mitigation onset and show that even short delays can substantially increase total costs—if the disease is severe.

Speaker: Laura Mueller (Max-Planck-Institute for Dynamics and Self-Organization; Institute for the Dynamics of Complex Systems, University of Göttingen)

6:00 PM Measles and mandates: A mathematical assessment of Florida's proposed school-entry vaccination mandate removal

Recent measles outbreaks in the United States and the United Kingdom have renewed public health concern over a disease once considered eliminated in these countries. Declining vaccination coverage, driven in part by changing public attitudes and policy discussions, has increased the risk of sustained transmission in previously protected populations. In particular, proposed changes to school-entry vaccination requirements in Florida raise important questions about the potential epidemiological consequences of reduced immunization.
In this work, we develop a compartmental framework stratified by age and vaccination status to derive and analyze conditions for disease persistence or eradication, such as the basic and control reproduction numbers, and the vaccine-induced herd immunity threshold. We incorporate Florida-specific demographic data, vaccination coverage among kindergarteners, and empirically estimated contact matrices to represent population mixing to explore how shifts in vaccination policy may influence transmission dynamics. This framework is extended to provide a flexible foundation for assessing the population-level impact of policy changes, possible pharmaceutical and non-pharmaceutical interventions, and identifying conditions under which measles resurgence is most likely.

Speaker: Alice Oveson (University of Maryland)

5:00 PM → 6:20 PM Recent perspectives on mathematical-biology education

5:00 PM Advances in Accessibility of Undergraduate Numerical Methods

Many mathematical problems that students encounter in typical undergraduate mathematics courses are designed so that an exact solution can be found without using a computational tool. While this is beneficial for learning fundamental mathematics, large-scale “real-world” applications that students may encounter after college, especially in the life sciences, frequently require complex and sophisticated computational algorithms. In undergraduate Numerical Methods, students learn how to build – and when to implement – algorithms to approximate solutions to common mathematical problems. This course therefore provides a critical foundation for students as they translate mathematical theory into future STEM careers.
An undergraduate numerical methods course is uniquely challenging because it requires treatment of concepts from both theoretical and practical perspectives, and a solid knowledge of several prequisites. In addition, many textbooks and programming languages used in this course are costly, further impacting its accessibility. To address these challenges, we worked to create a set of open-access ancillary materials to supplement free textbooks and coordinate with the introduction of Python as the primary programming language. These included computer programming activities with built-in scaffolding, a theoretical problem bank, a standard set of course notes, a review packet for prerequisite material, and a curated library of external multimedia resources. The work of creating these materials also led to increased conversations among the primary faculty and improved pedagogy. In this talk we will share some early results from development and implementation of these materials over the previous academic year.

Speaker: Laura Ellwein Fix (Virginia Commonwealth University)

5:20 PM Learning Differential Equation Modeling through Student-Driven Projects

Open-ended evaluated class projects provide an opportunity for students to take ownership of mathematical ideas, develop persistence, and enhance skills in communicating mathematics. By allowing students to choose project topics, they can engage with material that is relevant to their lives and interests. In this talk, I will reflect on my experiences in working with undergraduate students on student-driven projects, presenting some examples from an upper-level mathematical modeling course.

Speaker: Rebecca Everett (Haverford College)

5:40 PM Building Modeling Workshops at Biology Conferences

Workshops embedded within biologically focused conferences can be effective ways to bring new people into mathematical biology. They create accessible entry points for experimentalists, field biologists, and early-career researchers to learn modeling, while also giving mathematicians a chance to teach, build collaborations, and connect with real data and systems. In this talk, we share our experiences designing and running hands-on modeling workshops alongside domain-specific meetings, including one at the Global Amphibian and Reptile Disease (GARD) Conference and a recent workshop held just prior to the Ecology and Evolution of Infectious Diseases (EEID) 2026 conference. These particular workshops focus on approachable introductions to dynamical systems and epidemiological modeling, with a mix of short lectures and guided coding activities centered on simulation, parameterization, and working with data. We’ll also point to a growing set of publicly available resources, including curricula, code, and organizational tools, that make it much easier to develop and run these kinds of workshops. Overall, we highlight how these efforts can spark new collaborations, lower barriers to entry, and create meaningful connections between mathematical and biological communities.

Speaker: Dr Angela Peace (Virginia Tech University)

6:00 PM Does classroom-flipping improve analytical skills? Results from a cross-sectional comparison between undergraduate calculus exams

In a flipped life-sciences classroom, base concepts are presented asynchronously and students spend instruction time actively applying their problem-solving skills with the expert guidance of the teacher. Educational theory suggests that emphasizing application and analysis skills may benefit students, particularly in the advent of Artificial Intelligence as a learning tool for undergraduates. We analyzed the individual exam answers from three classrooms of MAT1332 students, one of which was flipped, to determine how flipped-classroom methods impacted student success. We explored what differences in question format, course sub-topic, final grade and question difficulty could reveal about student achievement on individual questions, and thus each section's methods for approaching the final exam. Students in the flipped classroom found greater success on analytical questions but less success on rote-application questions than the other two sections. Very low-achieving students (<45% final exam grade) and very high-achieving students (>80% final exam grade) were less affected by classroom flipping than mid-range students. Students in the flipped classroom performed worse on early-semester content, suggesting that an adjustment period to a flipped-classroom style may be necessary. Classroom-flipping seems to benefit life-sciences students by equipping them with the problem-solving-focused skills necessary to succeed on a final exam in the sciences. Mid-achieving students appear to see the greatest benefits of a classroom emphasis on problem-solving once they adapt to the novel learning method.

Speaker: Stacey Smith? (University of Ottawa)

5:00 PM → 6:20 PM Delay differential equation models in mathematical biology

5:00 PM Reaction-transmission delays in flocking models

Multiagent systems have attracted the attention of many researchers in recent years. Among them, there are the celebrated Hegselmann-Krause opinion formation model and its second-order version, the Cucker-Smale flocking model. Typically, for such systems, one is interested in investigating the asymptotic behavior of their solutions, namely the convergence to consensus for the Hegselmann-Krause model and the asymptotic flocking for the Cucker-Smale model. In such models, it is important to introduce time delay effects since time delays unavoidably appear as times needed to receive some information or reaction times. In this talk, we focus on a Cucker-Smale type model in presence of transmission-reaction delays. Unlike the existing related literature, the reaction delay and the transmission delay are allowed to have different sizes. Under suitable smallness conditions on the sizes of the time delays and on the initial conditions, we prove exponential flocking for the considered model.

Speaker: Elisa Continelli (University of Padova)

5:20 PM On the local stability of the elapsed-time model in terms of the transmission delay and interconnection strength

he elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models many interesting dynamics depending on the type of interactions between neurons. We investigate the linearized stability of this equation by considering a discrete delay, which accounts for the possibility of a synaptic delay due to the time needed to transmit a nerve impulse from one neuron to the rest of the ensemble. We state a stability criterion that allows to determine if a steady state is linearly stable or unstable depending on the delay and the interaction between neurons. Our approach relies on the study of the asymptotic behavior of related Volterra-type integral equations in terms of theirs Laplace transforms. The analysis is complemented with numerical simulations illustrating the change of stability of a steady state in terms of the delay and the intensity of interconnections.

Speaker: Nicolás Torres Escorza (Université Côte d’Azur)

5:40 PM Models with Memory and Delay in Molecular, Cellular, and Population Biology

Memory and delay naturally arise in mathematical models across physical scales. In molecular simulations, the generalized Langevin equation is a stochastic integro-differential equation describing a molecule (or a degree of freedom) subjected to colored (time-correlated) noise and a non-Markovian friction term~\cite{ref2,ref4}. In chemotaxis, cells respond to extracellular signals through intracellular signal transduction networks, and this internal dynamics naturally introduces delays and `chemical memory' in signal processing~\cite{ref1,ref4}. In collective animal behaviour, systems of interacting individuals base their observations and responses to stimuli not only on their present state but also on the system’s past history, with models accounting for transmission delays and reaction delays to signals~\cite{ref3,ref4}. In this talk, I will discuss how the parameters of delay equations relate to those of more detailed, non-delayed models and how population-level properties can be established for mathematical biology systems described by coupled delay equations.

Speaker: Radek Erban (Oxford University)

6:00 PM An Exact Solution and Amplitude Enhancement in a Non-Autonomous Delay Differential Equation

Delays in feedback mechanisms are well known to generate complex behavior, including oscillations. Understanding delay effects is therefore important in fields such as biology, mathematics, economics, and engineering. Delay differential equations (DDEs) provide a natural framework for analyzing such systems, yet exact analytical solutions are rare.

We present an exact solution of a simple non-autonomous DDE, which to our knowledge is the first analytical result of this type. Using this solution, we study a coupled system of two such equations. For suitable parameter values, the oscillation amplitude is dramatically enhanced - up to about 10 to the 8 times larger than in the uncoupled case.

Large collective oscillations are often assumed to require many interacting units. For example, the sinoatrial node, the heart’s primary pacemaker, contains thousands to tens of thousands of cells. Our results indicate that the presence of delay can produce strong amplification even in systems with only a small number of units.

Speaker: Toru Ohira (Nagoya University)

5:00 PM → 6:20 PM Novel Tools and Methodologies for Epidemiological Models

5:00 PM New approaches to old problems: data-driven models of dengue in emergent and endemic environments

Dengue, a mosquito-borne disease, is rapidly expanding its global distribution, emerging in previously naïve populations, while also causing more intense and more frequent outbreaks in endemic areas. There is an increasingly urgent need for innovative approaches for studying drivers of dengue emergence and spread, forecasting outbreaks, and determining how environmental suitability for dengue will change in the face of short- and long-term changes in climate patterns. In this talk, I will discuss recent work harnessing new approaches for modeling dengue emergence and spread in both the city of Córdoba, Argentina, where dengue first appeared in 2009, and the Dominican Republic, where dengue has long been endemic. Among the models I will discuss are machine learning and neural network models developed to study relationships between dengue cases climate with the goal of improving forecasts of dengue transmission. I will discuss our findings from these models in the context of developing early warning systems for predictions for future dengue outbreaks and working with local public health and vector control stakeholders to harness model results to improve dengue surveillance and control.

Speaker: Michael Robert (Virginia Tech)

5:20 PM Can We End the HIV Epidemic in the U.S.? A Multiscale Model Linking Clinical and Surveillance Data

The human immunodeficiency virus (HIV) epidemic remains a pressing public health challenge in the United States, despite major advances in treatment and prevention. Achieving the national Ending the HIV Epidemic (EHE) goals by 2030 requires a deeper understanding of the interplay between individual-level viral dynamics and population-level transmission. To address this, we develop and analyze a nested multiscale immuno-epidemiological HIV model that explicitly links within-host processes to epidemic outcomes. The model incorporates viral load–dependent transmission and treatment effects, allowing us to capture how immune responses and therapeutic interventions shape epidemic trajectories. We derive the basic reproduction number and establish threshold conditions for the existence and stability of the disease-free and endemic equilibria. We fit the multiscale model to within-host clinical data from 80 HIV-infected individuals and to national CDC surveillance data on incidence, diagnoses, and AIDS classifications. Our results show that reducing transmission from diagnosed individuals and increasing diagnosis rates could lead to epidemic declines consistent with EHE targets. This study highlights the importance of multiscale modeling in identifying intervention pathways and underscores the need for strengthened strategies to accelerate epidemic control.

Speaker: Necibe Tuncer (Florida Atlantic University)

5:40 PM From Bird Viremia to Bird Surveillance: Identifiability in a Multiscale Vector-Borne Model of Usutu Virus Infection

Usutu virus is an emerging mosquito-borne flavivirus, maintained through an enzootic cycle involving wild birds and mosquitoes, with occasional spillover to humans. Understanding how interactions across these biological scales shape transmission dynamics is essential for predicting outbreaks and improving surveillance strategies. In this study, we developed a multiscale vector-borne model of Usutu virus infection that links within-host viral kinetics in birds, the per-bite probability of mosquito infection, and population-level mosquito–bird transmission dynamics. Model parameters were validated using two laboratory datasets collected under an optimally designed experimental framework and one surveillance dataset from wild bird populations. Structural and practical identifiability analyses were conducted to evaluate parameter robustness under varying levels of measurement noise. We found that simultaneous multiscale fitting to integrated datasets improved parameter identifiability and robustness. These results highlight the importance of combining microscale and macroscale data to enhance the predictive reliability of vector-borne disease models and demonstrate the broader utility of multiscale modeling frameworks for understanding the transmission dynamics of emerging arboviruses.

Speaker: Quiyana Murphy (University of Michigan)

6:00 PM An immuno-epidemiological model with consideration for symptom score

The incorporation of human behavior into epidemiological models has been quite a popular topic as of late, and there are many effective ways to mathematically introduce behavior into such models. In this talk, we incorporate behavior into an epidemiological model for an upper respiratory infectious disease based upon the following assumption: “The more sick a person is the more likely they will reduce their contacts”. Our methodology in capturing this behavioral assumption will be through a nested-multiscale modeling approach. The within-host dynamics of a symptomatic individual is represented by a system of ODEs in which one of the compartments measures the symptom score of the infected individual. This model is then linked to an aged-structured between-host model (where age represents time since infection) by having a reduction in contact rate of symptomatic individuals be a function that depends on the individual's symptom score. In this talk, we present a flowchart of the model, some of the analytical results, and some simulations. In our simulations, we vary parameters of the linking function to investigate how the spread of the infection changes based on how reactive an individual is to their symptoms.

Speaker: Summer Atkins (University of Alabama, Huntsville)

5:00 PM → 6:20 PM Progresses in Mathematical and Computational Immunobiology and Infections

5:00 PM Modelling the HBV immune response: insights from virtual humanised mouse cohorts

Hepatitis B infections become chronic in approximately 5% of adult infections and 80-90% of childhood infections. Once HBV has become chronic, no cure exists yet. Current clinical research aims to reach a functional cure, defined as the sustained loss of HBV surface antigens (HBsAg). Lately, the GLP-26, a capsid assembly modulator leading to the release of uninfectious empty particles, has shown a decrease in HBV DNA, HBsAg, and covalently closed circular DNA (cccDNA) in humanised mice. Based on two cohorts (comprising 27 mice in total), we have HBV DNA and HBsAg dynamics for durations ranging from 18 to 24 weeks. We propose using non-linear mixed effect mechanistic models to reproduce the observed data and quantify the treatment effectiveness and the intensity of the immune-induced cytotoxic response. Using virtual mouse cohorts generated with the mechanistic model, we explore alternative treatment strategies and explain the mechanisms leading to clearance in our simulations. Our model can reproduce the observed HBV DNA and HBsAg dynamics, suggesting the underlying mechanisms are well captured. GLP-26 inhibits the HBV replication cycle and reduces the production of HBsAg. Our results suggest that an increase in treatment duration would also increase the proportion of mice controlling their infections. While not reaching a 100% response, a key emergent property is that the treated mice that controlled the infection present a strong adaptive immune response. A possible explanation is that GLP-26 could act as a facilitator by decreasing circulating HBsAg, allowing the immune system to neutralise infected hepatocytes. This work consist as a proof of concept on the methodology to use to build a mechanistic virtual mice cohort.

Speaker: Melanie Prague (Université de Bordeaux, Bordeaux Population health Inserm U1219, Inria, SISTM, Vaccine Research Institute)

5:20 PM Mechanistic mathematical modeling of PD-1/IL-10 co-blockade predicts post-ART SIV control

Dual IL-10/PD-1 blockade in ART-treated, SIVmac239-infected rhesus macaques (RMs) produced durable control of viral rebound after analytical treatment interruption (ATI). We analyzed the longitudinal data from 28 RMs randomized to vehicle (n=8), anti–IL-10 (n=10), or anti–IL-10+anti–PD-1 (n=10): plasma viremia, cell-associated vRNA/vDNA, intact proviral DNA (IPDA), and multiple immune markers were assayed. We compared different model classes by the corrected Bayesian Information Criteria. We used in-silico cohorts to simulate trial-level outcomes (controller frequency, viremia, CA-DNA/IPDA). Machine learning analyses of simulated trajectories identified a minimal predictive signature and linked pre-ATI immune markers to key parameters. Our models captured plasma viremia and CA-vRNA trajectories and predicted CA-DNA and IPDA dynamics across all RMs. Anti–IL-10 increased infected-cell loss rates by 29–80%, while anti–PD-1 enhanced effector cell exhaustion reversal by 2.5–4.7-fold. Parameter distributions showed that viremia control was mainly driven by treatment effects rather than baseline differences. A four-parameter classifier learned from the in-silico cohorts achieved 90% accuracy in predicting controller status. Mechanistic modeling indicates IL-10/PD-1 co-blockade synergistically enhances effector-cell function and reduces rebound risk, explaining high controller frequency after ATI.

Speaker: Ruy Ribeiro (Theoretical Biology and Biophysics, Los Alamos National Laboratory)

5:40 PM Uncovering the mechanisms of SHIV dynamics in rhesus macaques undergoing immune therapy

Understanding the mechanisms underlying post-therapy control of simian–human immunodeficiency virus (SHIV) is critical for the development of functional cure strategies. In this study, we develop viral kinetic models and validate them using viral load data from four cohorts of SHIV-infected nonhuman primates: untreated controls, animals receiving HuAd5 SIV Gag/Tat vaccination, animals treated with antibody therapy, and animals receiving combination therapy. Each model is fitted to longitudinal viral load measurements to quantify how different interventions alter viral dynamics. Using bifurcation analysis and numerical simulations, we identify parameter regimes in which therapy drives viral loads below the limit of detection. Furthermore, we characterize the conditions that enable sustained viral control after cessation or waning of immune-based interventions.

Speaker: Stanca Ciupe (Virginia Tech)

6:00 PM Multiscale modelling identifies a predictive relationship between circulating biomarkers and antiviral efficacy of new treatments for chronic hepatitis B virus infection

Chronic hepatitis B virus (HBV) infection is responsible for approximately one million deaths per year, worldwide. While existing therapies effectively block the production of new virus, viral rebound occurs rapidly if treatment is stopped. As a result, no cure for chronic HBV infection is currently available. Patients therefore typically receive treatment indefinitely with corresponding life-long treatment burden. Consequently, there is pressing need for new treatment options that block crucial steps in the viral life cycle. I'll show how multiscale mathematical modelling can illuminate biological mechanisms that would otherwise be inaccessible during typical clinical trials, identify circulating biomarkers of drug effectiveness, and help understand new treatments as possible functional cures for HBV. I’ll show how this multiscale modelling can identify a simple predictive relationship between circulating biomarkers and drug efficacy.

Speaker: Tyler Cassidy (University of Leeds)

5:00 PM → 6:20 PM Insights into cell-tissue interactions via mathematical modelling and computational simulations

5:00 PM Modeling antiangiogenic cancer therapy with an anti-VEGF drug: why that therapy alone is not enough

In this talk we illustrate two-interrelated models of, respectively, onset of tumor angiogenesis \cite{m1} and of the effect of an antiangiogenesis therapy \cite{m1}. The key component of the model is a chemotactic mechanism (CM) for new vessel cells sprouting induced by pro-angiogenic factors secreted by the tumor. Our approach is based on a statistical mechanics and it takes into the account both the bias induced by the angiogenic factor gradient and the stochastic changes of the velocity direction. Another distinguishing feature is the spatiotemporal dynamics of tumor-produced lactate.
We first simulated the current recommended drug schedules. The simulations suggests that: i) the therapy is only able to decelerate the tumor growth; ii) a small but not negligible amount of tumor cells situated close to the advancing tumor front is observed; ii) the effect of therapy on growth velocity is strongly delayed w.r.t. the therapy start
We also simulated the effect of alternative drug doses per bolus.
The simulations showed that: i) an increase in the drug dose is sublinearly effective; ii) even significant reductions of doses obtain satisfactory therapeutic results.

Speaker: Alberto D'Onofrio (Univerrsity of Trieste)

5:20 PM A Multiscale Model of Contact-Guided Cell Migration Incorporating Cell Morphodynamics

In this talk, I present a multiscale model for cell migration in fibrous extracellular matrix (ECM) structures. The microscopic dynamics account not only for the classical mechanism of contact guidance, but also for cell morphodynamics in response to the surrounding fibrous environment. Different migration modes and morphological adaptations are considered, together with their interplay. In particular, we recover key experimental observations concerning amoeboid versus mesenchymal morphologies and their dependence on the underlying fiber organization.
By deriving kinetic (mesoscopic) models, we gain insight into the aggregate statistical behavior of cells. This provides a consistent framework for the formulation of macroscopic models describing the evolution of cell number density, in which contact guidance dynamics are modulated by cell morphology and internal states.
We further discuss the role of morphology and polarization dynamics in determining cell persistence, and analyze how these factors influence migration patterns in spatially heterogeneous environments composed of unpolarized fibers, highlighting their impact on large-scale cell behavior and emergent transport properties, as observed, for example, in carcinoma cell invasion into aligned collagen matrices.

Speaker: Nadia Loy (Politecnico di Torino)

5:40 PM Multiphase cross-diffusion models for tissue structures

Motivated by a mechanical model of tumor encapsulation, we derive a generalized volume-filling cross-diffusion system for the components of tissue structures. The equations are formally derived from mass conservation laws and force balances in a multiphase approach. The model provides a general framework for studying tissue structures, and we show the analytical well-posedness of the system in general settings.
The existence of solutions is proven by using entropy methods, and the conditions for the existence of entropy structures are discussed from a modeling perspective.  Numerical simulations showcase the solution behavior beyond the entropy regime.

Speaker: Cordula Reisch (Roskilde University)

6:00 PM Modelling the dynamics of focal adhesions in cell migration using geometric surface PDEs

Cell migration is a complex biological process underlying phenomena such as wound healing, tissue morphogenesis, and cancer invasion. A key component of this process is the formation and turnover of focal adhesions, which provides a mechanical coupling between the cytoskeleton and the extracellular matrix. Actin filaments anchored at focal adhesions generate forces on the cell membrane, driving the formation of protrusions that regulates cell movement.

In this work, we develop a mathematical framework based on geometric surface partial differential equations (GS-PDEs) to investigate the role of focal adhesions in cell migration. GS-PDE models have shown strong potential in describing cell shape evolution and migratory behaviour. Building on this approach, we incorporate the maturation and dynamics of focal adhesions and examine their interplay with membrane forces generated by actin polymerisation at the leading edge. Our model enables us to study how focal adhesion growth and turnover influence protrusion formation and overall cell motility. This framework provides new insight into the mechanical processes governing cell migration.

Speaker: Sofie Verhees (University of British Columbia)

5:00 PM → 6:20 PM Dynamical Analysis of Biochemical Reaction Networks

5:00 PM Alternative equations for studying bifurcations in mass action networks

I'll outline some recent results on the geometry of the positive equilibrium sets of mass action networks. We obtain useful parameterisations of equilibria and bounds on the number of (positive, nondegenerate) equilibria a mass action network can admit on any stoichiometric class. The techniques also lead to new approaches to studying bifurcations in mass action networks. Sometimes, via relatively simple calculations, we are able to guarantee or rule out particular bifurcations in a network or class of networks. Moreover, in some cases, the theory gives us tools to obtain explicit parameterisations of bifurcation sets.

Speaker: Murad Banaji (Lancaster University)

5:20 PM Biochemical reaction networks: systematic design, limit cycles and properties of Hilbert-like numbers

I will discuss two types of mathematical models of biochemical reaction networks: (i) deterministic models described by reaction-rate equations, i.e., ordinary differential equations (ODEs) for the concentrations of the involved biochemical species~\cite{ref1,ref2}, and (ii) stochastic models described by the Gillespie stochastic simulation algorithm, which provides more detailed information about the simulated system than ODEs~\cite{ref3,ref4,ref5}. I will present methods for the systematic design of relatively simple reaction systems with prescribed dynamical behaviours, including systems with multiple oscillating solutions (limit cycles). We will focus on chemical reaction systems with two species, which under mass-action kinetics are described by planar autonomous ODEs whose right-hand sides are polynomials. The Hilbert number $H(n)$ is defined as the maximum number of limit cycles of a planar autonomous system of ODEs whose right-hand sides are polynomials of degree at most $n$. I will discuss analogues of the Hilbert number $H(n)$ for several classes of chemical reaction systems, including systems with reactions up to the $n$-th order and systems with up to $n$-molecular chemical reactions. Lower bounds on the modified Hilbert numbers will be presented~\cite{ref1}.

Speaker: Radek Erban (University of Oxford)

5:40 PM Exploring the effect of parametric model reduction on the structural identifiability of linear models

Structural identifiability answers a theoretical question about which parameter combinations of a mathematical model are uniquely recovered from ideal, noise-free input–output data. Identifiability has been long studied on linear compartment models, and is closely related to the algebraic structure of the input-output equation obtained from the model. In this work, we investigate how structural identifiability is affected under singular limits in which a single parameter of a model is sent to infinity. Such limits induce a collapse of the underlying linear compartment graph that resembles an edge contraction and results in a reduced model. Here, we show that the transfer function of the original model converges to the transfer function of the collapsed model. From this result, we can identify which parameter combinations survive the singular limit and characterize the resulting loss of identifiability. We illustrate these results on several families of linear compartment models, including mammillary, catenary, and cyclic networks, and discuss connections to model reduction and the geometry of parameter space under asymptotic limits.

Speaker: Sabina Haque (University of Michigan - Ann Arbor)

6:00 PM Simple chemical systems with chaos

Systems of $N$ first-order autonomous ordinary-differential equations with polynomials of at most degree $n$ on the right-hand side, called $N$-dimensional $n$-degree polynomial dynamical systems (DSs), can display a rich set of solutions whose complexity increases with $N$ and $n$. When $N \ge 3$ and $n \ge 2$, polynomial DSs can exhibit chaos — aperiodic long-term behavior that is sensitive to initial conditions.A number of simple three-dimensional quadratic DSs are reported in the literature that display chaos with various properties, containing as few as $5$ or $6$ monomials. However, none of these simple systems are chemical dynamical systems (CDSs) — a special subset of polynomial DSs that model the dynamics of mass-action chemical reaction networks. In this talk, I will present some properties of chaotic CDSs, and a systematic method for their design. Using both analytic and computational approach, I will present a number of simple three-dimensional CDSs with chaos, containing as few as $4$ or $5$ chemical reactions.

Speaker: Tomislav Plesa (University of Cambridge)

5:00 PM → 6:20 PM Universal Differential Equations in Mathematical Biology

5:00 PM Guiding the optimal use of hybrid mechanistic and data-driven models for individual prediction of platelet dynamics

Drug-induced damage to the blood-forming system, also called
hematotoxicity, is a frequent side effect of cytotoxic chemotherapy. Due
to high patient heterogeneity, it remains difficult to predict
individual treatment responses. Mechanistic models describing
thrombopoiesis provide some physiological interpretability but often
fail to capture individual irregular patient trajectories. Here, we
investigate hybrid mechanistic and data-driven approaches for
individualized prediction of platelet dynamics during chemotherapy. For
this purpose, we consider hybrid models that combine mechanistic
myelosuppression models with neural networks in a universal differential
equation framework. In addition, we present a purely data-driven
alternative, based on nonlinear auto-regressive exogenous models with
gated recurrent units. We systematically compare the approaches with
several mechanistic models across a range of real patient scenarios with
varying levels of toxicity risk, data availability and data sparsity.
Our results show that data-driven models substantially improve
predictive accuracy if sufficient longitudinal data are available,
particularly for high-risk patients with irregular platelet dynamics. In
contrast, mechanistic and hybrid approaches outperform purely
data-driven models in sparse-data regimes. These findings provide
practical guidance on modeling choices for different individual
scenarios to support clinical decision-making in chemotherapy management.

Speaker: Marie Steinacker (Leipzig University)

5:20 PM PEtab-SciML: The missing layer for accessible SciML modelling

Mechanistic ordinary differential equation (ODE) models are a powerful tool for studying biological systems. However, their predictive power is constrained by gaps, biases, and inconsistencies in the literature. They typically also require quantitative time-lapse data for training, which is time-consuming to collect. While training could benefit from integrating other modalities such as omics and patient metadata, doing so remains an open challenge. Conversely, machine-learning models lack interpretability and require large datasets. Hybrid scientific machine learning (SciML) models aim to address these shortcomings by combining mechanistic and data-driven modules.

Despite this promise, adoption of SciML modeling in biology remains limited by insufficient infrastructure. Dedicated software packages are needed because implementing end-to-end differentiable SciML workflows for state-of-the-art gradient-based training (parameter estimation) is technically challenging. In addition, model exchange is hindered by the absence of a standardized, reproducible format for specifying SciML training problems, analogous to the PEtab standard for ODE models. To address these gaps, we developed the PEtab-SciML extension to the PEtab format and implemented support in PEtab.jl and AMICI. We here present the PEtab-SciML format, show how it enables efficient training strategies such as curriculum learning and multiple shooting, and report benchmark results comparing training approaches.

Speaker: Sebastian Persson (Francis Crick Institute)

5:40 PM Symbolic regression enables coarse-grained model discovery for cancer-relevant signalling dynamics

Cells respond to their environment through protein networks often dysregulated in cancer, making predictive modelling crucial. Because experiments capture only limited observables, coarse-graining is needed to uncover low-dimensional descriptions. Yet classical approaches rely on idealised assumptions, leaving it unclear when partial experimental observations support reduced system dynamics. Here we show that symbolic regression (SR) provides a principled framework to probe the existence of coarse-grained dynamics and, when they exist, infers mechanistically interpretable models. In synthetic enzyme systems, SR recovers Michaelis–Menten kinetics for two- and three-step mechanisms, but not for a four-step dimerisation model. As data quality is degraded, SR simplifies toward effective kinetic laws while preserving correct theoretical limits. Applied to published time-resolved ERK phosphorylation data, SR identifies compact non-linear ERK rate laws in selected cancer-relevant overexpression contexts, yielding interpretable kinetic effects when models are predictive, and otherwise failing alongside our Neural ODE baseline, indicating missing observations. Together, these findings establish a data-driven approach to identifying coarse-grained models of signalling. More broadly, they establish symbolic regression as a framework for guiding experiment design by generating hypotheses where reduced laws emerge and motivating new measurements where they do not.

Speaker: Theodore de Pomereu (Francis Crick Institute)

6:00 PM Functional Identifiability for Universal Differential Equations

Parameter fitting workflows, in which model parameter values are recovered from data, are well established in mathematical biology. The introduction of universal differential equations (UDEs) extends this framework by enabling the estimation of not only scalar parameters but also unknown functions. Examples include learning a protein’s production rate as a function of its transcription factor concentration, or an infectious disease’s transmission rate as a function of the number of infected individuals. Within parameter fitting, the identifiability concept describes our ability to recover true parameter values from data. That is, identifiability analysis determines whether alternative parameter sets can produce equally good fits to observations. The absence of such alternatives suggests that the inferred parameters reflect the true system dynamics.

Here, we extend the concept of identifiability from scalar parameters to unknown functions. We demonstrate how to assess both structural functional identifiability (i.e. whether a function is fundamentally recoverable, even with perfect data) and practical functional identifiability (i.e. whether a function is recoverable given available data). In both cases, we show how to handle additional sources of nuisance that are not present for standard parametric identifiability. Finally, we show that UDE identifiability can be decomposed into parametric and functional components (with the parametric component assessable using classical parameter identifiability methods) together yielding a complete characterisation of UDE identifiability.

Speaker: Torkel Loman (University of Oxford)

5:00 PM → 6:20 PM State of the art methods in modeling for cell and developmental biology

5:00 PM Geometric control and mechanics in growing biological tissues

Biological tissues grow under strong mechanical constraints, leading to curvature control of their rate of growth. However, elucidating how this emergent control arises from dynamic cellular processes such as cell proliferation, cell migration, and cell mechanics remains a major challenge. In this talk, I will present recent advances from cell-based mathematical models and their continuum limit, that help disentangle how curvature dependences of tissue growth emerge from collective crowding effects and individual cellular processes. These models suggest two main mechanisms by which cells at a tissue interface may sense large-scale geometric features: a dynamic mechanism, related to changes in a cell’s tangential stress state, and a static mechanism, related to a cell’s normal stress state. The continuum limits of these models provide evolution equations of tissue stress that help shed new light on the continuum mechanics of biological tissue growth.

Speaker: Pascal Buenzli (Queensland University of Technology)

5:20 PM Uncovering noisy dynamics during cell growth using biologically-informed neural networks

Neural ordinary differential equation frameworks, such as Biologically-Informed Neural Networks (BINNs), have shown strong potential for learning mechanistic laws from sparse biological data. However, most existing approaches assume homoscedastic Gaussian noise, overlooking biologically meaningful variability arising from cell-to-cell heterogeneity and experimental measurement processes. In this work, we extend the BINN framework by introducing a learnable noise model that enables the identification of additive, multiplicative, or mixed noise structures directly from data. Using population growth systems motivated by cell proliferation assays, we demonstrate that the approach accurately recovers underlying noise types, captures state-dependent variability, and produces well-calibrated uncertainty estimates. These results highlight the importance of modelling structured noise for interpreting biological dynamics and provide a general framework for integrating data-driven uncertainty into neural ODE models, with applications to developmental and cellular systems.

Speaker: Rebecca Crossley (University of Oxford)

5:40 PM First-passage times and queueing behavior of stochastic search with dynamic redundancy and mortality

Stochastic search is ubiquitous in cell biology, from the propagation of action potentials via synaptic transmission to the spatial regulation of patterning during tissue development via cytoneme-based morphogenesis. In dynamic systems like these, the number of 'searchers' is rarely constant: new agents may be recruited while others can abandon the search. Despite the ubiquity of these dynamics, their combined influence on search times remains largely unexplored. In this talk we will introduce a general framework for stochastic search in which agents progressively join and leave the process, a mechanism we term 'dynamic redundancy and mortality'. Under minimal assumptions on the underlying search dynamics, our framework yields the exact distribution of the first-passage time to a target region and further reveals surprising connections to stochastic search with stochastic resetting, wherein a single searcher is randomly 'reset' to its initial state. We will then treat the target region as a queue, which we show has interarrival times governed by a nonhomogeneous Poisson process. Altogether this work provides a rigorous foundation for studying stochastic search processes with a fluctuating number of searchers. This work is in collaboration with Dr. Aanjaneya Kumar (Santa Fe Institute) and Jose Giral-Barajas (Imperial College London).

Speaker: Samantha Linn (Imperial College London)

6:00 PM Plant Cortical Microtubules: Curvature Sensing by Elastic Curves on Smooth Surfaces

The self-organization of microtubule (MT) polymers along the inner surface (cortex) of the plant cell membrane is an essential element in facilitating directional cell growth. The key questions are: what gives rise to the ordering and orientation of MT patterns? Mathematical and computational modelling has proven successful in providing insights: the process is distilled into a system of interacting curves on a 2D surface. There has been interest in the role of cell geometry in this process. Our recent work revisited a common assumption, that MT shapes are described by geodesics. More realistically, MTs are relatively rigid filaments and should seek to minimizing bending, resulting in elastic curves. Our model of elastic curves on cylindrical cells has shown that the curvature influence on MTs should orient MTs in directions opposite to what is biologically favourable. I present our work in generalizing this model to other geometries: we solve for elastic curves on various surfaces to show bifurcations and diverse curves resulting from non-local curvature sensing. This opens the field to realistic models on complex geometries. Our model indicates that there must be additional processes involved to overcome geometric influences. The identity of these processes is the subject of active debates, with many hypotheses being proposed. Lastly, I present the current state of the field and the ongoing effort to overcome the associated modelling challenges.

Speaker: Tim Tian (University of British Columbia)

5:00 PM → 6:20 PM Newtonian and non-Newtonian Biofluidmechanics: Integrating Theory, Experiments, Modeling, and Simulations

5:00 PM Seeing new depths: Three-dimensional flow of a free-swimming alga

A swimming microorganism stirs the surrounding fluid, creating a flow field that governs not only its locomotion and nutrient uptake, but also its interactions with other microorganisms and the environment. Despite its fundamental importance, capturing this flow field and unraveling its biological implications remains a challenge. Here, we report the first direct, time-resolved measurements of the 3D flow field generated by a single, free-swimming microalga, Chlamydomonas reinhardtii, a model organism for microbial locomotion and flagellar dynamics. Supported by hydrodynamic modeling and simulations, our measurements resolve how established 2D flow features such as in-plane vortices and the stagnation point emerge from and shape the 3D structure of the algal flow. More importantly, we reveal unexpected low-Reynolds-number flow phenomena including micron-sized vortex rings and periodically recurring translating vortices and uncover topological changes in the underlying fluid structure associated with the puller-to-pusher transition of an alga. Biologically, access to the 3D flow field enables rigorous quantification of the alga’s energy expenditure, as well as its swimming and feeding efficiency, improving the precision of these key physiological metrics. Our study demonstrates rich vortex dynamics in inertialess flows and shows their influence on microbial motility. The work also introduces a new method for mapping the fluid environment sculpted by beating flagella.

Speaker: Sookkyung Lim (University of Cincinnati, USA)

5:20 PM Swimming-limited aggregation of Escherichia coli bacteria in liquid crystals

Liquid crystals serve as model systems for structured environments and represent a broader class of anisotropic, non-Newtonian fluids encountered by bacteria, such as host mucus [1] and extracellular polymeric substances involved in biofilm formation [2]. In this study, we investigated the collective swimming of fluorescently labelled Escherichia coli in nematic liquid crystals and observed the emergence of long-lived chains of bacteria swimming along the nematic director, similar to those observed for Proteus mirabilis by Mushenheim et al. [3]. Remarkably, we found that longer chains swim faster, contrary to predictions from fundamental force-balance models and observations of merging bacterial pairs. To explain this counterintuitive behaviour and identify the physical mechanism driving bacterial aggregation in liquid crystals, we combined experiments with agent-based simulations and minimal theoretical modeling. By incorporating the intrinsic speed distribution of individual bacteria, our simulations revealed a positive correlation between chain length and swimming speed, consistent with experimental observations. A minimal aggregation model, based on encounter probabilities between a bacterium and its two nearest neighbours, further supports our interpretation that longer chains swim faster because they are more likely to contain faster-swimming individuals, which meet and merge with their neighbours in less time.

[1] N. Figueroa-Morales, L. Dominguez-Rubio, T. L. Ott, and I. S. Aranson. Mechanical shear controls bacterial penetration in mucus. Sci. Rep. 9: 9713, 2019.

[2] A. Repula, E. Abraham, V. Cherpak, and I. I. Smalyukh. Biotropic liquid crystal phase transformations in cellulose-producing bacterial communities. Proc. Natl. Acad. Sci. U.S.A. 119: e2200930119, 2022.

[3] P. C. Mushenheim, R. R. Trivedi, H. H. Tuson, D. B. Weibel, and N. L. Abbott. Dynamic self-assembly of motile bacteria in liquid crystals. Soft Matter 10:88–95, 2014.

Speaker: Maria Tǎtulea-Codrean (University of Amsterdam, Netherlands)

5:40 PM Parallel computing methods for large-scale simulations of flagellar dynamics

The Method of Regularized Stokeslets (MRS) provides a robust, mesh-free framework for resolving the fluid-structure interactions of these filaments [1]. It has two critical bottlenecks: the spatial complexity of pairwise hydrodynamic calculations and the temporal stiffness arising from the material properties of the rod. To address these challenges, we first discuss a parallel-in-time approach based on the Parareal algorithm [2], in which we construct a novel coarse solver using a data-driven method based on Dynamic Mode Decomposition in place of a classic time marching scheme. Then we will present a heterogeneous CPU–GPU computing framework that synergistically addresses the challenges in space and time complexity to enable scalable, high-fidelity simulations of flagellar dynamics.

[1] R. Cortez. The method of regularized Stokeslets. SIAM Journal on Scientific Computing, 2001, 23(4): 1204-1225.
[2] J.-L. Lions, Y. Maday, G. Turinici. A parareal in time discretization of PDE’s. Comptes Rendus del’Academie des Sciences Paris Ser. I Math., 2001, 332(7): 661-668.

Speaker: Weifan Liu (Beijing Forestry University, China)

5:00 PM → 6:20 PM Novel Approaches in Mathematical Biology

5:00 PM Scientific Machine Learning Methods for Extracting ODE Models of EBV-Driven B-Cell Fate Trajectories from scRNA-seq Data

Epstein-Barr virus (EBV) infection drives a coordinated cascade of B-cell state transitions underlying both primary infection and EBV-associated malignancies \cite{sorelle_time-resolved_2022}. scRNA-seq provides high-dimensional snapshots of these transitions across thousands of individual cells, yet current clustering-based approaches capture only a fraction of the quantitative information available. We present an equation learning pipeline that extracts the underlying dynamical structure directly from EBV-driven B-cell scRNA-seq data. First, the raw data is processed via UMAP-based dimensionality reduction and clustered to identify discrete cell states, then mapped onto trajectories using pseudotime. These trajectories serve as input to a hybrid scientific machine learning method in which a structured candidate library encodes known biological relationships alongside neural network terms that capture unknown dynamics. SINDy is applied to recover a parsimonious ODE system whose structure reflects both the data and the underlying biology of EBV-induced B-cell differentiation \cite{wu_data-driven_2025}.The learned system can identify known and unknown cell state transitions and generate mechanistic hypotheses. This method bridges single-cell transcriptomics and scientific machine learning, offering a principled framework for extracting mechanistic structure from high-dimensional omics data and advancing our understanding of EBV-driven B-cell fate decisions.

Speaker: Melanie Sadecki (North Carolina State University)

5:20 PM Multivariate drivers of the heterogeneous within-host immune response during influenza

Influenza infections exhibit substantial heterogeneity in viral shedding and
immune responses, along with varying widely in severity and outcome. While viral load
dynamics and certain immune responses are often assumed to correlate with disease
severity, experimental observations suggest that these relationships are not always
straightforward and can change across the duration of infection. To investigate the
multivariate sources of this variability and how it relates to severity, we turn to
mechanistic modeling. We apply a system of differential equations describing influenza
viral replication and CD8+ T cell dynamics to human challenge data. Model parameters
are estimated across individuals to characterize meaningful variability that governs
infection kinetics. Through model-based analysis and clustering of infection trajectories,
we identify multivariate drivers that contribute to heterogeneous infection courses. We
further extend the model to incorporate symptom development and a wide range of data
sources, including human clinical data as well as additional immune cell and cytokine
data. These results highlight the value of mechanistic modeling for disentangling the
biological processes underlying variable immune responses and provide a framework
for improving the predictability of influenza infection dynamics.

Speaker: Nicole Bruce (University of Tennessee Health Science Center)

5:40 PM Predicting the impact of gene therapy in preventing HIV transmission

To date, the only instances of HIV ‘cure’ were the result of transplantation with stem cells containing mutated genes for the CCR5 coreceptor, a cell-surface protein required by most HIV strains to enter and infect a cell. Thus, researchers are pursuing different gene therapy methods to reduce CCR5 expression without the need for a stem cell transplant, but it is unclear what fraction of target cells must be gene edited to achieve HIV cure or prevent transmission. To answer this question, 73 mice underwent human stem cell transplantation with varying mixtures of CCR5 intact and knock-out stem cells. Animals were subsequently inoculated weekly with HIV, and the time-to-infection was monitored.
The observed risk of infection per inoculation decreased from 28% to 0% in animals receiving only intact CCR5 vs. only CCR5 knock-out stem cells. To mechanistically characterize the effect of CCR5 knock-out on infection risk, we developed a probabilistic model of the expected number of infected cells as a function of the fraction of CCR5 knock-out cells. We then predicted the impact of editing rate on human HIV infection by shifting the parameters of this model to values relevant to the human context. We estimated that to sufficiently suppress replication to prevent transmission would require an editing rate of 88%. This rate is beyond the capabilities of current technologies, although rates of up to 80% have been reported in gene therapy clinical trials for other diseases.

Speaker: Steffen Docken (Infection Analytics Program, Kirby Institute, University of New South Wales Sydney)

6:00 PM 3D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation

Once diagnosed, cancer requires a fast, inexpensive and reliable assessment of the current state and potential progression of the disease. A new method for estimating tumor cell diffusivity $D$ and proliferation rate $\gamma$ from single-point-in-time routine biopsies aims to deliver just that, and the ratio of its estimates $D/\gamma$ is a promising candidate for a new biomarker for risk-stratification in radiotherapy. Here, we extend the findings of the researchers at MD Anderson Cancer Center \cite{Pasetto.2024}, who developed the method, by providing a simulation-based validation. The method is applied to \textit{in silico} biopsies which are generated by solving the three-dimensional reaction-diffusion (RD) equation for different growth terms (exponential and logistic) with a Dirac-Delta initial condition, and transforming the continuous results into spatial point patterns via a form of reverse coarse-graining.

First results of this validation process have been presented at SMB 2025, which were performed using a less realistic two-dimensional RD equation and an inferior reverse coarse-graining algorithm.

Speaker: Veronika Hoffman (School of Computation, Information and Technology, Technical University of Munich)

5:00 PM → 6:20 PM Personalized forecasting in oncology informed by multiscale multimodal data

5:00 PM Multimodality Stacking with Blockwise missing values and application to the PIONeeR biomarkers study for prediction of resistance to immunotherapy

Integrating multimodal datasets in clinical oncology is frequently hindered by high dimensionality and blockwise missingness, where entire data sources are unavailable for specific patient subsets. Standard survival models often struggle with these gaps, leading to biased results or patient exclusion.
We introduce Multimodality Stacking with Blockwise missing values (MSB), a late-fusion framework for survival analysis that independently models modalityspecific features before aggregating predictions via a cross-validated stacking meta-learner. MSB was validated on the PIONeeR study (n=443 patients, 378 biomarkers across eight heterogeneous sources) to predict progression-free survival in advanced non-small cell lung cancer patients receiving immunotherapy. MSB yielded higher predictive performance (C-index) than baseline algorithms.
Improvements varied by baseline strength: linear models showed a 15.9% increase (p < 0.001 for the Wilcoxon signed-rank test, consistent across 15 cross-validation folds), random survival forests gained 5.4% (p = 0.002), and gradient boosting methods improved by 2.1% (p = 0.030). Beyond discrimination, MSB reduced the generalization gap (train-test difference in 5 folds cross-validation repeated 3 times: 0.055 vs 0.380 for linear models). Permutation importance analysis identified routine laboratory markers, clinical features, and PD-L1 expression as primary predictive drivers. Missing block indicators showed negligible importance, suggesting the model learned from biomarker values rather than data availability patterns.
MSB provides a statistically validated framework for multimodal survival prediction with blockwise missingness. By enabling systematic biomarker evaluation without requiring complete data, MSB offers a practical tool for predictive modeling in biomedical research, pending external validation.

Speaker: Mohamed Boussena (INRIA, France)

5:20 PM Probabilistic Modeling of AML Using Multi Omics and Multimodal Longitudinal Data

Acute myeloid leukemia (AML) evolves through stochastic and interconnected changes in cell differentiation, clonal composition, and immune response, revealed through longitudinal multi-genomic profiling. We present a stochastic modeling framework in which a Langevin equation describes noise driven fluctuations in genomic states in a mouse model of AML. These dynamics are embedded within a state space model that integrates time resolved multimodal data, including bulk and single cell RNA and microRNA expression, epigenomic features, and immune profiling features, into latent variables that summarize disease progression and therapeutic response. The Fokker–Planck equation corresponding to the Langevin equation of motion in the state-space gives the evolution of probability densities over these high dimensional genomic states, enabling predictive modeling of disease trajectories and treatment outcomes.

By coupling multi omic longitudinal sequencing with a stochastic dynamical systems model, we link complex genomic dynamics to individualized probabilistic predictions in AML. In this talk, I will show how mouse models, publicly available multimodal datasets, and mechanistic mathematical modeling converge to generate new insights into AML evolution and response to therapy, and outline our efforts to translate these methods into clinical trials at City of Hope.

Speaker: Russell Rockne (Professor & Chair, Department of Computational and Quantitative Medicine Beckman Research Institute, City of Hope.)

5:40 PM Feeding Less, Modeling More: Can Mathematics Optimize Intermittent Fasting in Cancer?

A growing body of experimental and clinical evidence indicates that intermittent fasting can exert beneficial effects in cancer prevention and therapy. Preclinical studies consistently show that fasting cycles can slow tumor growth, enhance tumor cell sensitivity to chemotherapy and radiotherapy, and protect normal tissues. Early-phase clinical trials further suggest that intermittent fasting is feasible, safe, and may reduce treatment-related toxicity while improving therapeutic response. These benefits should not be conflated with chronic caloric restriction, which does not confer therapeutic advantage. Thus, the potential value of intermittent fasting in oncology lies in its structured, time-limited metabolic modulation rather than generalized nutritional deprivation \cite{clifton_intermittent_2021}.

Current evidence remains limited by small sample sizes, heterogeneous protocols, and an incomplete mechanistic understanding of metabolic–tumor interactions, limitations that may be addressed through mathematical modeling.

Metabolic scaling laws provide a mechanistic link between tumor growth dynamics and energetic balance \cite{perez-garcia_universal_2020}. In this talk, I describe a minimal conceptual model revealing an Allee effect driven by tumor energetic availability. I then present more detailed nutritional models incorporating glucose, insulin, and glucagon dynamics. Theoretical results are complemented by in silico digital twin simulations calibrated with tumor growth and patient metabolic data, leading to optimized fasting schemes for different primary cancers. Our findings illustrate the potential of mathematics to guide nutritional strategies in oncology.

Speaker: Víctor M. Pérez-García (Mathematical Oncology Laboratory (MOLAB), University of Castilla-La Mancha, Spain)

6:00 PM Data-efficient early prediction of treatment response using mechanistic tumor growth models

Personalized forecasting in oncology requires models that are both mechanistically interpretable and effective with limited data. I will present recent unpublished results on predicting treatment response in mouse tumor models using a library of mechanistic growth and treatment models, including 1D formulations (exponential, logistic, weak Allee, strong Allee, and piecewise exponential growth) and 2D models with sensitive/resistant subpopulations under related growth structures, plus a frequency-dependent evolutionary game model. These models are applied to two longitudinal datasets: a chemotherapy dataset from NSG mice and a radiotherapy dataset from WT and SIRPα-deficient mice. Models are evaluated by both goodness of fit and ability to predict outcome (relapse versus durable control). Prediction performance is high across both datasets. For chemotherapy, strong Allee model parameters are highly informative: using only one measurement before and one after treatment, prediction achieves balanced accuracy 0.946 and AUC 1.0. For radiotherapy, the same sparse design yields balanced accuracy 0.874 and AUC 0.964. These results suggest that low-dimensional mechanistic models, combined with machine learning, can provide early, data-efficient forecasts of treatment response and identify interpretable biomarkers for adaptive oncology.

Speaker: Yi Jiang (Georgia State University, US)

5:00 PM → 6:20 PM Mathematical Foundations of Biochemical Computing

5:00 PM Limits of Equilibrium Computation in DNA Seesaw and Dimerization Networks

DNA strand displacement systems have enabled the construction of molecular circuits capable of performing complex computations, typically relying on irreversible reactions and non-equilibrium dynamics for signal amplification and restoration. An alternative paradigm is equilibrium computation, where outputs are determined by the steady-state concentrations of molecular species.

In this talk, we investigate the computational limits of equilibrium seesaw networks. We prove that, under constraints on species concentrations, the influence of an input signal decays exponentially with its distance from the input. This result implies that signal amplification is impossible and that large-scale equilibrium circuits inherently suffer from vanishing signal propagation. Extending our analysis, we connect seesaw networks to broader classes of equilibrium systems, including ligand–receptor and dimerization networks, and discuss how similar limitations arise in these models.

Overall, our results identify a fundamental barrier to scalable equilibrium computation in molecular systems, highlighting the necessity of non-equilibrium mechanisms or carefully engineered regimes for robust information processing at scale.

Speaker: Ho-Lin Chen (National Taiwan University)

5:20 PM Designing optimal computational networks: a case study from maximum likelihood estimation

A fundamental question in the field of molecular computation is what computational tasks biochemical systems are capable of carrying out. In this talk, we will see that chemical reaction networks can do maximum likelihood estimation of log-affine models in the following sense: Given a basis for the kernel of the design matrix of a given model, we construct a detailed-balanced network such that the MLE can be read off from the unique equilibrium when the initial concentrations are set to the observed distribution. Interestingly, the choice of basis for the kernel in the construction has a large influence on the dynamical properties and chemical complexity of the network. The desire to make this choice "optimally" (in a number of different senses of the word) leads to several interesting questions at the crossroads between dynamics, chemistry, statistics, and algebra. This is based on the paper \cite{HARY25}.

Speaker: Oskar Henriksson (Max Planck Institute)

5:40 PM Recurrent neural chemical reaction networks: a versatile way of generating complex dynamics in chemical systems

A common goal in the theory of Chemical Reaction Networks (CRNs) is to design systems that reproduce or approximate a desired dynamics. This theory supports ongoing efforts in synthetic biology and molecular nanotechnology to emulate the functional molecular networks seen in nature. Here, we propose a molecular version of a recurrent artificial neural network, the RNCRN, which we prove is able to approximate arbitrary dynamics, and demonstrate that functionality for systems that exhibit multi-stability, oscillations and chaos. The neural net nature of the RNCRN means that it is particularly well suited to extrapolating a CRN, defined for all concentrations of the executive species, from a relatively small region of defined target behaviour. We show that this property allows the RNCRN to approximate exotic limit cycles that are not easily expressed as an attractor of a simple dynamical system. Similarly, the RNCRN can interpolate between two defined regions of qualitatively different target behaviour, automatically generating an appropriate bifurcation.

Speaker: Tom Ouldridge (Imperial College)

6:00 PM Computing with reaction networks at input-independent speed: exponential and logarithmic functions

The concept of input-independent computational time for chemistry-based analog computers was introduced in \cite{anderson2025arithmetic}, where it was shown that arithmetic operations can be computed in a fixed time independent of the input values. Here, by inputs we mean the numerical values encoded by the initial concentrations of designated input species, with the underlying reaction network and rate constants held fixed. Combining these operations via power series approximations to compute transcendental functions is possible in principle, but requires a number of chemical species that grows with respect to the number of terms retained.

In this talk we focus on two widely used transcendental functions, the exponential and logarithmic functions. We construct reaction network modules that compute these functions directly, without relying on truncated power series. We show that the resulting modules are mass-action systems, and prove that they achieve arbitrary accuracy given sufficient time while operating at input-independent speed. These two functions serve as foundational cases and are intended as building templates for computing more general transcendental functions via chemical reaction networks.

Speaker: Tung Nguyen (University of California Los Angeles)

6:20 PM → 7:00 PM ERC & NSF Math Bio Funding Session

Speakers: Maria Siomos (European Research Council (ERC)), Zhilan Feng (National Science Foundation (NSF))

Tue, July 14

8:30 AM → 9:20 AM Estimating tipping points in climate

In recent years there has been an increasing awareness of the risks of collapse or tipping points in a wide variety of complex systems, ranging from human medical conditions, pandemics, ecosystems to climate, finance and society. Even in systems where governing equations are known, such as the atmospheric flow, predictability is limited by the chaotic nature of the system and by the limited resolution in observations and computer simulations. These phenomena are naturally modelled by strongly nonlinear stochastic processes, which permit a statistical description. In this talk I will present methods to model and analyze data from such complex systems, with application to an important tipping element in the climate, the Atlantic Meridional Overturning Circulation.

Speaker: Susanne Ditlevsen (University of Copenhagen)

9:20 AM → 10:10 AM An intro to shape spaces - from differential geometry to the drosophila testis

Shape is a central principle in biology, linking form to function across scales. It determines ecological fit at organism level, assists physiological function at the organ level, and drives macroscopic form through growth and patterning at the (sub-)cellular level. Quantifying and comparing shape or morphology may therefore provide a powerful tool to understand phylo- and ontogenesis as well as biological organization in general. I will give an introduction into the mathematics of shape spaces and the theoretical and computational tools that allow to perform statistical and regression analyses of shapes, touching upon recent mathematical developments as well as applications.

Speaker: Prof. Benedikt Wirth (University of Münster)

10:10 AM → 10:40 AM Coffee Break

10:40 AM → 12:00 PM GLIMPRINT Minisymposium: From Mechanistic Multiscale Immune Models to Digital Twins

10:40 AM Introductions + Junior member mini-presentation

Introductions
Lorenzo Veschini
We will outline GLIMPRINT activities and introduce the speakers to the audience.

Junior member mini-presentation
James Doran, Bath University, UK

Equation Learning for multiscale models of infectious diseases

Tuberculosis (TB) is an airborne disease caused by the pathogen Mycobacterium tuberculosis. In 2023, according to the World Health Organization, it “probably” replaced COVID-19 as the leading cause of death from an infectious agent globally; in the nineteenth century, one in seven of all humans deaths were as a result of tuberculosis. More than 10 million people are diagnosed with TB every year. The majority of cases in adults occur in males (62.5% of all global adult cases in 2023, compared to 37.5% in females). The main reasons for males suffering from a higher burden of global TB cases, compared to females, is likely to be a combination of within-host factors, such as differences in immune response, and population-scale factors, such as likelihood of completing treatment. To investigate the impact different scales have in determining this higher TB burden in males, we have developed a gender/sex-stratified multiscale framework. We have learnt ordinary differential equations (ODEs) to capture the average output of an agent-based within-host model, and used the resulting equations to describe the within-host scales of the multiscale framework. We evolve the population demographics at the between-host scale using ODEs and link the scales with stochastic coupling functions. We have considered counterfactual scenarios to elucidate the impact of sex and gender on the infectious disease dynamics of TB. This paper is intended to provide a proof-of-concept for the development and implementation of the presented multiscale framework

Speaker: Lorenzo Veschini (Indiana Uniersity)

11:00 AM Multiscale modeling of the innate immune response to respiratory pathogens

This talk will describe agent-based modeling of the early immune response to fungal and viral respiratory pathogens and some applications.

Speaker: Reinhard Laubenbacher (University of Florida)

11:20 AM A Large-Scale Logic-Based Model of the Human Immune System as a Foundation for Mechanistically Interpretable Clinical Prediction and Immune Digital Twins

Predicting patient-specific immune outcomes requires frameworks that are mechanistically grounded, scalable across disease contexts, and capable of producing interpretable clinical predictions. We present an integrated pipeline built around a large-scale logic-based mechanistic model of the human immune system.
The model encodes Boolean regulatory logic derived from 449 human experimental publications, representing 88 immune cell types across innate and adaptive compartments, 37 secretory factors, and 11 disease environments connected through 1,450 regulatory interactions. Validation against independent human data confirmed the model's capacity to reproduce pathogen-specific cytokine signatures and cell dynamics across nine pathogens, with agreement rates of 75–90%.
We leverage this validated model to generate synthetic datasets of in silico patient profiles by systematically varying immune state activity across the full spectrum from healthy to severely dysregulated. Machine learning models trained on these data identify patient-specific biomarkers predictive of pathogen clearance, hospitalization, and ICU admission across IAV, SARS-CoV-2, CMV, and Plasmodium falciparum. Critically, because each biomarker is a node in the underlying mechanistic model, its predictive weight can be traced directly to causal regulatory logic, addressing the interpretability gap that limits purely data-driven tools.
This pipeline provides a generalizable approach to mechanistically grounded biomarker discovery and a methodological foundation for personalized immune digital twins.

Speaker: Tomas Helikar (University of Nebraska, Lincoln)

11:40 AM Using an Agentic AI Critical Illness Digital Twin to rescue from immune exhaustion in sepsis

Critical illness (CI) represents a highly significant healthcare issue, not only because of the resources required for its acute management in ICUs, but also in terms of the lingering health effects as a chronic disease on survivors. A central hallmark of CI is immune dysfunction, with both early hyperactivation leading to organ dysfunction and subsequent immunocompetency leading to increased susceptibility to infection and shortened life. The effective control of CI requires personalized precision medicine, which requires the capabilities provided by digital twins compliant with industrial standards and consistent with the definition put forth by the National Academies of Science, Engineering and Medicine (NASEM) in 2024. The Critical Illness Digital Twin (CIDT) is a proposed cyberphysical system compliant with the NASEM report that melds mechanistic models with machine learning and artificial intelligence and intrinsically incorporates control via an ongoing bidirectional sense-actuate connection to a real-world individual patient. We propose embedding the CIDT in an agentic-AI system that can evolve patient state space characterization, forecast capability and control policy optimization with the goal of rescuing ICU patients with immune exhaustion. Key points are the necessary integration of the virtual assets with sensor/assay technology and control modalities flexible enough to accomplish the stated goal.

Speaker: Gary An (University of Vermont)

10:40 AM → 12:00 PM Mechanisms of Brain Development, Structure, and Metabolic Impacts

10:40 AM Sub-diffusion Compartmental Model for Diffusion MRI to Probe Brain Microstructural Information: Insights from a Simulation Study of White Matter

Axon radius and extra-axonal volume fraction are fundamental descriptors of white matter microstructure, critically shaping conduction velocity and the efficiency of neural communication. Although existing diffusion MRI models have attempted to estimate these parameters, their limited sensitivity and constrained assumptions often result in unstable and biased estimates. Such bias typically arises from inappropriate compartmental modelling that can not capture the underlying biophysical processes accurately, and from confounding effects among the fitted model parameters. To overcome these limitations, we propose a novel sub-diffusion compartmental model that achieves accurate estimation of axon radius and extra-axonal volume fraction in axon substrates with both uniform and gamma-distributed radii. Using numerical simulations of white matter microstructure with varying axon radii, diffusion times, and noise levels, we demonstrate that the proposed model yields improved stability of extracellular volume fraction and axon radius estimates compared to a mono-exponential extracellular diffusion model. These results suggest that incorporating sub-diffusive extracellular dynamics can mitigate diffusion time-dependent bias in compartmental DW-MRI modelling.

Speaker: S M Erfanul Kabir Chowdhury (School of Mathematical Sciences, Queensland University of Technology, Australia)

11:00 AM Energy Constraints and Neural Strategy Transitions in Alzheimer’s: A Game-Theoretic Model

While many mechanisms have been proposed to drive Alzheimer’s disease, particularly the accumulation of amyloid plaques and hyperphosphorylation of tau proteins, emerging evidence suggests that they may be the byproducts of earlier damage rather than initiating events. Instead, metabolic dysfunction and the inability of neural cells to support their energetic demands may be a more plausible trigger for subsequent pathological cascade (the neuron energy crisis hypothesis). Here we highlight how type 2 diabetes (T2D) can contribute to neurodegeneration by impairing brain energy metabolism. We present a game-theoretic framework, where neurons face trade-offs between energy efficiency and information fidelity. We show that under metabolic stress, neural networks can evolve toward smaller group sizes that prioritize energy efficiency over information quality, which may underlie the observed collapse of cognitive capacity during neurodegeneration. We conclude with a discussion of interventions, ranging from antidiabetic drugs to cognitive engagement and sensory stimulation, aimed at reducing metabolic stress and preserving cognitive function.

Speaker: Dr Irina Kareva (Department of Biomedical Engineering, Northeastern University, U.S.A.)

11:20 AM Biomechanical Forces and Tensions that Contribute to Cortical Folding in the Brain

The outermost layer of the brain’s surface, the cerebral cortex, consists of gyri (hills) and sulci (valleys). In humans, cortical folding begins around the 16th week of gestation, and the most obvious cortical folding changes occur during the 26th week of gestation. The mechanism by which the folding pattern develops remains unknown; however, several hypotheses suggest that cortical folding occurs through biochemical or biomechanical mechanisms. The axonal tension hypothesis in particular claims that folding is caused by mechanical tension in axons. Based on a previous model that uses the location and magnitude of stress-strains to simulate cortical folding, our current model simulates biomechanical forces that contribute to cortical deformations over a series of time steps. We represent our model cortex with a semicircular mesh discretized into linear, quadrilateral elements, and a finite element method process is used to numerically compute the updated nodal displacements at each time step. We test our model with ferret MR imaging data, and our model is used to anticipate the biomechanical forces observed. In modeling the deformations, we gain insight into how sulci develop through the evolution of time.

Speaker: Julianna Capece (Department of Mathematics, Florida State University)

11:40 AM A Biomchemical Model of Cortical Folding via Turing Patterns

Turing pattern formation has been used to model many biological patterns including animal coat, fish, and butterfly patterns. We apply a Turing reaction-diffusion system to a prolate spheroid domain representing the developing cortex, to study cortical folding pattern formation. The brain's cerebral cortex has complex folds with hills (gyri) and valleys (sulci). While the mechanism for the development of cortical folds is not understood, one proposed theory suggests that patterning of a non-uniform distribution of intermediate progenitor (IP) cells during neurodevelopment correlates with cortical folds. We model IP cell patterning via the activator morphogen of the Turing system. Patterns generated by our Turing system represent prepatterns of self-amplification of IP cells. Our results demonstrate that cortical folding patterns are influenced by the shape of the domain, growth rate, and genetic control. Using these parameters, our Turing models of cortical folding can be used to explain diseases of cortical folding pattern formation, such as lissencephaly and polymicrogyria.

Speaker: Dr Monica Hurdal (Department of Mathematics, Florida State University)

10:40 AM → 12:00 PM Multiscale modelling and simulation of stochastic gene regulation

10:40 AM The role of DNA methylation and DNA sequence in epigenetic plasticity

DNA methylation is a ubiquitous epigenetic mark that plays important yet disparate roles in gene regulation. On the one hand, genome-wide methylation patterns help establish and maintain distinct cell types, and these patterns are stably maintained. On the other hand, patterns in some loci are dynamic, facilitating nimble cellular responses to environmental stimuli. This talk will present our efforts combining discrete stochastic mathematical modeling with data-driven statistical inference approaches to shed light on enzymatic mechanisms that enable the mammalian DNA methylation system to accomplish both stability and responsiveness \cite{BONSU2026}. Integration with sequencing data is enabled by a novel mean-field approximation that can efficiently handle collective behavior among multiple genomic sites. We show how local genetic and non-genetic factors control a sensitive DNA methylation switch. As DNA methylation works in concert with other epigenetic mechanisms, our results could contribute to improved models of gene regulatory networks and epigenetic landscapes.

Speaker: Elizabeth Read (University of California, Irvine)

11:00 AM Joint trajectory and gene regulatory network inference using a mechanistic optimal transport-based framework

A key challenge in inferring gene regulatory networks (GRNs) governing cellular processes, such as differentiation and reprogramming, from experimental data lies in the impossibility of directly observing protein trajectories at the single-cell level, which prevents establishing causal relationships between regulator activity and target responses.
In this talk, we present CardamomOT, a new algorithm that uses temporal snapshots of scRNA-seq data to calibrate a mechanistic model of gene expression \cite{mauge2026}. The method reconstructs both the GRN and the unobserved protein trajectories using an innovative mechanistic optimal transport framework. We present some results on both in silico and experimental datasets, demonstrating the ability to accurately recovers velocity fields driving cellular trajectories and unobserved protein levels, alongside reliable GRN structures. We finally show that the calibrated mechanistic model can be used as a generative model to predict cellular responses to unseen perturbations.

Speaker: Elias Ventre (INRIA Centre d'Université Côte d'Azur)

11:20 AM A domain decomposition approach to the construction of Markov state models for stochastic gene regulatory networks

Within a cell, gene expression levels are governed by molecular regulators interacting with each other in gene regulatory networks (GRNs). In this talk, we present an efficient computational framework for analyzing stochastic GRNs, in which cellular behavior is characterized by multiple metastable phenotypes and rare transitions between them. The dynamics of stochastic GRNs is described by the chemical master equation (CME), whose high dimensionality makes direct analysis computationally prohibitive. To address this, a domain decomposition approach (DDA) has been introduced \cite{yousefian2025efficient}, in which the state space is discretized using Voronoi tessellations and reduced to a Markov state model (MSM) \cite{chu2017markov}. In this setting, adaptive stochastic sampling combined with spectral clustering in terms of PCCA+ \cite{frank2024spectral} enables the identification of metastable states and their transition dynamics without relying on high-performance computing. Evaluation on two biological models, one for the genetic toggle switch and one for macrophage polarization, shows that the method accurately detects metastable phenotypes, estimates transition probabilities, and provides uncertainty quantification. Our findings highlight that accuracy is mainly driven by the number of Voronoi cells, while uncertainty is controlled by the sampling effort. The approach is computationally efficient and easily parallelizable, offering a practical tool for studying complex stochastic cellular dynamics and advancing the understanding of gene regulation and phenotype switching.

Speaker: Maryam Yousefian (University of Bergen (UiB))

11:40 AM From Simulation to Macroscopic Dynamics: Learning Reaction Coordinates and Sampling Rare Transitions in Stochastic Gene Regulatory Networks

Rare transitions between metastable states in stochastic gene regulatory networks are difficult to resolve in practice, as direct stochastic simulations require large amounts of data to capture these events reliably. In this talk, we present a neural network–based approach (ISOKANN) to learn low-dimensional reaction coordinates that describe the slow dynamics of such systems \cite{SikorskiCapturing, yousefian2025exploring,sikorski2024learning}.
These coordinates provide both a coarse-grained, dynamical view of the system and a basis for adaptive sampling. Starting from unbiased simulations, computational effort is iteratively focused on transition regions by resampling along the learned coordinate. This substantially reduces the amount of simulation time required while improving the resolution of transition pathways. At the same time, the learned representation captures the dominant slow processes in a dynamically consistent way.
We illustrate the approach on prototypical stochastic gene regulatory models and discuss how combining representation learning with adaptive sampling enables an efficient analysis of rare event dynamics. The emphasis is on intuition and practical insights rather than technical details.

Speaker: Alexander Sikorski (Freie Universität Berlin)

10:40 AM → 12:00 PM Modelling the interplay between radiotherapy, cell metabolism, and tumor dynamics

10:40 AM Quantifying the effect of initial cell density on hypoxia-induced radioresistance: experimental analysis and compartmental modeling of cell state dynamics

More than 50% of patients with cancer receive radiotherapy to kill tumor cells. Several mathematical models predicting post-irradiation cell survival are used clinically to plan treatment; however, they often neglect the tumor microenvironment, which can modulate radiotherapy response. A key driver of radioresistance in solid tumors is hypoxia.
In this project, we focus on the effect of initial cell density on hypoxia-induced radioresistance. Our experiments are designed to quantify how reduced oxygen levels before and after irradiation and initial cell density affect survival and post-treatment dynamics. We show that the hypoxia-induced radioresistance is stronger for high initial cell densities. We also present a biologically motivated compartmental model to analyze the dynamic transitions of cells between distinct states (e.g., repaired, senescent, and unrepaired subpopulations) under different conditions. By fitting time-course data, the model estimates key transition rates and incorporates oxygen dependence, enabling accurate simulation of cellular responses under hypoxic conditions. This work provides insight into the oxygen-dependent responses of cancer cells to radiation, informing more effective and context-aware therapeutic strategies.

Speaker: Botao Dai (CNRS, Grenoble-Alpes University, TIMC , Paris Saclay University, Paris Cité University, IJCLab, France)

11:00 AM Exploring how metabolism comes into play with radiations: a mechanistic approach

The reciprocal interactions between ionising radiation (IR) and glucose metabolism in mammalian cells have gained interest over these last decades. While reactive oxygen species (ROS) and HIF-1α emerge as key mediators in these interactions, the influence of ROS on HIF-1α following irradiation is still being debated. Different types of intermediate entities between ROS and HIF-1α have been proposed, each with different modes of action. In this study we propose to identify potential intermediates through their mode of action for several cell types studied in the literature. This is realized by reproducing the measured dynamics of key metabolic proteins following IR, specifically the LDH protein involved in glycolysis or ATP dynamics experimentally measured in cell cultures. These findings are then transposed in a tissue scale model – the spheroid – that allows to address the metabolic interactions between cells. To that end, a hybrid multiscale model based on the PhysiCell framework has been developed. It integrates individual cell metabolic states – previously defined - and incorporate cell-cell interactions in relation to the evolving environmental conditions for the spheroid exposed to IR. In light of the identified ROS-HIF relationships, our model aims to gain insight into the metabolic dynamics within an irradiated spheroid - dynamics which could be observed in future experiments.

Speaker: Damian Bimbenet (1. Univ. Grenoble Alpes, CNRS, UMR 5525, VetAgro Sup, Grenoble INP, TIMC, 38000 Grenoble, France 2. Department of Mathematics, Swansea University, Swansea SA1 8EN, UK)

11:20 AM Geometric Adversarial Learning for Reconstruction of Right-Censored Tumor Dynamics

To predict radiotherapy patient outcomes under clinically realistic right-censoring, we
model longitudinal gross tumor volume (GTV) dynamics using a geometric adversarial
learning framework rather than predefined mathematical growth equations. In this setting, patient trajectories are observed only up to a given follow-up time, after which
tumor evolution continues but remains unobserved. Instead of assuming a specific
functional form (e.g., exponential, logistic, or Gompertz growth), our approach (GAN-
GAF framework) first transforms observed GTV trajectories into Gramian Angular Fields
(GAFs), two-dimensional representations that encode pairwise temporal correlations
across the entire observation window, and then learns to complete these correlation
manifolds using adversarial training (GAN). Thus, right-censoring is implemented by
withholding the terminal portion of each patient’s trajectory, with the generator inferring
plausible continuations by restoring missing correlation structure in GAF space. This
enables uncertainty-aware reconstruction of post-observation tumor dynamics that
preserves amplitude, trend, and long-range temporal dependencies reflective of
individual treatment response heterogeneity, without requiring mechanistic assumptions
or parameter fitting. The GAN-GAF framework operates directly on real-time clinical
data, enforces global geometric consistency, and provides a data-driven alternative to
classical mathematical modeling for inference under right-censored radiotherapy follow-
up.

Speaker: Nahum Puebla-Osorio (University of Texas MD Anderson Cancer Center)

11:40 AM A new metric for functional drug screening: combing radiation with systemic therapies

We will present a modelling
study to provide a longitudinal response quantification of
efficacy for single and combination therapies of 11 compounds and
radiation (at different doses). This is based on the design of a
flexible ODE model accounting for different mechanisms of cell
death/modes of action induced by the different treatments, paired
with a modelling of synergies and scheduling. We will also
motivate possible alternative combination strategies regarding
order/schedule based on these models. The results are presented
across two cell lines, with an emphasis on the modeling approach,
and motivation of a new response metric that disentangles
intrinsic efficacy from dynamic response observation.

Speaker: Sarah C. Brüningk (University of Bern)

10:40 AM → 12:00 PM A Co-production Approach to Epidemic Modelling of Infectious Diseases

10:40 AM Involving communities in epidemic modelling: an introduction to co-production principles and tensions

Co-production, defined as collective knowledge making across different groups of stakeholders, has been suggested as the most effective strategy for mobilising evidence in policy and practice contexts \cite{bandola2023co}. While co-production is becoming an increasingly popular term in research, it is not always evident what counts as co-production: what is being produced, under what circumstances, and with what implications for participants \cite{filipe2017co}.

With co-production becoming more of a priority, its place in non-clinical research can be difficult to navigate. We will explore the arguments for co-production within modelling, taking into account the national and international context and co-production’s place in the wider knowledge exchange agenda.

We will use the COMMET (co-produced Mathematical Modelling of Epidemics Together) project as a case study to examine processes of co-production as way of making better decisions in epidemic modelling, since co-production is increasingly recognised as a way of ensuring that models reflect the realities and values of those most affected and avoiding harm. We will share examples of how co-production has been put into practice in the case study of the COMMET project and present our experiences as a co-producer and facilitator of co-production respectively.

Speakers: Dr Lucy Rycroft-Smith (University of Cambridge), Ms Sarah Barnes (University College London)

11:00 AM Neat Models, Messy Lives: Social Science as a Bridge to Lived Experience

Mismatches between modelled and real-world outcomes frequently arise from misplaced assumptions about how people live, interact, and respond to infectious disease threats and interventions. Co-production is increasingly recognised as a way of ensuring that models reflect the realities of those most affected. Without it, models risk overlooking context, perpetuating inequities, and causing inadvertent harm, particularly among marginalised groups.

Meaningful co-production requires more than collaboration; it depends on methods, frameworks and values that enable the systematic integration of diverse forms of knowledge into the modelling process. Social science disciplines and methods that generate evidence on behaviour, social structure and wider cultural and political context provides a foundation for this work.

In my talk, I will introduce key social science approaches and frameworks including qualitative and participatory methods, and assumptions about knowledge showing how they can facilitate co-production. I will argue that social science helps create the conditions for inclusive co-production, supports its integration across all stages of modelling, and enables its evaluation. Drawing on examples from literature and from our own team’s work, I will demonstrate how social science strengthens both process and input, helping to ground models in the messy realities of the lives they seek to represent.

Speaker: Dr Shema Tariq (University College London)

11:20 AM How Close is Too Close? Modelling Sexual and Non-sexual Transmission Pathways of Mpox in the UK

The 2022 mpox outbreak disproportionately affected gay, bisexual, and other men who have sex with men (GBMSM) in the United Kingdom, prompting the need for models that reflect both the epidemiological realities of transmission and the lived experiences of affected communities. We developed a dynamic network model capturing sexual and non-sexual close contact transmission dynamics. Central to this work is a co-production process with team members bringing lived experience and alongside broader community engagement workshops to bring modellers and GBMSM community members together to jointly refine assumptions, clarify behavioural patterns, and shape research priorities. These collaborative sessions were aimed at improved transparency, strengthened trust, and ensuring that the final model realistically represented diverse sexual partnerships and patterns and types of sexual behaviour, and community informed understandings of non-sexual exposure risks. Through this co-production approach we demonstrate how lived experiences can meaningfully shape the model structure, improve the relevance of transmission scenarios, and support more effective and equitable public health responses. In this talk I explain our modelling process and illustrate how co-production has influenced its development.

Speaker: Dr Zviiteyi Chazuka (University College London)

11:40 AM The MEMVIE public involvement framework: Developing a framework for public involvement in epidemiological and health economic modelling to bring dynamism to vaccination policy recommendations

The Mathematical and Economic Modelling for Vaccination and Immunisation Evaluation project (MEMVIE) involves the construction of epidemiological models and evaluating the cost-effectiveness of different vaccination interventions to help inform vaccination policy in the UK.

A contributor to the MEMVIE project is our MEMVIE public involvement group. The MEMVIE public involvement group and academic contributors are exploring, capturing and supporting the potential contribution of the public to epidemiological and health economic modelling.

This talk overviews the MEMVIE public involvement framework that has been iteratively co-produced through this process. The MEMVIE public involvement framework identifies points of collaborative public contribution to modelling and supports its implementation \cite{staniszewska2021}.

Speaker: Dr Edward Hill (University of Liverpool)

10:40 AM → 12:00 PM Making cells dance: modelling gene regulation and cell fate from transcriptomics

10:40 AM Inferring RNA processing dynamics across cell states and fates from single-cell snapshot data

With single-cell genomics datasets, it is possible to assay the transcriptome in thousands to millions of cells as they undergo development, differentiation and external perturbation. These data are ripe for investigation into how regulation of RNA processing governs the myriad cell states comprising these systems.

However, despite our ability to assay these states, single-cell data is sparse and noisy, a result of both innate biological features of the RNA molecules and technical effects in RNA capture and sequencing. Standard analyses often rely on heuristic application of dimensionality reductions to remove noise, and focus on mean-level (observational) changes in gene expression to define cell states.

Here we demonstrate how stochastic, biophysical models of RNA processing can be applied to snapshot single-cell data to reveal underlying mechanisms of observed gene expression patterns across heterogenous cell states. By explicitly realizing the biophysical and technical processes underlying the sparse, discrete molecular data, we can reveal altered dynamics of bursty transcription, splicing and degradation between populations of cells. We can additionally resolve heterogeneous regulation within these populations, and propose combinatorial strategies of regulation guiding these distinct fates. Together this work enables hypothesis-driven experimentation by proposing key points of transcriptional regulation underlying higher-level changes in gene expression and noise.

Speaker: Tara Chari (Eric and Wendy Schmidt Center at the Broad Institute of MIT and Harvard)

11:00 AM Inferring Cellular Dynamics through Ordered Diffusion Kernels

Single-cell RNA-sequencing (scRNA-seq) data provides a detailed view into the gene regulatory landscape that cells traverse during differentiation from pluripotent to mature cell types. However, analysing these datasets remains challenging due to their sparsity, high dimensionality, lack of temporal information, and high levels of technical noise, necessitating the development of numerous specialised analytical methods.

We introduce and apply Ordered Diffusion Kernels (ODKs) to model cellular differentiation as a drift-diffusion Markov process by biasing transition probabilities with an ordering function from which we can compute velocity estimates, terminal states, stationary distributions, passage times and trajectory inference. Furthermore, we propose transforming snapshot scRNA-seq data into a pseudo-trajectory dataset with ODKs for purpose of applying powerful tools from the time series analysis literature to perform equation discovery and infer gene regulatory networks.

Speaker: Jack Soulsby (Imperial College London)

11:20 AM Inferring causal gene regulatory relationships from time-resolved single-cell transcriptomics

Deciphering gene regulatory networks is central to understanding how cells orchestrate gene expression programmes. Single-cell RNA sequencing (scRNA-seq) has enabled the investigation of genome-wide regulatory relationships through pairwise gene correlations. Yet, interpreting these correlations is challenging due to confounding factors such as biological sources of covariation or technical noise. Time-resolved scRNA-seq with metabolic RNA labelling provides access to transcription dynamics, offering opportunities to address these challenges. We introduce a modelling framework integrating mechanistic models of gene regulation with machine learning to analyse regulatory relationships in time-resolved scRNA-seq data. We build stochastic models of causal gene regulatory relationships, including direct regulation and co-regulation, capturing key confounders such as extrinsic noise, cell cycle coupling and technical noise, to simulate temporal summary statistics. A neural network supervised by these simulations learns to classify regulatory scenarios, mapping observed correlation patterns to underlying causal models, while leveraging gene-specific priors inferred from the data. Applied to real time-resolved scRNA-seq data, the framework predicts causal gene–gene relationships while quantifying uncertainty. Overall, our approach shows that mechanistically informed machine learning enables interpretable gene regulation inference from single-cell data.

Speaker: Dimitris Volteras (The Francis Crick Institute)

11:40 AM Decoding gene regulatory networks and cellular dynamics

RNA velocity has emerged as a popular approach for modeling cellular change along the phenotypic landscape but routinely omits regulatory interactions between genes. Conversely, methods that infer gene regulatory networks (GRNs) do not consider the dynamically changing nature of biological systems. To integrate these two currently disconnected fields, we present RegVelo, an end-to-end dynamic, interpretable, and actionable deep learning model. RegVelo learns a joint model of splicing kinetics and gene regulatory relationships and allows us to perform in silico perturbation predictions. When applied to datasets of the cell cycle, human hematopoiesis, and murine pancreatic endocrinogenesis, RegVelo provides reliable predictive power for terminal states, gene interaction and perturbation simulations. To leverage RegVelo’s full potential, we studied the dynamics of zebrafish neural crest development and underlying regulatory mechanisms using deep full-transcript-length Smart-seq3 dataset and shared gene expression and chromatin accessibility measurements. Using RegVelo's in silico perturbation predictions, supported by CRISPR/Cas9-mediated knockout and single-cell Perturb-seq, we establish transcription factor tfec as an early driver and elf1 as a novel regulator of pigment cell fate. Together, RegVelo provides a powerful framework for quantitatively bridging gene regulation and cell fate decisions.

Speaker: Weixu Wang (ICB, Helmholtz Munich)

10:40 AM → 12:00 PM Methods to integrate -omics data into mechanistic models

10:40 AM Informing Macrophage phenotypic change over the endometrial cycle using omics data

The endometrial cycle is known to be mediated via the endocrine system, with both estradiol and progesterone hormones heavily implicated in menstruation. Throughout this cycle, the tissue undergoes vast changes in tissue and cellular-level function, including phagocytosis and apoptosis, cell proliferation, both tissue and vascular remodelling, and extracellular matrix construction. Macrophages are a key component of the regulation of these vastly different function, and have traditionally thought of as either M1-like (pro-inflammatory) phenotype, or M2-like (anti- inflammatory) phenotype. However, a paradigm shift is underway, where macrophages are increasingly observed to exhibit characteristics of each phenotype simultaneously. This is referred to as the “continuum spectrum of Macrophage phenotypes”.

In this work, we present a mathematical model of a continuous macrophage phenotype. We utilise openly available, single cell transcriptomics data, and the fact that the endocrine system is a driver of endometrial cycle dynamics, to validate our model. This validated models allows us to understand how the macrophages change their phenotype along this continuous spectrum throughout the hormonal cycle. We then use our validated model for hypothesis generation, in the context of immune dysfunction and its potential consequences, for example for the uterine disease endometriosis.

Speaker: Domenic Germano (University of Melbourne)

11:00 AM Transcriptome-informed flux predictions revealed temporal metabolic reprogramming and branch points mediating cold stress-growth trade-offs in rice

Rice (Oryza sativa) is highly sensitive to cold stress, imposing major constraints on its productivity and geographical distribution. Elucidating cold-induced metabolic reprogramming is essential for understanding the underlying mechanisms of rice adaptive responses.

Constraint-based metabolic modeling is a powerful framework for capturing metabolic interactions. A key challenge, however, is selecting an appropriate objective function, a decision that is critical for model predictions. In this study, we integrated transcriptomics data with a genome-scale rice metabolic model using the E-Flux algorithm to construct a temporal model of cold stress response. We analyzed the resulting model via two approaches: (i) random sampling of the transcriptome-informed solution space, and (ii) Pareto frontier analysis quantifying trade-offs between biomass production and proline accumulation, a well-studied stress marker.

Pareto analysis revealed carbon flux redistribution to support increased substrate availability for proline biosynthesis. We identified branch points where proline accumulation competes with growth, which can serve as potential engineering targets for improving cold resilience without yield penalties. Machine learning-assisted pathway enrichment analysis of the sampling data highlighted temporal metabolic transitions across time points. These findings offer a pathway-level view of cold-induced metabolic reprogramming in rice and targets for crop improvement.

Speaker: Fatemeh Soltani (Institute for Plant Sciences, Cluster of Excellence on Plant Sciences (CEPLAS), University of Cologne)

11:20 AM From genome sequencing to metabolic modelling and dynamic flux balance analysis extensions

Genomic sequencing data can be used to identify gene-protein-reaction (GPR) rules for microbial species, which determine how the genes corresponding to enzymes catalyse specific metabolic reactions. GPRs can thus be combined to create genome-scale metabolic models (GEMs) for any organism for which a genome sequence is available. Mathematically, GEMs are large stoichiometric matrices that can be used to predict which reactions are vital for their metabolism. GEMs are then used to construct kinetic models, which are often very large systems of ODEs. In this talk, I will describe how GEMs are constructed and how flux balance analysis (FBA) is used to calculate a biologically feasible combination of fluxes for an organism at steady state. Next, I will extend FBA to consider dynamic environments (dFBA) to describe scenarios such as growth in a bioreactor where resources are finite. This requires a quasi-steady-state approximation where the intracellular metabolism is assumed to be at steady state. dFBA has been applied with much success to model microbial metabolism, both in industry and research. In the remainder of this talk, I will present my own work on extending dFBA to consider variable objective functions, including how an organism’s cellular objective might change in response to a dynamic environment. Notably, this will include an algorithm for solving these extended problems efficiently, minimising the number of times the LP problem must be solved.

Speaker: Thomas Munn (University of Birmingham)

11:40 AM Inferring mass isotopomer distribution dynamics from partial isotopic labeling data: Implications for flux estimation

Isotopically non-stationary metabolic flux analysis (INST-MFA) enables the estimation of intracellular fluxes from time-resolved labeling data but remains limited to medium-scale networks due to experimental constraints on metabolite coverage. Extending INST-MFA toward large-scale models with high confidence in flux estimates requires extensive labeling datasets. Here, we employ a neural network approach to infer complete mass isotopomer distribution (MID) dynamics from partial $^{13}$C-isotopic labeling data. The model is trained on synthetic time-resolved MID datasets generated from a large-scale network of Chlamydomonas central metabolism. We show that MID trajectories can be accurately reconstructed for a broad set of metabolites from limited observable inputs. Furthermore, we apply the approach to labeling data from different green algae and investigate to what extent predicted complete MID datasets can support downstream flux estimation by comparison to previously published flux estimates derived using scale-free constrained regression and a state-of-the-art tool for INST-MFA, INCA \cite{SFCR}. Together, our findings highlight the potential of neural network based MID prediction as a tool toward precise large-scale flux estimation from isotopic labeling data. By augmenting incomplete labeling datasets with predicted MID dynamics, this approach provides a pathway to overcome current limitations in metabolite coverage and improve the reliability of flux estimates in INST-MFA.

Speaker: Anika Küken (Bioinformatics, Institute of Biochemistry and Biology, University of Potsdam)

10:40 AM → 12:00 PM Methodological Advances in Modeling Human Behavior and Infectious Disease Spread

10:40 AM MS171-1

11:00 AM Coupled Dynamics: How Genes Shape Epidemics (and Epidemics Shape Genes)

Host genetic structure can significantly alter disease transmission dynamics and long-term disease outcomes. Past work by Beck, Keener, Hoppensteadt, Feng, and others has shown that when pathogen transmission interacts with evolving host traits—such as susceptibility, recovery, or disease-induced mortality—the resulting coupled system can exhibit novel dynamics. These models demonstrated that genetic composition within a host population can shift during an epidemic, and conversely, infection pressures can reshuffle genetic frequencies, producing true feedback between genes and epidemics.
In this talk, I will discuss a specific example of this phenomenon, focusing on the interaction between Plasmodium vivax and the Duffy antigen, a host genetic trait that confers partial protection against infection.

Speaker: Joan Ponce (Arizona State University)

11:20 AM Models that ignore behavior underestimate the basic reproduction number

Behavioral responses during epidemics alter transmission, yet most epidemiological models assume constant contact rates. We assessed the resulting bias by fitting a baseline SEIR model with fixed transmission and three behavioral variants, in which transmission declines with increasing mortality, to COVID-19 mortality data from 30 U.S. states during the first wave (March-July 2020).

Behavioral models fit the data better in 28 of 30 states, with Bayes factors giving substantial to decisive support in those same states. Ignoring behavioral feedback produced consistent inferential errors: baseline models systematically underestimated the basic reproduction number (R0) while simultaneously overestimating the final epidemic size. Posterior R0 estimates were higher under behavioral models across all states, yet baseline models predicted substantially larger cumulative infection burdens.

Synthetic-data experiments showed that these discrepancies are caused by model misspecification rather than noise or data limitations. Analytically, we show that for fixed R0, models without behavioral feedback overestimate epidemic size whenever mortality reduces transmission. Explicit behavioral modeling is therefore essential for reliable epidemic inference and forecasting.

Speaker: Marko Lalovic (Network Science Institute, Northeastern University London, London, UK)

11:40 AM Highlights of projects funded through the Mathematical Biology program and other initiatives at the US NSF

The Mathematical Biology program and other programs in the Directorate of Mathematical and Physical Sciences at the US National Science Foundation have funded many high impact research projects on various topics including mathematical modeling of infectious diseases. Some highlights will be presented.

Speaker: Zhilan Feng (National Science Foundation)

10:40 AM → 12:00 PM Multicellular Modelling and Simulation Tools - The OpenVT Project

10:40 AM Chaste: a computational framework for multicellular modelling

Problems in biology are intrinsically multi-scale, with processes occurring on many disparate spatial and temporal scales. Here we present a multiscale framework for the mathematical modelling of biological systems. Utilising the natural structural unit of the cell, the framework consists of three main scales: the tissue level (macro-scale); the cell level (meso-scale); and the sub-cellular level (micro-scale), with interactions occurring between all scales. The cell level is central to the framework and cells are modelled as discrete interacting entities using one of a number of possible modelling paradigms, including lattice based models (cellular automata and cellular Potts) and off-lattice models (cell centre and vertex based representations). The sub-cellular level concerns numerous metabolic and biochemical processes represented by interaction networks rendered stochastically or into ODEs. The outputs from such systems influence the behaviour of the cell level affecting properties such as adhesion and also influencing cell mitosis and apoptosis. Tissue level behaviour is represented by field equations for nutrient or messenger concentration, with cells functioning as sinks and sources. This modular approach enables more realistic behaviour to be considered at each scale.

The multi-scale framework is implemented in an open source software library known as Chaste (https://chaste.github.io/). This software library consists of object orientated C++, developed using an agile development approach. All software is tested, robust, reliable and extensible. The library enables general simulations to be undertaken and includes tools to atomically curate and store simulation results expediting model development. In this talk we introduce the framework and give some key examples of its use.

Speaker: James Osborne (University of Melbourne)

11:20 AM Vivarium: a compositional framework for multiscale modeling

Multicellular biological systems span many spatial and temporal scales, yet models of these systems are often developed in isolation, using different assumptions, algorithms, and software frameworks. Vivarium is an open-source compositional framework designed to make these models interoperable by allowing independently developed components to be connected through standardized interfaces and shared state variables. Rather than building monolithic simulations, Vivarium enables researchers to assemble complex models by composing modular processes representing different biological functions and modeling formalisms, including agent-based models, differential equations, flux balance analysis, and spatial simulators. In this talk, I will introduce the core ideas behind Vivarium and show how this compositional approach supports multiscale simulations of microbial and multicellular systems while enabling integration with existing modeling tools. By focusing on modularity, explicit interfaces, and reusable components, Vivarium aims to lower the barrier to composing large biological simulations and to support a more collaborative ecosystem for building and connecting models across the community.

Speaker: Eran Agmon (University of Connecticut)

11:40 AM Bringing biology to the browser with Artistoo

The cellular Potts model (CPM) is a powerful in silico method for simulating biological processes at tissue scale. Their inherently graphical nature makes CPMs very accessible in theory, but in practice, they are mostly implemented in specialised frameworks users need to master before they can run simulations. Artistoo (Artificial Tissue Toolbox) is a JavaScript library for building ‘explorable’ CPM simulations where viewers can change parameters interactively, exploring their effects in real time. Simulations run directly in the web browser and do not require third-party software, plugins, or back-end servers. The JavaScript implementation imposes no major performance loss compared to frameworks written in C++ and remains sufficiently fast for interactive, real-time simulations.

In this talk, I will discuss the design philosophy behind Artistoo and show how it provides an opportunity to unlock models for a broader audience: interactive simulations can be shared via a web page in a zero-install setting, but models can also run from the command line for large-scale scientific applications. I will discuss applications in research, science dissemination, open science, and education, and demonstrate how the modular design of Artistoo makes it easy for users to plug in their own model terms when needed.

Speaker: Inge Wortel (Radboud University)

10:40 AM → 12:00 PM Delay differential equation models in mathematical biology

10:40 AM → 12:00 PM Mathematics and the Life-Sciences: dedicated to 65th Birthday of Angela Stevens

10:40 AM Kinetic equations and mathematical epidemiology

In 1914 McKendrick came up with a method inspired by L. Boltzmann to describe the evolution of statistical distributions in an - in principle continuous - parameter space, also for the life sciences and the social sciences.This method leads to partial differential equations. Nevertheless, the Kermack-McKendrick models are often misinterpreted solely as the well-known SIR ODE-system for the dynamics of susceptibles, infectious and removed during an epidemic.

But McKendricks equations are by far more general. For instance the hydrodynamic limit of a stochastic epidemiological model, where two infection scenarios alternate, namely a) infections in separated groups of finite size; b) and infections at meeting places of finite capacity, where individuals meet randomly, also results in such a type of McKendrick system with polynomial infection force.

For this system of kinetic equations we derive invariants which uniquely determine the outcome of the model epidemics. Such kinetic equations allow to link global data of an epidemic with not so easily observable local rate dependencies.

Speaker: Prof. Angela Stevens (University of Muenster)

11:00 AM Bacterial movement by run and tumble: the flux-limited Keller-Segel equation

At the individual scale, bacteria as E. coli move by performing so-called run-and-tumble movements. This means that they alternate a jump (run phase) followed by fast re-organization phase (tumble) in which they decide of a new direction for run. For this reason, the population is described by a kinetic-Botlzmann equation of scattering type. Nonlinearity occurs when one takes into account chemotaxis, the release by the individual cells of a chemical in the environment and response by the population.

These models can explain experimental observations, fit precise measurements and sustain various scales. They also allow to derive, in the diffusion limit, macroscopic models (at the population scale), as the Flux-Limited-Keller-Segel system, in opposition to the traditional Keller-Segel system, this model can sustain robust traveling bands as observed in Adler's famous experiment.

Furthermore, the modulation of the tumbles, can be understood using intracellular molecular pathways. Then, the kinetic-Boltzmann equation can be derived with a fast reaction scale. Long runs at the individual scale and abnormal diffusion at the population scale, can also be derived mathematically.

Speaker: Prof. Benoit Perthame (Laboratoire J.-L. Lions, Sorbonne Université)

11:20 AM Oncogenic transformation of tubular epithelial ducts: how mechanics affects morphology

Epithelial tissues at a pre-tumoral stage exhibit morphological changes: in particular epithelial ducts depart from the cylindrical shape, showing invaginations and evagination in the regions of the surface with malignant cells. Experiments report that at the inner and outer boundary of the epithelial sheets are concentrated molecular motors able to generate a surface active tension, that can vary between healthy and tumor cells. The mechanical origin of such morphology can be mathematically tackled by a continuum mechanical model \cite{ambrosi_1} able to relate, also quantitatively, the role of the impaired surface tensions.

The mathematical model, derived from first principles, accounts for the competition between the bulk elasticity of the epithelium and the surface tension of the apical and basal boundaries. The variation of the energy functional yields the Euler-Lagrange equations to be numerically integrated. The numerical results reproduce a variety of morphological shapes, from invagination to evagination, depending on the ratio between bulk and surface energy at variance of the length of the section. In particular, using parameters independently measured, we are able to reproduce experimental data reported for a ring partially made of transformed cells.

The numerical results obtained with a mathematical model that accounts, in a suitable way, for the thickness of the epithelial wall, prompt us to a deeper mathematical characterization that we address exploiting the Euler Elastica. In this framework we study the variety of possible shapes that a planar inextensible closed rod can take because of a piecewise inhomogeneity in its natural curvature. On the basis of numerical simulations, perturbation analysis and geometrical arguments, we are able to devise three morphological regimes and we provide a first order approximation of the curves that separate the shape regimes in the (k, s0 ) plane, k being the jump in natural curvature in the relative curvilinear coordinate s0. Our perturbation analysis, supported by geometrical arguments, compares well with the numerical results based on the fully nonlinear theory.

Speaker: Prof. Davide Ambrosi (Polytechnic University of Turin)

11:40 AM Minimal Principles for Dynamics in Reaction Networks

Biochemical networks are notoriously large and complex and involve many unknown parameters. As a consequence, various reduction methods for their analysis have been proposed. A common critique of this approach is that biochemical complexity is intrinsic and that any “reduced” model is therefore doomed to miss essential features. However, minimal models can be particularly valuable to illustrate/investigate/suggest general and fundamental qualitative mechanistic principles, rather than to provide quantitative predictions or detailed explanations of specific phenomena.

In this spirit, I will present a few minimal models that produce characteristic dynamical behavior, such as the emergence of periodic oscillations or multistability arising from symmetry breaking. The examples are taken from joint work with Alex Blokhuis and Peter Stadler (oscillations), and with Angela Stevens (symmetry breaking and multistability).

Speaker: Dr Nicola Vassena (Leipzig University)

10:40 AM → 12:00 PM Quantitative Models of Immune Regulation and Therapeutic Response in Cancer

10:40 AM Modelling monoclonal antibody transfer across the human placenta

Monoclonal antibody (mAb) therapies, although widely established in cancer treatment, are increasingly being developed and repurposed for the long term management of chronic autoimmune and inflammatory conditions such as multiple sclerosis, rheumatoid arthritis, and inflammatory bowel disease. Many of these conditions disproportionately affect women, raising important questions about fetal exposure when mAbs are taken during pregnancy, whether inadvertently or as part of maternal disease control. Most therapeutic mAbs are engineered from human immunoglobulin G (IgG) and therefore interact with the same pathways as endogenous IgG antibodies. This includes the pathways which allow maternal IgGs to pass to the fetus through the placenta. In this work, we present a mathematical model of mAb transport across the human placenta, calibrated using experimental data from ex vivo placental perfusion studies. The human placenta contains two circulations, maternal and fetal, that come into close contact to allow for the transfer of oxygen and nutrients, however, are anatomically separate. Using ODEs we model the placental compartments, FcRn expression, and associated transport processes to explore how these factors influence fetal exposure to mAbs. Understanding placental mAb transfer is essential for informing regulatory decisions on mAb use in pregnancy, and our model provides a mechanistic framework to predict fetal exposure and quantify risks.

Speaker: Eleanor Doman (University of Manchester)

11:00 AM Modelling Hematopoietic Dynamics in H3K27M-Driven Preleukemia and Implications for AML Therapy

Acute myeloid leukemia (AML) is an aggressive blood cancer driven by genetic and epigenetic alterations that disrupt normal hematopoiesis. Among these, the H3K27M mutation, originally identified in pediatric high-grade gliomas, reshapes gene repression programs by reducing global H3K27 trimethylation. Although rare, H3K27M mutations have been detected in preleukemic hematopoietic stem cells (HSCs) of AML patients, suggesting its role in early leukemogenesis and identifying it as a promising therapeutic target. Here, we investigated how H3K27M alters hematopoiesis using a longitudinal xenotransplantation model of human HSCs carrying either H3-K27M or wild-type H3. To quantify hematopoietic dynamics, we developed a collection of mathematical models representing alternative lineage hierarchies and fitted them to our longitudinal experimental data. Using information criteria and global sensitivity analysis, we identified the model that best capture blood dynamics in each condition. Our results show that H3K27M promotes the expansion of HSCs, common myeloid progenitors, and megakaryocyte-erythroid progenitors while inducing a delayed block in erythroid differentiation. By stimulating HSC proliferation, H3-K27M dynamics allowed us to distinctly characterize mouse HSC subpopulations (HSC1 and HSC2). Together, our results provide the first quantitative framework to reveal how H3K27M influences hematopoietic hierarchy roadmap and alters blood cell dynamics in preleukemia.

Speaker: Mia Brunetti (Université de Montréal/Sainte-Justine University Hospital Research Centre)

11:20 AM Model selection and parameter inference for p53-driven bone marrow failure

Hematopoietic stem cell (HSC) maintenance depends on the regulation of ribosome function. Mutations in ribosome-associated genes disrupt this regulation, leading to congenital disorders characterized by anemia, bone marrow failure, and an increased risk of hematologic malignancies. These pathologies are associated with the activation of the p53 stress response arising through ribosomal dysfunction. We investigated the role of MYSM1 (Myb-like, SWIRM, and MPN domains 1), a deubiquitinating enzyme and transcriptional co-activator essential for HSC maintenance and immune development. MYSM1 deficiency has been linked to p53 activation, and hematopoietic defects are rescued in Mysm1/p53 double knockout models, yet the dynamical mechanisms connecting p53 activation to bone marrow failure remain unclear. To model the regulatory interactions between MYSM1, p53, and their downstream targets in the bone marrow, we developed systems of ordinary differential equations to represent normal and aberrant hematopoietic hierarchies. Using murine experimental data, we evaluated competing mechanistic hypotheses through parameter estimation and model selection. This framework quantifies how MYSM1 deficiency perturbs hematopoietic dynamics and clarifies the contribution of p53-mediated pathways to stem cell depletion. This work provides mechanistic insight into the bone marrow failure consistent with MYSM1-related ribosomopathies, with implications for cancer predisposition and therapeutic targeting.

Speaker: Patricia Lamirande (Université de Montréal)

11:40 AM Modeling immune-mediated effects of RAGE inhibition and radiotherapy in malignant gliomas

The dynamics of malignant neoplasms of the central nervous system, such as malignant gliomas and brain metastases, are strongly shaped by the blood–brain barrier and by interactions between tumor cells and immune populations within the tumor microenvironment. In particular, tumor-associated myeloid populations—including microglia and macrophages—can promote tumor growth through immunosuppressive and pro-tumoral signaling pathways. Among the molecular regulators involved in these interactions, the receptor for advanced glycation end-products (RAGE) has emerged as a key mediator linking inflammation, immune dysfunction, and tumor progression.
Azeliragon (AZG), a small-molecule RAGE inhibitor, has recently shown promising preclinical results in combination with radiotherapy (RT), and clinical trials are currently underway to evaluate its therapeutic potential (e.g., NCT05635734 and NCT05789589). Motivated by these findings, we developed an ordinary differential equation model of malignant gliomas that explicitly incorporates tumor–immune interactions and the combined effects of RT and AZG. This framework enables the quantitative exploration of treatment schedules through in silico trials and provides a mechanistic tool to investigate how RAGE inhibition may reshape the tumor immune microenvironment and enhance radiotherapy efficacy. The proposed framework also provides a quantitative basis to investigate similar immune-mediated treatment strategies in other intracranial malignancies, where activation of the S100A9–RAGE signaling axis has been identified as a driver of radiotherapy resistance. I will discuss the theoretical foundations of the model, and its validation with clinical data as well as the extension of the concepts to brain metastases, a more frequent malignancy where similar biological processes are also present.

Speaker: Miguel Perales-Patón (University of Castilla-La Mancha)

10:40 AM → 12:00 PM Newtonian and non-Newtonian Biofluidmechanics: Integrating Theory, Experiments, Modeling, and Simulations

10:40 AM Swimming Strategies of Bipolar Flagellated Bacteria

Flagellated bacteria navigate complex environments by modulating flagellar rotation. The properties of the flagella, together with the cell body shape, govern the dynamics of bacterial motion and resulting swimming strategies. While the motility of many flagellated bacteria is well understood, comparatively little is known about bipolar flagellated species. In this talk, we present a mathematical model for the motility of Campylobacter jejuni, which drives a flagellum at each pole to move through the viscous mucosa of its host’s gastrointestinal tract [1]. We investigate how the interplay between the helical body shape and spatially non-uniform rigidities of the flagella gives rise to distinct swimming modes. In particular, we highlight the wrapping mode, in which the leading flagellum wraps around the cell body.

[1] E. J. Cohen, et al. Campylobacter jejuni motility integrates specialized cell shape, flagellar filament, and motor, to coordinate action of its opposed flagella. PLoS pathogens, 16.7 (2020): e1008620.

Speaker: Jeungeun Park (State University of New York at New Paltz, USA)

11:00 AM Modeling the Transposition of Deformable Bacteria Through Membrane Pores

From research to clinical development and production, Mycoplasma are well-recognized and widespread contaminants in biopharmaceutical manufacturing. Their successful proliferation despite the ultrafiltration performed to eliminate them has been attributed in part to the flexibility of their cell walls.

How does this bacterium manage to squeeze through pores that are, in some cases, one-third of its size? We build on a force-balance approach to quantify a threshold transmembrane pressure that determines retention versus passage, then use semi-analytical modeling based on elasticity relations, Stokes equations, and the method of reflections to explore the deformation and motion of a bacterium once it has trespassed into a pore.

This work aims to identify the maximum flow conditions at which membrane filtration remains a viable strategy for the filtering out of Mycoplasma from permeate to effectively inform the processes and materials employed to eradicate it. This research is funded by NSF CBET-2211001.

Speaker: Abigail Drumm (Worcester Polytechnic Institute, USA)

11:20 AM Computational modeling and analysis of collective motion of methanotrophs

Global warming, driven significantly by methane emissions, poses severe threats to ecosystems and society. Methanotrophs - microorganisms capable of metabolizing methane into methanol - offer a promising bioconversion strategy to mitigate greenhouse gases while producing valuable, eco-friendly fuel. To optimize the efficiency of this methane-to-methanol conversion, it is essential to understand the collective swimming dynamics of dense methanotrophic suspensions. These dense bacterial suspensions generate chaotic, flow-like patterns known as ’active turbulence.’ Unlike classical inertial turbulence, active turbulence possesses distinct physical properties that remain incompletely understood despite previous phenomenological modeling efforts.

In this study, we characterize the collective swimming behavior of methanotrophs by performing a computational fluid dynamics analysis of two-dimensional active turbulent flow fields using the Toner-Tu model [1,2]. By comparing our numerical results with experimental data from methanotrophic suspensions, we successfully model the governing equations of motion for methanotrophic active turbulence [3]. Ultimately, these findings provide a deeper understanding of these previously uncharacterized microbial dynamics and demonstrate the potential to optimize the performance of methane-to-methanol bioreactors through predictive simulations under varied operational conditions.

[1] S. Mukherjee, R. K. Singh, M. James, and S. S. Ray. Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence. Nature Physics, 19(6):891-897, 2023.
[2] J. Toner and Y. Tu. Flocks, herds, and schools: A quantitative theory of flocking. Physical Review E, 58(4):4828, 1998.
[3] H. H. Wensink, J. Dunkel, S. Heidenreich, K. Drescher, R. E. Goldstein, H. Lwen, and J. M. Yeomans. Meso-scale turbulence in living fluids. Proceedings of the National Academy of Sciences, 109(36):14308-14313, 2012.

Speaker: Jongmin Seo (Kyung Hee University, Republic of Korea)

10:40 AM → 12:00 PM Mechanical models of collective cell dynamics

10:40 AM Mechanical regulation of the G1/S checkpoint in collective cell migration: a two-stage age-structured model

Cell proliferation and migration are tightly regulated by mechanical cues, particularly crowding through contact inhibition. A central control point is the G1/S restriction point (R-point), an irreversible checkpoint in late G1 where mammalian cells integrate environmental signals, such as cell density, with intrinsic regulatory cues to commit to DNA replication and division. We introduce a two-stage age-structured model of collective cell migration that resolves the G1 and S/G2/M phases, with both density-dependent and age-dependent regulation acting at the G1/S transition. We investigate the checkpoint-mediated coupling between cell-cycle progression and crowding, and determine how contact inhibition shapes wave speed, front structure, and the age distribution of migrating cell populations.

Speaker: Stéphanie Abo (University of Oxford)

11:00 AM From discrete models of cell mechanics to continuum descriptions of tissue growth

The rate at which biological tissues grow is regulated by the interplay between geometry, cell mechanics, and cellular processes. In scenarios where tissue growth occurs primarily at the surface of a confined environment -- such as bone remodelling, wound healing, and tissue growth within engineered scaffolds -- cells compete for space as they deposit new material. This competition leads to cell crowding or spreading depending on substrate curvature and generates mechanical stresses that may influence cellular processes including proliferation, differentiation, and survival. We present a discrete mathematical model for simulating tissue growth in confined geometries. The tissue interface is represented as a chain of mechanically interacting cells (modelled as springs) that simultaneously generate new tissue material. To more accurately capture cell population dynamics during tissue growth, we incorporate cell proliferation, death, and embedment as stochastic processes. To describe the collective behaviour of the cell population, we derive a continuum limit by representing each cell with $m$ subcellular mechanical components and taking the limit as $m\to\infty$. This derivation yields a reaction–diffusion partial differential equation governing the evolution of cell density along a moving interface parameterised by arc length.

Speaker: Shahak Kuba (Queensland University of Technology)

11:20 AM Toward a unified theory of curvature-guided epithelial migration: ER remodeling, cytoskeletal polarity, and cell mechanics

Curvature-dependent epithelial migration is usually described at the level of actin and adhesion, but recent experiments reveal a central role for organelle mechanics. We combine new experimental evidence on wound-edge geometry with a unified variational model of single-cell migration to argue that the endoplasmic reticulum (ER) acts as a mechanotransducer linking curvature, cytoskeletal forces and migration mode. In epithelial gaps, convex edges promote ER tubules, perpendicular focal adhesions and lamellipodial crawling, whereas concave edges promote ER sheets, parallel adhesions and purse-string-like contraction. Building on these findings, we formulate a thermodynamically consistent framework that couples ER sheet--tubule remodeling, membrane curvature elasticity, actin turnover, microtubule reorganization, intracellular flow, and cell polarity within a diffuse-interface description. The model explains how geometry and force bias intracellular organization through strain-energy minimization and predicts how perturbations of ER structure reshape polarity and motility. Together, this work provides a route toward a predictive theory of epithelial migration in which intracellular architecture is not a passive readout of mechanics, but an active regulator of cell movement.

Speaker: Fabian Spill (University of Birmingham)

11:40 AM Modelling bulk mechanical effects in a planar cellular monolayer

The 2D vertex model is successful in capturing many phenomena observed in epithelia but does not consider out-of-plane mechanical effects. To understand how 3D effects can be captured in 2D, we introduce a model for a monolayer of columnar cells where the energy includes terms relating to volume, surface area, lateral adhesion and cortical tension. When reduced to a 2D formulation, bulk effects due to volume and surface area introduce coupling between the apical area and perimeter. This coupling is not captured in the standard 2D model and leads to a more complex phenomenology. The reduced 2D model has five independent parameters, each of which can lead to a rigidity transition when varied; these are the target apical perimeter as used in the standard 2D model, as well as parameters controlling the strength of adhesion, cortical line tension, total area tension, and constrictive forces at the apical cortex. This reveals multiple potential mechanisms by which tissues can lose rigidity. We also find a sharp continuous squamous to columnar transition in the fixed volume limit, where a floppy region connects the two rigid states. In the rigid regime, the model shows how lateral crowding in a disordered isolated monolayer can lead to cell elongation towards the monolayer centre.

Speaker: Natasha Cowley (Department of Mathematics, University of Manchester)

10:40 AM → 12:00 PM Stochastic Chemical Reaction Networks

10:40 AM Stability of reaction networks with randomly switching parameters

Since the dawn of stochastic chemical reaction network theory over 50 years ago, there have been many general results about (positive) recurrence, especially in the case of mass-action kinetics. One less-explored area is that of mass-action models whose rate constants, rather than being static, are themselves stochastic. Such models have relevance in applications, since biomolecular systems rarely exist in isolation and their rates often depend on time-changing quantities.

This talk will present matrix conditions for positive recurrence and transience in the case where the system is switching between finitely many possible choices of rate constants. These conditions will depend on the specific choice of parameters for the model, which makes it possible to uncover phase transitions where the stability behavior of the model varies. We will see that the speed at which the rate constants are changing plays an important role, with the model behaving as one with averaged rate constants when this speed is high and behaving as though the rate constants were unaveraged when this speed is low. This talk is based on joint work with Daniele Cappelletti and Chuang Xu.

Speaker: Aidan Howels (Polytechnico Torino)

11:00 AM Weakly Reversible Chemical Reaction Networks Are Recurrent in 2d

We prove that, for weakly reversible chemical reaction networks with stochastic mass-action kinetics in two species, the associated continuous-time Markov chain is positive recurrent on each closed irreducible communicating class. Equivalently, the process returns to finite sets infinitely often with finite expected return times, and it possesses an invariant probability measure supported on the class.
The proof is based on a Foster–Lyapunov argument. Exploiting weak reversibility together with the geometric constraints of the two-dimensional state space, we construct a Lyapunov function allowing to establish, using pathwise large deviations estimates, sufficient asymptotic dissipation of the given process.

Speaker: Andrea Agazzi (Bern University)

11:20 AM Sensitivity of dynamics in Autocatalytic Reaction Networks of Togashi-Kaneko type

The Togashi–Kaneko (TK) model is a prototypical example of an auto- catalytic reaction network exhibiting dramatic switching behavior that is a result of the stochastic dynamics at small volumes. I will present a study of the TK model with additional mutations, using a stochastic averaging principle to make use of the multi-scale feature of its dynamics. I will demonstrate a sensitivity of the model to even slight departures from symmetry in the autocatalytic reactions, using a detailed analysis of the stationary distribution of the fast process when the state of the slow process is fixed. This is joint work with Yi Fu, HyeWon Kang, Wasiur Khudabukhsh, Greg Rempala and Ruth Williams.

Speaker: Lea Popovic (Concordia University)

11:40 AM Noise induced stabilization in stochastic chemical reaction network.

Chemical reaction networks (CRNs) are commonly analyzed through deterministic or stochastic models that track molecular populations over time. In regimes with large molecule counts, stochastic dynamics are typically approximated by deterministic mass-action kinetics. We present a CRN that defies this expectation: while the deterministic system is unstable, exhibiting finite-time blow-up of trajectories within the interior of the state space, its stochastic counterpart is positive recurrent.

Speaker: Lucie Laurence (Bern University)

10:40 AM → 12:00 PM Automated discovery of dynamical digital twins from time series

10:40 AM Sparse identification of renewal equations with application to disease transmission dynamics

Data-driven model discovery has become a powerful approach for identifying governing equations of dynamical systems using temporal data. The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, initially developed for ordinary differential equations (ODEs) \cite{bpk16}, has been extended to more general classes of problems, recently including also deterministic and stochastic delay differential equations with discrete delays \cite{bbt24,bcd26,pec25}. However, its application to systems with distributed delays and renewal equations remains unexplored.
Distributed delays, at the core of renewal-type integral equations, involve integration over a continuum of past states. Related models are prevalent in biological and ecological applications to describe, e.g., structured populations and epidemics. They portrait memory-dependent dynamics but are challenging to identify due to the inherent complexity of delay kernels and renewal processes. Building on the integral formulation of SINDy for ODEs, we propose a novel extension of the SINDy framework to recover the (possibly nonautonomous) kernel of distributed delays through the use of quadrature formulas. As such the new approach aims at providing a sparse interpretable model rather than just a black-box right-hand side.
We demonstrate the efficacy of the new method first on academic examples and then by applying it to real data of the transmission dynamics of Severe Fever with Thrombocytopenia Syndrome (SFTS) \cite{CSIAM-LS-1-2}, an emerging tick-borne disease.

Speaker: Dimitri Breda (University of Udine, Italy)

11:00 AM Discovering Dynamical Digital Twins from Time Series through Bayesian Sparse Regression

The automated discovery of dynamical digital twins from time series data, known as model learning, is a central challenge in systems biology, particularly in the presence of noise, partial observability, and limited data availability.

We recently conducted a comprehensive review of available methods for data-driven discovery of dynamical systems, and identified 117 algorithms based on either symbolic or sparse regression, which we evaluated across eight key biological and methodological challenges \cite{metayer2026data}.

We then propose a novel method based on sparse Bayesian inference that jointly estimates the structure and parameters of dynamical models while incorporating biological prior knowledge. The approach is specifically designed to integrate multi-condition data, as commonly encountered in biological experiments.

The method was first validated on simulated systems, where it exhibits robust performances in recovering interactions under multiple noise levels. It was then applied to circadian gene expression data from human lung cells to automatically infer the dynamical interactions between the clock and the innate immune receptor NLRP3. The ambition is to provide interpretable representations of the underlying biological processes and enable the exploration of system perturbations.

Overall, this work contributes to the development of automated pipelines for constructing biologically grounded digital twins, with potential applications in personalized medicine.

Speaker: Clémence Métayer (Institut Curie, INSERM U1331, Cancer Systems Pharmacology team)

11:20 AM Bayesian discovery of biochemical reaction networks from time-course data with projection predictive inference

Mechanistic ordinary differential equation models are central to systems biology, pharmacology and emerging dynamical digital twins, but they are still commonly built by hand through extensive literature review, manual specification of reaction mechanisms, and repeated parameter fitting. As biological datasets become larger and more diverse, this process becomes difficult to scale, motivating automated approaches to mechanistic model discovery.

We present a Bayesian framework for discovering biochemical reaction networks directly from time-resolved concentration data under mass-action kinetics. Starting from a library of candidate reactions, we infer parsimonious networks and rate parameters with full posterior uncertainty, using a projection-predictive search strategy in trajectory space that favors compact reaction sets while preserving predictive dynamics. We demonstrate the approach on synthetic benchmarks and real biological time-course data, where it recovers interpretable reaction networks, while quantifying structural uncertainty.

This work contributes a biologically grounded route toward automated, uncertainty-aware inference of reaction networks from limited experimental data.

Speaker: Julien Martinelli (Aalto University)

11:40 AM Global modelling of algae blooms from time series: comparison of chaotic attractors

Global modelling such as GPoM \cite{Mangiarotti2012} is a tool for constructing systems of polynomial differential equations from time series. We present one use of this tool for variable selection. We study the bloom of the toxic algae (\textit{Ostreopsis} cf. \textit{ovata}) \cite{FabriRuiz2024} and look for strong relationships between the alga and its environment (from COPERNICUS datasets) through the lens of dynamics. Using time series, we have highlighted other links that exist between the proliferation of this algae and salinity, oxygen, or nutrient concentrations.

The second part of the talk is dedicated to the chaotic dynamics emerging from the numerous ordinary differential equations systems generated with GPoM. The comparison of models is performed using topological characterization of the chaotic attractors \cite{rosalie2016template, Rosalie2025}. It enables to reduce the number candidates to a smaller set of systems that are able to reproduce dynamics observed in the data. Structures of the polynomial models of ordinary differential equations systems will be discussed as well.

Speaker: Martin Rosalie (Université de Perpignan Via Domitia, France)

10:40 AM → 12:00 PM Collective dynamics at multiple scales

10:40 AM How perception and neural weighting can drive the geometry of decision-making in target pursuit

Recent research, grounded in experiments (notably by Iain Couzin and collaborators), has connected neural ring models of vision to how animals navigate a complex landscape of attractive targets. In this talk we investigate the mathematical and biological implications of a three-stage model where animals pre-process visual stimuli to identify a discrete set of targets, process this input to select the dominant targets, and then post-process this information to navigate the landscape. Incorporating finite target sizes and a neural density allows consistent target acquisition and pursuit reflecting what is seen in nature. Mathematically, we show this model corresponds to an energy minimization problem, simplifying both its analysis and numerical implementation. Biologically, we argue that the model reproduces experimental observations and presents a fairly direct pathway to decoding neural geometry via empirical data.

Speaker: Christopher Strickland (University of Tennessee, Knoxville)

11:00 AM Small Organism Collective Behavior in Fluid Environments

The movement and behavior of small organism collectives can often play a key role in ecosystem function. One example is marine larval plankton which are critical for the health of filter feeders such as coral reefs and jellyfish. However, holistic modeling of scenarios like these can be a difficult multiscale problem involving individual locomotion dynamics within larger-scale flows. To address this problem, Dr. Christopher Strickland has developed an open-source, agent-based modeling library in the Python programming language called Planktos. It is targeted at collective behavior in 2D and 3D fluid environments with immersed structures and readily interacts with computational fluid dynamics data generated externally. In this talk, I present mathematical models for collective behavior and then apply them to novel and biologically interesting scenarios involving fluid flows and immersed boundaries- all within the Planktos framework.

Speaker: Margie Knight (University of Tennessee, Knoxville)

11:20 AM Pattern formation through collective behavior in plant pigment systems

Anthocyanins are glycosidic flavonoid pigments responsible for most of the red, purple, and blue colors in flowers, fruits, leaves, stems, bracts, seeds, and pollen. These multifunctional secondary metabolites reside primarily in epidermal vacuoles and act as antioxidants, providing photoprotection, contributing to wound healing, and offering freeze protection. In the crowded vacuolar environment (pH 3–6), anthocyanins undergo a complex series of molecular transformations governed by pH, metal ions, copigments, and concentration. Color is determined by kinetic and thermodynamic relationships among anthocyanin species, as well as by concentration-dependent associative self-assembly.
Microscopic analysis of live epidermal cells reveals multiple anthocyanic phases with sizes ranging from 1–10 μm. Self-assembly is driven by intra- and intermolecular π–π stacking, hydrogen bonding, ion pairing, and charge-shift interactions, leading to amphiphilic micelle formation. These associations can generate spatial patterning in petals. In our mathematical framework, pattern formation results from collective behavior due to emergent structures and pathways arising from interactions among many coupled species. We have also developed microfluidic, self-reporting spectroscopic methods to study these phase behaviors.

Speaker: Patrick Shipman (University of Arizona)

11:40 AM Data Assimilation and Model Selection for Collective Motion in Locust Swarms

In a striking example of collective behavior, swarms of locusts march in an apparently coordinated direction. Various swarm morphologies emerge in these groups that aid in feeding or migration, depending on the environment through which the swarm moves. However, unlike eusocial insects (such bees or ants) locusts have no social structure (or queen) to facilitate this directed motion. Instead, agent-based models with identical individuals are a natural lense with which to study the collective motion of locusts. In this talk, we will introduce a framework for evaluating the appropriateness of several models for individual interaction. The work is made possible by recent advances in the availability and magnitude of trajectory data on individual locusts within a swarm. We formulate a Bayesian particle filter to estimate parameters of a given model for individual interaction based on these data. We next conduct a simulation study using the given model with parameters from the posterior distribution. Finally, we compare quantities aggregated from the simulated data and the empirical data to determine if the model recreates similar collective motion.

Speaker: Rebecca Everett (Haverford College)

10:40 AM → 12:00 PM Modeling, Forecasting, and Management of Public Health and Ecological Threats

10:40 AM Mathematical Models for Understanding and Managing Biological Invasions

Invasive species pose major challenges for biodiversity and ecosystem management. In this talk, I present mathematical models to understand how biological invasions emerge, spread, and can be controlled. I first focus on early invasion stages, where stochastic effects are important, and discuss extinction probabilities and invasion thresholds. I then address invasion dynamics at larger spatial and temporal scales, with an application to the invasion of black cherry (Prunus serotina) in France, using an age-structured and spatially explicit model. I conclude with perspectives on spatial control strategies and coordinated management.

Speaker: Ousmane Ousmane Seydi (Université Le Havre Normandie, France)

11:00 AM A Hybrid Modeling Framework for Forecasting the 2025 Texas Measles Outbreak and Evaluating Vaccination Strategies

In this talk, we discuss a hybrid modeling framework to analyze measles transmission and vaccination strategies during the 2025 Texas outbreak. A deterministic model incorporating single- and double-dose vaccination with vaccine efficacy was calibrated to reported Texas measles data from January 20 to May27, 2025. To complement the mechanistic analysis, time-series forecasting methods, Facebook Prophet and a Gated Recurrent Unit are applied to predict daily new cases. The Prophet model outperforms the GRU based on standard performance metrics. Both models project continued low-level transmission, with an estimated average of 1–2 daily cases (95% CI: 1–2) through August 30, 2025, in the absence of additional interventions. These results highlight the importance of maintaining high vaccination coverage to prevent future outbreaks and reduce the risk of measles endemicity in Texas.

Speaker: Chidozie Williams Chukwu (Georgia Southern University, Statesboro Georgia, USA)

11:20 AM Coupled Dynamics of COVID-19 and Drug Overdose Deaths

The simultaneous escalation of COVID-19 and drug overdose deaths motivates the development of mathematical frameworks capable of capturing interacting population-level processes across disparate time scales. We propose a coupled dynamical systems formulation that represents the joint evolution of an infectious disease process and a mortality process associated with substance use. The framework allows interactions to be encoded through coupling operators, time-dependent forcing, and feedback mechanisms arising from behavioral and structural drivers. The formulation is amenable to analytical investigation, including questions of well-posedness, stability, and sensitivity to perturbations, and provides a basis for integration with data assimilation. This work establishes a general mathematical foundation for studying the dynamics of co-occurring public health crises.

Speaker: Folashade Agusto (University of Kansas, USA)

11:40 AM Asymptotic behavior of an epidemic model with infinitely many variants

We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number R0 of the pathogen can be defined in that case and corresponds to a threshold between the persistence ($R_0 > 1$) and the extinction ($R_0 \leq 1$) of the pathogen. When $R_0>1$ and the maximal fitness is attained by at least one variant, we show that the systems reaches an equilibrium state that can be explicitly determined from the initial data. When R0>1 but none of the variants attain the maximal fitness, the situation is more intricate. We show that, in general, the pathogen is uniformly persistent and all families of variants that have a uniformly dominated fitness eventually get extinct. We derive a condition under which the total mass of pathogens converges to a limit which can be computed explicitly. We also find counterexamples that show that, when our condition is not met, the total mass of pathogen may converge to an unexpected value, or the system can even reach an eternally transient behaviour where the mass oscillates between several values. We illustrate our results with numerical simulation.

Speaker: Quentin Griette (Université Le Havre Normandie, France)

10:40 AM → 12:00 PM Molecular Computing: Theory and Implementations

10:40 AM From CRN to CNN: Deep Learning with Stochastic Chemical Reaction Networks

Advances in deep neural networks (DNNs) have revolutionized our ability to model complex data via the capacity to approximate continuous functions with arbitrary accuracy. DNN models have been used to achieve or surpass human-level performance in tasks such as image classification, generative modeling, and scientific discovery. Recent studies of chemical reaction networks (CRNs) suggest similar potential; for example, it has been shown that stationary distributions of particular stochastic CRNs can closely approximate any distribution on the nonnegative integer lattice \cite{cappelletti_stochastic_2020}.

To explore this potential, we develop well-mixed stochastic CRN models with mass-action kinetics whose equilibrium behavior enables accurate image classification and realistic image generation. We construct our models as multilayer regulatory cascades with network motifs implementing standard neural network operations such as convolution, pooling, and nonlinear activation. To efficiently calibrate and evaluate these models, we apply the linear noise approximation (LNA), which provides a second-order approximation of the system size expansion of the chemical master equation (CME). We benchmark the ability of our models to classify and generate realistic images of handwritten digits based on the classic MNIST dataset, showing performance competitive with that of DNNs. Our results underscore the ability of CRNs to be universal approximators and suggest new methodological innovations for modeling complex data.

Speaker: Bernie Daigle (The University of Memphis)

11:00 AM Buffered Chemical Reaction Networks for Reusable Computation

Synthetic chemical reaction networks (CRNs) typically operate in closed systems with finite reactants, limiting most circuits to a single round of computation. This constraint prevents sustained dynamics such as repeated execution of Boolean logic.

Here a simple motif, called a CRN buffer, is described that enables repeated circuit operation. CRN buffers consist of high concentration reversible reactions, analogous to acid-base pH buffers, and can maintain the availability of species by reversible activation and deactivation. As long as the buffer concentration remains high, circuits continue to operate over multiple cycles.

We show theoretically how this motif extends a range of chemical computations from single-use to multi-cycle operation, enabling reusable digital logic, sequential logic, sustained analog arithmetic, robust oscillators, and stable reaction-diffusion systems that can maintain spatial patterns over extended durations.

We then present preliminary experimental implementations using DNA strand-displacement (DSD) reactions, including a simple DSD reaction that operates for ten cycles. Our experimental results incorporate recent advances in circuit preparation that reduce leak in high-concentration regimes, enabling reliable operation under the conditions required for buffering.

Buffered reaction networks provide a general strategy for sustaining chemical computation, enabling chemical circuits to operate for many cycles in closed systems.

Speaker: Dominic Scalise (Washington State University)

11:20 AM Event-based reservoir computing via chemical reaction networks

We investigate a reservoir computing framework based on unimolecular (linear) chemical reaction networks. While the mean-field dynamics are linear, stochastic dynamics can induce richer input–output behaviour through long-time statistics. Using tools from ergodic theory and reaction network structure, we study how such systems generate feature representations and assess their expressive potential under simple readouts, with preliminary indications of universal approximation under suitable conditions. These observations suggest that stochasticity and long-time behaviour can enable nonlinear computation within structurally simple biochemical systems.

Speaker: Jinsu Kim (Pohang University of Science and Technology)

11:40 AM Heterochiral DNA for intracellular computing

Many societal challenges, including the diagnosis and treatment of disease, can be tackled by harnessing the unique capabilities of biology. A key goal in biomedical engineering is to improve human health via personalized biomedicine, which promises targeted treatment guided by the patient's physiology. To this end, I work to engineer and build programmable biological systems for autonomous sensing, decision-making, and response in living organisms, combining experimental validation with formal computational methods for the specification, compilation, and verification of designs. In this talk, I will outline some of my contributions, focusing on the use of heterochiral DNA, which combines both naturally occurring D-DNA and chiral mirror image L-DNA, to build robust nanodevices for sensing and decision-making in the harsh environment of a living cell. My work has shown that DNA strand displacement reactions can be used to translate nucleic acid signals between chiralities \cite{LakinMR:robhsd}, and that L-DNA can be used to protect D-DNA molecular components from degradation in biological environments \cite{LakinMR:prohdn,LakinMR:degilh}. I will also discuss some preliminary work on the transfection of heterochiral components into living mammalian cells \cite{LakinMR:hetmer}.

Speaker: Matthew Lakin (University of New Mexico)

12:30 PM → 2:30 PM SMB Business Meeting

Speaker: Reinhard Laubenbacher (University of Florida)

2:30 PM → 4:30 PM BMB Board Meeting

Speaker: Matthew Simpson (Queensland University of Technology)

3:00 PM → 4:20 PM Reaction Networks in Modern Mathematical Biology

3:00 PM Thermodynamics of Chemical Reaction Networks: From Circuits to Metabolism

After a brief overview of the thermodynamic framework for open chemical reaction networks (CRNs) \cite{Rao2016}, I will introduce a circuit-theoretic approach that provides thermodynamically consistent schemes for coarse-graining CRNs \cite{Avanzini2023}. I will then illustrate how this framework can be used to analyse energy transduction in metabolic networks, emphasising how network structure constrains pathways of free-energy conversion and shapes their efficiency and regulation in biological systems \cite{Wachtel2022,Bilancioni20251,Bilancioni20252}.

Speaker: Massimiliano Esposito (University of Luxembourg)

3:20 PM Hypergraph-based models of random chemical reaction networks: Conservation laws, connectivity, and percolation

Random graph models have been instrumental in characterizing
complex networks, but chemical reaction networks (CRNs) are better
represented as hypergraphs. Traditional models of random CRNs often
reduce CRNs to bipartite graphs, representing species and reactions as
distinct nodes, or simpler derived graphs, which can obscure the
relationship between the statistical properties of these
representations and the physical characteristics of the CRN. We
introduce a straightforward model for generating random CRNs that
preserve their hypergraph structure and atomic composition, enabling
the direct study of chemically relevant features. Notably, our
approach distinguishes two notions of connectivity that are equivalent
in graphs but differ fundamentally in hypergraphs. These notions
exhibit percolation-like phase transitions, which we analyze in
detail. The first type of connectivity has relevance to steady-state
synthesis and transduction, determining the effective reactions an
open CRN can perform at steady state. The second type is suitable to
identify which species can be produced from a given initial set of
species in a closed CRN. Our findings highlight the importance of
hypergraph-based modeling for uncovering the complex behaviors of CRNs.

Speaker: Nahuel Freitas (University of Buenos Aires)

3:40 PM Positive algebraic geometry for mathematical biology

Power-law dynamical systems are widely used as models in chemistry and biology (e.g., in ecology and epidemiology), as well as in economics and engineering. We study positive solutions to parametrized systems of generalized polynomial equations (with real exponents) in abstract terms. In particular, we identify the relevant geometric objects: the coefficient polytope, the monomial difference, and the monomial dependency subspaces.

Using only linear algebra and polyhedral geometry, we rewrite these polynomial equations and inequalities in terms of binomial equations. The resulting solution sets are then studied using analytical methods; for example, we characterize unique existence for all parameters using Hadamard’s theorem. Furthermore, we revisit mass-action systems that are decomposable and essentially univariate, providing an extension of the classical deficiency one theorem.

Speaker: Stefan Müller (University of Vienna, Faculty of Mathematics)

1. Parametrized systems of generalized polynomial inequalities

2. Existence of a unique solution for all parameters

3. Decomposable and essentially univariate mass-action systems

4:00 PM Widespread biochemical reaction networks enable Turing patterns without imposed feedback

Understanding self-organized pattern formation is fundamental to biology. In 1952, Alan Turing proposed a pattern-enabling mechanism in reaction-diffusion systems containing chemical species later conceptualized as activators and inhibitors that are involved in feedback loops. However, identifying pattern-enabling regulatory systems with the concept of feedback loops has been a long-standing challenge. To date, very few pattern-enabling circuits have been discovered experimentally. This is in stark contrast to ubiquitous periodic patterns and symmetry in biology. In this work, we systematically study Turing patterns in 23 elementary biochemical networks without assigning any activator or inhibitor. These mass action models describe post-synthesis interactions applicable to most proteins and RNAs in multicellular organisms. Strikingly, we find ten simple reaction networks capable of generating Turing patterns. While these network models are consistent with Turing’s theory mathematically, there is no apparent connection between them and commonly used activator-feedback intuition. Instead, we identify a unifying network motif that enables Turing patterns via regulated degradation pathways with flexible diffusion rate constants of individual molecules. Our work reveals widespread biochemical systems for pattern formation, and it provides an alternative approach to tackle the challenge of identifying pattern-enabling biological systems.

Speaker: Tian Hong (UT Dallas)

3:00 PM → 4:20 PM Behaviour and Individuality in Population Level Epidemiological Models

3:00 PM The effectiveness of non-pharmaceutical interventions against COVID-19

We have developed and age and immunity-structured model of COVID-19 infections and interventions. We have employed this model to assess the effectiveness of vaccination and various non-pharmaceutical interventions (school closure, work-from-home, closing of public places) in reducing COVID-19 spread and the healthcare demand. In this presentation, we will share our results for Canada (Ontario), USA (Utah, Washington, New York), Sweden, Hungary, and Italy.

Speaker: Jane Heffernan (York University)

3:20 PM Infectious disease surveillance using deep learning models

Social media data has become increasingly used to monitor infectious diseases. This presentation will showcase case studies on Mpox and Lyme disease, demonstrating how social media data can support the prediction of cases and other disease-related characteristics.

Speaker: Bouchra Nasri (Université de Montréal)

3:40 PM Cross-border transmission, vaccination heterogeneity, and structural inequity during the 2025 measles outbreak in Chihuahua, Mexico

In early 2025, a measles outbreak emerged in West Texas, USA, and spread into northern Mexico, with Chihuahua becoming the epicenter of Mexico's largest measles resurgence in decades. The outbreak affected Mennonite colonies, Indigenous Rar\'amuri (Tarahumara) communities in the Sierra Tarahumara, and highly mobile agricultural worker populations.
We analyzed municipality-level confirmed case counts in Chihuahua using a generalized logistic growth model to estimate early epidemic growth rates and characterize deviations from exponential growth. Uncertainty was quantified by bootstrap resampling under a negative binomial observation model. We linked epidemic dynamics to structural deprivation using hierarchical clustering based on poverty municipal indicators. To conceptualize cross-border coupling under heterogeneous immunization, we summarize a two-population vaccination model.

Speaker: Jorge Velasco (UNAM)

3:00 PM → 4:20 PM Computational and Theoretical Advances in cfDNA and ctDNA Modeling

3:00 PM Mechanistic modeling of joint size-dependent cell-free DNA concentrations and tumor kinetics for immunotherapy resistance prediction

Plasma cell-free DNA (cfDNA) shows promise as a predictive biomarker of treatment resistance in cancer patients. However, the mechanisms governing its production, fragmentation, elimination, and their relationships with tumor burden and disease progression, remain poorly understood. We developed a mechanistic model jointly describing the dynamics of short (75-<580 bp) and long (≥580-1650 bp) cfDNA fragments alongside tumor kinetics in 112 advanced cancer patients receiving immune checkpoint inhibition, using a population modeling approach, to characterize inter-individual variability in cfDNA kinetic parameters. The model captured complex longitudinal cfDNA patterns, including early treatmentassociated spikes. Analysis revealed substantial inter-patient variability and demonstrated a 7.4-fold higher shedding rate for short versus long fragments. A model-derived parameter estimated at 6 weeks of treatment—reflecting increased release or reduced elimination of short fragments—was significantly associated with progression-free survival (PFS, HR=1.6, 95% CI: 1.2–2.2, p=0.001). Incorporating this parameter to baseline clinical variables significantly improved PFS prediction (C-index: from 0.78 [95% CI: 0.73-0.89] to 0.80 [95% CI: 0.74-0.90], p<0.0001). This framework provides quantitative insights into cfDNA biology and o ers a noninvasive approach for early prediction of treatment resistance, with implications for adaptive therapeutic strategies from longitudinal liquid biopsy.

Speaker: Linh Nguyen Phuong (INRIA)

3:20 PM ctDNA precedes imaging: A predictive model for real-time treatment adaptation in HPV-associated anal squamous cell carcinoma

Background: Real-time treatment response assessment in HPV-associated anal squamous cell carcinoma (ASCC) remains challenging. Traditional tumor volume measurements require serial imaging that is costly, time-intensive, and delays clinical decisions. Circulating tumor DNA (ctDNA) offers a more accessible, real-time alternative biomarker, yet its predictive value for guiding treatment adaptation remains undefined.
Methods: We developed a mechanistic mathematical model of tumor volume-ctDNA dynamics using longitudinal data from 32 HPV-associated ASCC patients receiving pembrolizumab (every 3 weeks, up to 2 years). The model was fit across three scenarios: simultaneous measurements (8 patients), volume preceding ctDNA (14 patients), and ctDNA preceding volume (2 patients).
Results: ctDNA showed strong positive correlation with tumor burden and predicted clinical response within 4 weeks of treatment initiation. ctDNA kinetics preceded volume changes in multiple patients, providing early response signal before imaging confirmation. The model robustly captured heterogeneous patient dynamics across all scenarios.
Conclusions: ctDNA functions as a leading indicator biomarker for early treatment response identification in HPV-associated ASCC. Our framework translates this biomarker into actionable clinical predictions for real-time treatment escalation, maintenance, or de-escalation—replacing burdensome imaging with accessible blood-based monitoring, particularly impactful for underserved populations. Future studies will prospectively validate this model for personalized, adaptive treatment strategies.

Speaker: Phebe Havor (Moffitt Cancer Center)

3:40 PM Coupled SDE-ODE Modeling of Tumor-Immune Dynamics to Infer Biomarker Release

Tumor–immune interactions are central to cancer progression and treatment response, driving cell death through immune-mediated killing and resource-limited competition. In early-stage disease or following effective treatment, cancer populations are often small and difficult to observe directly. Disease monitoring therefore relies on biomarkers such as circulating tumor DNA (ctDNA) as noisy proxies for tumor size. Existing approaches lack robust frameworks to infer tumor burden from these signals near detection thresholds.

We present a coupled deterministic–stochastic framework linking tumor–immune dynamics to biomarker release. A two-prey, one-predator Lotka–Volterra model captures interactions between immune cells and competing tumor subpopulations under shared resource constraints. Biomarker production is modeled via stochastic differential equations driven by tumor cell death from immune-mediated apoptosis and competition-induced necrosis. We incorporate both square-root (CIR-type) noise, capturing count-limited fluctuations near detection, and multiplicative (geometric-type) noise, representing proportional variability at higher concentrations. We derive analytical expressions for biomarker trajectories and first-passage statistics, including mean detection times. Our results show how tumor heterogeneity, immune pressure, and stochastic variance structure jointly shape biomarker detectability.

Speaker: Pujan Shrestha (Texas A&M University)

4:00 PM Linking cfDNA clearance to fragment length with mechanistic models

Liquid biopsy studies consistently report both elevated circulating cell-free DNA (cfDNA) concentrations and shortened fragment lengths in cancer. These features are often attributed to tumor-specific processes, despite tumor-derived cfDNA frequently constituting less than 1% of the total. Here, we consider an alternative explanation: Saturation of cfDNA clearance, which prolongs cfDNA circulation time, increases exposure to plasma nucleases, causing fragments to shorten. By combining a mechanistic model of cfDNA fragmentation with analyses of two independent cancer patient cohorts, and publicly available clearance-perturbation experiments, we show that elevated cfDNA levels in cancer patients are accompanied by a characteristic leftward shift in fragment length distributions consistent with impaired hepatic clearance. This signature is highly correlated with cfDNA concentration, independent of circulating tumor DNA (ctDNA) fraction, and independently prognostic of patient survival. In contrast to hepatic clearance reduction, DNA-protecting antibodies cause a systematic rise in short cfDNA fragments. Our model allows us to directly identify the parameter governing fragmentation kinetics and predict the effect of antibody priming on cfDNA concentration. Together, these results identify saturating clearance as a central determinant of cfDNA abundance and fragment length. More broadly, they highlight the value of mechanistic modeling of clearance processes in extracting clinically meaningful signals from cfDNA fragmentation data.

Speaker: Thomas Rachman (Carnegie Mellon University)

3:00 PM → 4:20 PM Stochastic Modelling for Inference with Gene Expression data: Methods and Applications

3:00 PM Integrating Single-Cell Experiments and Stochastic Models to Infer a Predictive, Mechanistic Understanding for Glucocorticoid Receptor Transport and DUSP1 mRNA Expression Dynamics

Biochemical assays have made outstanding progress to elucidate how cells sense and respond to stimuli, but mechanistic and parametric uncertainties preclude quantitative predictions for the full spatial, temporal and heterogeneous responses of signal-activated gene expression. Stochastic models use random noise as an abstraction to account for unknown or uncertain dynamics. When inferred from appropriate single-cell experiments, such as smFISH or immunocytochemistry (ICC), these models can quantitatively predict complex biological responses in new environments. However, many smFISH/ICC experiments are possible for different induction levels, measurement times, or observables, and each may be time consuming, expensive, or subject to labeling, imaging, or data processing errors. We introduce the Finite State Projection based Fisher Information Matrix (FSP-FIM) as a rigorous guide for the design of single-cell experiments \cite{b}. We extend the FSP-FIM with empirical probabilistic distortion operators to account for unavoidable measurement errors. By analyzing different combinations of models, experiment designs, and data distortions, we discover practical working principles to simplify single-cell experiments while allowing for the use of inexpensive ‘crappy’ imaging conditions. We validate the FSP-FIM approach in HeLa cells using ICC data for glucocorticoid receptor transport and smFISH data for DUSP1 gene regulation upon stimulation with a synthetic corticosteroid.

Speaker: Brian Munsky (Colorado State University)

3:40 PM MS160-01

Speaker: TBA

4:00 PM Predicting Single-Cell RNA Expression Variability from DNA Sequence and Epigenetics

Single-cell technologies have unearthed vast heterogeneities in gene expression across cell populations. Understanding these cell-to-cell differences is essential for determining how DNA sequence specifies cellular function and drives phenotypic diversity. Recent advances in machine learning and AI have enabled the development of DNA sequence-to-expression prediction models. These models are typically trained on bulk expression data—how well they predict single-cell gene expression remains unclear. Here, we develop a joint machine learning and inference framework to parameterise stochastic models of transcription using biological features extracted from sequence-to-expression models and regress them against statistics derived from single-cell RNA-seq data. We further integrate epigenetic measurements, including DNA methylation and chromatin accessibility, to assess whether combining sequence and epigenetic information improves prediction of single-cell variability. We investigate the effects of technical sequencing noise and extrinsic biological variability on model performance, evaluating how well these approaches explain observed heterogeneity in single-cell RNA expression. This framework enables investigation of how mutations in DNA sequence influence regulatory dynamics in single-cell populations.

Speaker: Andrew Nicoll (University of Edinburgh)

3:00 PM → 4:20 PM Dynamics of Vector Populations and Pathogen Transmission

3:00 PM Unseen but not unstoppable: Quantifying the impact of human compliance and mass screening and treatment on cryptic asymptomatic malaria transmission

Abstract: Malaria, a mosquito-borne disease, is transmitted to humans by the bite of an infectious female Anopheles mosquito and remains a major global public health burden. As of 2024, malaria accounted for an estimated 282 million cases and 610,000 deaths worldwide. In malaria transmission dynamics, asymptomatic individuals play an important role. Although such individuals do not exhibit clinical symptoms, they may still carry malaria parasites in their blood and, hence, serve as a hidden reservoir of infection. Because they often do not seek treatment due to the absence of symptoms, they can remain infectious for relatively long periods, thereby allowing susceptible mosquitoes to acquire the parasite during blood feeding and subsequently transmit it to susceptible humans. Consequently, asymptomatic infections can sustain community-level malaria transmission, particularly in endemic regions, and thereby complicate malaria control and elimination efforts. In this talk, I will present a new deterministic mathematical model, formulated as a nonlinear system of differential equations, which incorporates the effects of human behavioral change and the detection and treatment of asymptomatic infections in assessing malaria transmission control.

Speaker: Arnaja Mitra (University of Maryland)

3:20 PM Decision-Support Modeling for One Health Pathogens: Using Mechanistic Models for Surveillance and Forecast Design

We present an in development simulation-based framework for evaluating inference and decision procedures in multi-host, One Health infectious disease systems. The framework integrates surveillance design, forecasting, and scenario analysis within a unified pipeline built around mechanistic transmission models that serve as synthetic data-generating processes and known ground truth. Structured multi-population differential equation models represent coupled human, animal, and vector dynamics, incorporating demographic turnover, trait structure, and spatial heterogeneity. Empirical estimates and expert elicitation inform parameterization, while a stochastic observation layer maps latent states to synthetic surveillance data through explicit reporting and sampling processes.
This generative environment enables systematic comparison of mechanistic, statistical, and machine-learning approaches under controlled observation error, partial observability, and model misspecification, with performance assessed using robustness and decision-relevant metrics. We illustrate the framework using a multi-host ODE-PDE hybrid model of Crimean–Congo hemorrhagic fever virus, a tick-born orthonirovirus, in Uganda, demonstrating the utility our our framework for studying identifiability, forecasting, and surveillance optimization across heterogeneous one-health systems.

Speaker: Joshua Macdonald (Johns Hopkins University)

3:40 PM Rethinking mosquito biting rates: exploring how disturbed blood-feeding shapes vectorial capacity

Mosquito-borne diseases are increasing in incidence and geographic range, renewing interest in how mosquito behavior shapes disease transmission. One unresolved issue is how disturbed feeding affects transmission. Many models assume that mosquito biting can be represented by a single, constant contact rate, implicitly treating feeding as instantaneous and always successful. In reality, defensive behaviors interrupt blood-feeding, causing a mosquito to leave without completing its blood meal. In this case, the mosquito may need to feed on additional hosts, thereby increasing the number of contacts per reproductive cycle. 

Combining laboratory experiments with mathematical modeling, this project revisits the common modeling assumption that biting should be represented by a single, constant contact rate. With video tracking, we measure how disturbance affects the duration and success of different feeding stages in Aedes aegypti. We track whether mosquitoes persist in feeding, abandon it, or otherwise change their behavior in response to disruption. The resulting measurements are used to parameterize a model that treats blood-feeding as a sequence of behaviors rather than as a single event. By focusing on variation in feeding behavior among individual mosquitoes, this study explores how disturbed feeding may influence vectorial capacity and outbreak risk. The study aims to connect individual-level behavior to population-level patterns of mosquito-borne disease transmission.

Speaker: Kyle Dahlin (Virginia Tech)

4:00 PM Variable impact of density-dependent life history traits on the success of mosquito population reduction strategies

Population growth is often mediated by density-dependent regulation, which can impact different life history traits, such as reproduction, development, or survival. The way and extent that density dependence alters these traits can substantially change population dynamics, which may have important consequences for control efforts. We develop an ordinary differential equations model including density dependence in various life history traits – reproduction of juvenile mosquitoes, development of juveniles to adults, and mortality of adult mosquitoes. We then examine how these various incorporations of density dependence affect the success of population reduction strategies mediated by the endosymbiont bacteria, Wolbachia. We use a combination of analysis and numerical simulations to show that when density dependence impacts the development of juvenile mosquitoes, Wolbachia-based control strategies may have the unintended effect of increasing population size. In contrast, when density dependence only impacts mortality or reproduction, Wolbachia-based control behaves as expected, reducing the mosquito population. Our results demonstrate that understanding how and to what extent density dependence alters various mosquito life history traits is crucial to unraveling the impacts of control efforts.

Speaker: Lauren Childs (Virginia Tech)

3:00 PM → 4:20 PM Symposium in memory of Professor Béla Novák

3:00 PM Thirty Years of Cell Cycling with Bela

In 1993, Novak & Tyson published a comprehensive model of M-phase control in frog egg extracts (J. Cell Sci. 106, 1153-1168). The model, soundly based on known molecular mechanisms, provided a unified understanding of cell-cycle transitions, mitotic oscillations, checkpoints, and wave propagation in frog eggs, yeast cells and fruit fly embryos. It made many non-intuitive predictions that were later confirmed experimentally. Later work by Novak, Tyson and their students and collaborators led to a general 'dynamical perspective for molecular cell biology,' based on detailed numerical simulations and generic bifurcation diagrams. In this talk, I will give a brief survey of how the theory developed over the intervening 30+ years.

Speaker: John Tyson (VirginiaTech, VA, USA)

3:15 PM Unlike networks, molecules are dreams - the early years of systems biology with Bela Novak.

In this presentation, I will start from my own experience in the lab of Bela Novak to discuss some results on cell cycle regulation, remember his figure as a mentor, and I will discuss the importance of doing basic science slowly and in depth. In particular, I will discuss the last stretch of 'hungarian years' in Bela's work (early 2000s up to 2007), when he had the freedom to do research in relative isolation and with little external pressure. This mostly theoretical work laid the ground for the very fruitful interactions with experimental biologists that took place in Oxford, which brought to Bela an even wider recognition among experimentalists.

Speaker: Andrea Ciliberto (IFOM)

3:30 PM Modeling the Cell Cycle: Reflections Inspired by Béla Novák

My scientific path has been deeply shaped by my collaboration with Béla Novák and John Tyson. Working on the early embryonic cycles of Drosophila melanogaster, I was introduced to a way of thinking that seeks simple, robust principles behind complex biological phenomena.
Beyond the specific results, Béla Novák’s approach, which combines conceptual clarity with biological insight, left a lasting mark on how I approach modeling. This influence continues to guide my work at Institut Curie, where I continue to explore the cell cycle in cancer. There, I have moved from deterministic ODE models toward a stochastic Boolean framework to better capture the heterogeneity and variability of tumor systems.
This presentation is both a reflection on our early work and a personal tribute to Béla’s enduring impact on our scientific thinking.

Speaker: Laurence Calzone (Institute Curie)

3:45 PM Positive feedback + negative feedback = “bloody complicated”

I started working with Béla as an undergraduate and remained in his lab for more than a decade, continuing to learn from him even until he left us. Together with John, he taught me how to analyse biological regulatory systems with both positive and negative feedback loops. The combination of these two can lead to fascinating dynamical behaviours. As Béla used to say: “it is bloody complicated” to understand what type of spatial and temporal pattern such combined systems might show. I will present biological examples showing how the combined effects of these two feedback types explain the observed behaviour.

Speaker: Attila Czikasz-Nagy (Pázmány Péter Catholic University Faculty of Information Technology and Bionics / Cytocast)

4:00 PM A systems biology study of autophagy induction playing a key role in survival upon cellular stress

As a PhD student, I began working with Prof. Béla Novák, and I learned virtually everything about the theoretical biology approach from him. The years I spent in his group at Oxford truly showed me how to combine theoretical biology techniques with molecular biology methods.

Later, I tried to apply this knowledge when I began studying autophagy induction at Semmelweis University. Although autophagy is traditionally classified as a cell-death mechanism, many scientific results have revealed that autophagy has an essential role in cellular survival upon various stress events (such as starvation or bacterial infection).

Our goal is to identify the essential regulatory motifs of autophagy control network and to explore their roles in cellular stress-induced life-and-death decision directly focusing on the inter- and intra-molecular-crosstalks of the system. By discovering the dynamics of the key feedback loops using both molecular and theoretical biological techniques, we try to understand how autophagy-dependent cellular survival can be extended.

Speaker: Orsolya Kapuy (Semmelweis University)

3:00 PM → 4:20 PM Multiscale perspectives on cancer resistance: from intracellular networks to population dynamics

3:00 PM Mechanistic modeling of psuedoprogression and circulating tumor DNA in immune checkpoint inhibitor treatment

Pseudoprogression is a confounding treatment response pattern characterized by apparent disease progression followed by eventual treatment response. Patients who eventually experience clinical benefit may be incorrectly classified as progressors by RECIST criteria, leading to premature cessation of treatment. The exact mechanism of pseudoprogression is not fully understood and existing mathematical models of treatment response often are unable to exhibit dynamics of pseudoprogression. We develop a novel mechanistic ODE model of tumor-immune dynamics and ctDNA shedding and in response to immune checkpoint inhibitor treatment that is capable of naturally exhibiting pseudoprogression. We then demonstrate how ctDNA dynamics may be able to distinguish pseudoprogressors from true progressors.

Speaker: Aaron Li (University of Minnesota)

3:20 PM Co-expression Networks in Cancer

Recent advancements in high throughput RNA sequencing technologies have generated unprecedented amounts of high-dimensional genomic data, enabling more detailed analysis. Techniques from network science are widely used to analyze such data, but face significant challenges. One shortcoming of these methods is that many of them use thresholding. The lack of consensus regarding the method for choosing the threshold value leads to substantial variability in downstream results and biological interpretations. Furthermore, many networks are constructed based on pairwise relationships between genes, disregarding potential contributions of higher order interactions. We explore Persistent Homology, a key method from Topological Data Analysis that quanti?es topological features across multiple scales and joint cumulants, that capture higher order dependencies, in order to address these limitations. We investigate advantages of using hypergraphs as a framework for modeling higher order interactions and the concept of Structural Balance as a method for incorporating edge sign information. We will present preliminary results.

Speakers: Bernadette Stolz (Max-Planck-Institut for Biochemestry, Am Klopferspitz 18, 82152 Martinsried, Germany), Britta Daub (MAX-PLANCK-INSTITUT), Daniel Roggenkamp (Max-Planck-Institut for Mathematics in the Sciences, Inselstraÿe 22, 04103 Leipzig, Germany)

3:40 PM Personalized treatment schedules for metastatic prostate cancer — A set of novel mathematical biomarkers

Adaptive therapy is an evolution-based treatment paradigm in metastatic cancer, which dynamically adjusts treatment to control, rather than minimize, tumor burden. Promising clinical results in prostate cancer indicate the potential of adaptive treatment protocols to delay relapse, but demonstrate broad heterogeneity in patient response. This naturally leads to the question: why does this heterogeneity occur, and is a ‘one-size-fits-all' protocol best for all patients?

Using a Lotka-Volterra model for tumor dynamics, we predict the expected benefit of adaptive therapy and extend this to a trio of mathematical biomarkers that can predict the time to progression and mean daily dose under a range of clinically realistic treatment protocols. Our mathematical framework accurately identifies patients with the greatest delay to progression, or reduction in mean daily dose, enabled by adaptive therapy. Our novel mathematical biomarker approach stratifies patients into distinct treatment protocols based on their initial treatment response, allowing for a personalized, mathematically informed approach to treatment scheduling.

Speakers: Alexander Anderson (Moffitt Cancer Center), Dr Jingsong Zhang (Department of Genitourinary Oncology, Moffitt Cancer Center, Florida, USA.), Kit Gallagher (Harvard Medical School), Maximilian Strobl (Imperial College & The Institute of Cancer Research, UK), Philip Maini (Mathematical Institute, Oxford University), Robert Gatenby

4:00 PM Modeling resistance multiverse: from metabolic activity to immune evasion

The words “resistance” and “relapse” are used interchangeably, and statements such as “treatment resistance remains a critical limitation to the success of cancer therapy” are flooding the introductions of research papers in (mathematical) oncology. Is this practice correct and appropriate? Does it matter in the clinic?

In this talk, I will contrast my preclinical research studies in targeted therapy (Non-Small Cell Lung Cancer) and radioimmunology (HPV+ Head & Neck cancer) to demonstrate that the distinction between resistance and relapse is not just semantics. A clear, measurable definition of resistant disease and how it’s different from therapy failure can change the disease management plan and outcomes.

Central to my message are the definitions of the terms “treatment resistance” and “treatment failure”. I will show how different mathematical and statistical models skew our perception of cancer treatment modeling, and what can be done to address such limitations. My conclusion is the word of caution and advocacy for a combination - a multiverse - of imperfect, yet complementary models to address the most urgent clinical needs in oncology.

Speaker: Malgorzata Tyczynska (MD Anderson Cancer Center)

3:00 PM → 4:20 PM Mathematical Insights into Ageing, Evolution, and Cell Dynamics

3:00 PM MS168-1

Speaker: Alexandre Perrrin

3:20 PM MS168-2

Speaker: Luce Breuil (Ecole polytechnique)

3:40 PM MS168-3

Speaker: Sarah Kaakai (Sorbonne Paris-Nord)

4:00 PM MS168-4

Speaker: Sylvie Méléard

3:00 PM → 4:20 PM Multicellular Modelling and Simulation Tools - The OpenVT Project

3:00 PM Compucell3D: Python-scripted open-source multiscale modeling framework

CompuCell3D is an open-source multiscale modeling environment for multicellular systems that combines biological realism, computational flexibility, and ease of learning. Based on the cellular Potts/Glazier-Graner-Hogeweg formalism, it supports explicit dynamic cell shape, adhesion, motility, growth, elastic solid-like junctions, filopodia, extracellular transport, and coupling to intracellular regulatory and signaling models encoded in SBML, Antimony, CellML, and MaBoSS. CompuCell3D has also evolved into a Python library, enabling interoperability with other Python-accessible modeling tools, and includes a Vivarium wrapper that allows it to serve as a component in the Vivarium ecosystem. Its high-level model specification, interactive tools, and multithreaded execution on multicore CPUs lower barriers to entry while supporting sophisticated multiscale applications.

Over the past two decades, CompuCell3D has been used in a broad range of applications, including embryonic development, morphogenesis, cancer, angiogenesis, immune response, viral infection, regeneration, tissue engineering, and toxicology. I will present the framework’s core ideas and distinctive capabilities, highlight representative applications, and describe current OpenVT efforts to create reference models supporting reproducibility and output comparability across CPM-based platforms such as CompuCell3D, Morpheus, Artistoo, and CHASTE. This work underscores the central role of open sharing, FAIR and CURE principles, and reproducible model exchange in building a robust community ecosystem for multicellular systems biology.

Speakers: James Glazier (Indiana University), Joel Vanin (Indiana University Bloomington)

3:20 PM Morpheus: User-friendly multiscale modeling

Collaborative modeling and simulation become increasingly important to study complex developmental processes across molecular to organism scales. To support interdisciplinary workflows in quantitative multicellular biology we designed the extensible open-source modeling framework Morpheus. It is centered around the cellular Potts model (cell behavior), allows for tight integration with intra-cellular regulation models (e.g. SBML) and fluently couples cells to neighboring cells and their extracellular environment (1,2,3).
A user-friendly GUI allows to formulate the multiscale models in an accessible modular modeling language (MorpheusML), rendering Morpheus applicable for a broad scientific community, beyond skilled programmers. Numerical simulations are automatically composed by extracting the graph of model components from the MorpheusML model definitions and scheduling suitable solvers in the simulator. The associated FitMultiCell toolbox supports parameter estimation for stochastic Morpheus models (4,5).
MorpheusML models can easily be exchanged, versioned, extended and shared through a FAIR model repository (6). It already presents more than 100 hundred models in valuable detail, the majority published in peer-reviewed journals.
(1) Starruß et al. (2014). Bioinformatics 30, 1331.
(2) Morpheus homepage: https://morpheus.gitlab.io
(3) Open source code: https://gitlab.com/morpheus.lab/morpheus
(4) Alamoudi et al. (2023). Bioinformatics 39, btad674.
(5) FitMultiCell toolbox: https://gitlab.com/fitmulticell/fit
(6) Model repository: https://morpheus.gitlab.io/models

Speaker: Jörn Starruß (TU Dresden)

3:40 PM PhysiCell: multiscale modeling with a grammar

PhysiCell (physicell.org) is an open source physics-based multicellular modeling framework. A cell is defined by a (off-lattice) centroid and volume and several phenotypic parameters that define its behavior (cell cycle, death, mechanics, motility, secretion, etc). It is bundled together with the BioFVM diffusion solver for cell secretion/uptake. PhysiCell has many predefined (but modifiable) model parameter values and several sample models bundled with the (C++/OpenMP and XML) software. A notable, recent addition is a simple English grammar that lets a modeler write rules that define cells’ behaviors based on one or more signals. PhysiCell also allows for intracellular models as addons, e.g., libRoadrunner for ODEs in SBML, and PhysiBoSS for boolean networks. PhysiCell Studio is a desktop GUI (written in Python) that makes it easier to build models and visualize simulation results. The Studio is also available as an interactive tool on the Web-based Galaxy platform. In this talk, I plan to show a live demo of immunology dynamics.

Speaker: Randy Heiland (Indiana University)

4:00 PM PolyHoop & SimuCell3D: Open-source tools for high-resolution cell dynamics

Cellular tissue simulations can be computationally demanding, which restricts them to simplified cell geometries and low spatial resolution. Here I present two recently introduced cell-based simulation programs written in C++, PolyHoop and SimuCell3D, which are designed to efficiently model cellular tissues with detailed subcellular resolution. PolyHoop simulates cellular monolayers in 2D using flexible hoops to represent individual cell membranes, while SimuCell3D models cell membranes, nuclei, and extracellular matrices in 3D using triangulated surfaces and an automatic cell polarization algorithm. Both tools are highly efficient, enabling simulations with many thousand deformable cells. They are open source, freely available, and easy to use. In this talk, I will give a short live demo that shows the tools in action in a typical scenario featuring a proliferating tissue.

Speaker: Roman Vetter (ETH Zurich)

3:00 PM → 4:20 PM Population level models of bacterial processes and interaction

3:00 PM Toward Sustainable Corrosion Control: Identifying tuning parameters associated with Biofilm-Induced corrosion Inhibition in a mathematical framework

Microorganisms play a pivotal role in corrosion processes, exerting profound effects on the integrity of metallic surfaces across agricultural machinery, transportation infrastructure, and energy systems, leading to substantial economic losses and environmental risks. Depending on the species and environmental context, microbial activity can either accelerate or inhibit corrosion, making their role complex and multifaceted. Understanding the interactions between biofilms, hydrogels, and metallic surfaces is essential for elucidating the mechanisms driving corrosion and for developing effective mitigation strategies. In this work, we introduce a mathematical biology framework for the study of Microbiologically Influenced Corrosion (MIC), based on a spatiotemporal modeling approach. This framework enables systematic investigation of how environmental factors influence microbial activity and corrosion dynamics, while also providing a platform for evaluating potential strategies to inhibit or control MIC. The approach integrates mechanistic modeling with predictive analysis, offering new insights into corrosion processes and informing targeted interventions.

Speaker: Blessing Emerenini (RIT)

3:20 PM A Predictive Model of Subaerial Biofilms: Insights into Daily Dynamics and Environmental Changes

Subaerial biofilms (SABs) are microbial communities on air-exposed surfaces that play key roles in biogeochemical cycling and deterioration of built heritage. Their activity and persistence strongly depend on environmental conditions, particularly moisture and carbon availability. A mathematical framework is presented to investigate SAB dynamics and ecology. The model describes SABs as thin mixed biofilm-water layers on stone surfaces and is based on ODEs governing the dynamics of key components - including cyanobacteria and heterotrophs - together with intracellular pools of carbon, nitrogen, and energy. These components interact through dominant metabolic pathways constrained by biotic and abiotic factors. Daily cycles of temperature, humidity, light, and CO$_2$ are incorporated to capture effects on water availability and metabolism.

Simulations explore SAB dynamics in a real-world context and reveal distinct daily windows of microbial activity primarily controlled by water availability and light. Heterotrophs contribute to SAB stability by recycling organic matter and regulating pH. The model assesses long-term stability under future environmental scenarios. While temperature increases alone produce limited effects on SABs, elevated CO$_2$ may enhance carbon fixation and productivity. Relative humidity emerges as the key factor regulating SAB viability through water availability.

Speakers: Alberto Tenore (Univ Naples), B Buttaro (Temple University), Fabiana Russo (University of Naples Federico II), Isaac Klapper (Temple University), J. Jacob (US National Park Service), J.D. Grattepanche (Temple University)

3:40 PM Aspects of Nonlinear Dynamics, Spatial Effects and Cellular Memory in Bacterial Quorum Sensing

Many bacterial species employ quorum sensing as a communication
mechanism to coordinate collective behaviours such as pathogenicity or
major lifestyle transitions. Gene regulatory networks govern these
processes, that typically involve coupled positive and negative feedback
loops, giving rise to nonlinear dynamics and, under suitable conditions,
bi- or multistability. Additionally, intervention strategies, including
classical antibiotics as well as quorum quenching, may play a role.
The diffusion of signalling molecules introduces an additional layer of
complexity. In particular, the coupling of nonlinear reaction kinetics
with diffusion processes naturally leads to reaction–diffusion systems,
in which spatial inhomogeneities can induce pattern formation,
travelling waves, or spatially heterogeneous switching between stable
states.
Beyond these effects, increasing evidence suggests that bacterial cells
can exhibit memory-like behavior, where prior exposure to signals or
environmental conditions influences current responses. From a modeling
perspective, such effects can be incorporated e.g. via additional
dynamical variables or delayed terms in the underlying nonlinear system.
Our aim is to analyse these mechanisms by combining dynamical systems
and reaction–diffusion approaches and to discuss the biological meaning
behind.

Speaker: Christina Kuttler (TU Munich)

4:00 PM Towards a mechanistic model of the mercury methylation process

Mercury methylation is a microbially mediated process that occurs in anaerobic soils, sediments, and at the water-sediment interface. Sulfur-reducing bacteria (SRB) uptake substrates, namely sulfate and dissolved organic carbon for growth, and transform inorganic mercury into methylmercury. Methylmercury is the most abundant and toxic organic mercury compound that bio-accumulates in tissues and bio-magnifies in the food chain. It is a neurotoxin that is a threat to all trophic levels and all stages of human life.

We present a model of the mercury methylation process that considers the governing chemical reactions; the production of methylmercury by SRB and the inhibition by sulfide, the product of the redox reaction that supports SRB proliferation, at high enough concentrations. In a first study, the model is studied in a chemostat setting. We perform model analysis and validation, and numerical simulation experiments to explore the system dynamics.

Speaker: Grace D'Agostino (University of Guelph)

3:00 PM → 4:20 PM Introduction to chemical reaction network modelling and simulation with Catalyst.jl

3:00 PM Introduction to Catalyst.jl and Applications in Chemical Reaction Network Modeling

Modern mathematical biology requires moving seamlessly from model construction to highly optimized simulation and deep mathematical analysis. In this first of two sessions, we introduce Catalyst.jl, a domain-specific language and symbolic modeling platform within the Julia SciML ecosystem designed for the rapid, intuitive modeling of complex biological networks. With a special focus on the newly released Catalyst 16, attendees will learn how to construct systems and automatically generate ordinary differential equations (ODEs), stochastic differential equations (SDEs), and jump processes models. We will highlight new Catalyst 16 capabilities such as adding coupled jump-diffusion equations, enabling the simulation of advanced systems like stochastic neuron models and reaction networks that include dynamic, fluctuating, cell volumes. We will also present performance optimization strategies for speeding up simulations.

Complementing basic model construction and simulation, we will demonstrate how Catalyst easily integrates with packages throughout the broader Julia ecosystem. First, we will consider how HomotopyContinuation.jl and Catalyst enable finding all of a model's steady states. Next, we will show how to compute bifurcation diagrams using BifurcationKit.jl. Finally, we will show how such packages can leverage Catalyst’s network analysis functionality, including the automatic detection and computation of conservation laws.

Speakers: Samuel Isaacson (Boston University), Torkel Loman (University of Oxford)

3:00 PM → 4:20 PM Progresses in Mathematical and Computational Immunobiology and Infections

3:00 PM KIRs and T cell dynamics

Studying immunology in humans is extremely challenging, for obvious ethical reasons. Mathematics, combined with experiment, can provide a unique and valuable insight. We will focus on a family of immune receptors called KIRs (killer immunoglobulin like receptors). We combine analysis of genetic data from large patient cohorts with mechanistic mathematical modelling and assays of in vitro and in vivo T cell dynamics to gain insight into the relationship between iKIRs, T cell dynamics and human health. We suggest that KIRs enhance T cell survival and that this in turn impacts on clinical outcome in viral infection (HCV, HTLV-1, HIV-1) and autoimmunity (type I diabetes).

Speaker: Becca Asquith (Imperial College London)

3:20 PM Modeling the Interferon Responses to Influenza A Virus Infection

Influenza A virus infections are a major cause of human morbidity and mortality worldwide. A key aspect of the immune response, bridging innate and adaptive immunity, is the role of interferons. Here, we present experimental data identifying the primary producers of Type II interferon and providing novel insights into production rates via the integrated Median Fluorescence Intensity. This approach offers a new modelling opportunity, allowing us to quantify production rates at the population level and uncover production and binding mechanisms that would likely be overlooked from population data alone. Building on these insights, we present a novel viral dynamics model that incorporates Type II interferon production and binding. Using this framework, we investigate how interferon responses may be associated with infection severity and consider potential binding mechanisms that could contribute to this relationship.

Speaker: Cailan Jeynes-Smith (Department of Pediatrics, University of Tennessee Health Science Center)

3:40 PM Towards a generalized framework for validating biological fidelity in immunobiological virtual patients

High-fidelity synthetic data is a critical frontier for
disease modelling, yet few generalized methods exist to quantify
whether generated virtual patients maintain physiological resemblance.
Building on our previous work in machine learning-enabled immune
profiling [1], we introduce a robust framework to assess the quality
of synthetically generated immunobiological datasets. We deploy
supervised and unsupervised generative methods, such as conditional
variational autoencoders (cVAEs) and Gaussian Mixture Models, to
generate virtual patients across multiple medical and immunobiological
datasets and develop an algorithm to assess synthetic data fidelity.
To determine ‘physiological resemblance’ between synthetic and real
data we implement a series of tests, including a
discriminator-as-evaluator layer in the algorithm. In this approach,
random forest (RF) classifiers are trained to distinguish real from
synthetic data, with classifier performance serving as a proxy for
generative success. When the classifier performs near chance, the
synthetic dataset is effectively indistinguishable from the real data.
Beyond straightforward validation, our framework provides diagnostic
feedback by identifying specific physiological deviations, such as
shifts in statistical properties or multidimensional
interdependencies, thereby allowing for the iterative refinement
towards high-fidelity virtual patients and ensuring transparency in
synthetic data applications.

[1] C.S. Korosec et al., Patterns, vol. 7, no. 3, Mar. 2026.

Speaker: Chapin Korosec (University of Guelph)

4:00 PM Novel regulators found by network perturbation of sex-specific influenza A infection in clinical samples

Cellular protein interactome data are fundamental to determine mechanisms of pathogens, infection progression, and potential drug targets. Performing network analysis provides a data-driven middle ground between differential gene expression analysis, which assumes that gene expression is largely independent, and highly detailed mathematical models, which require careful measurements or estimation of parameters from training data. In the absence of detailed mathematical behaviors, network analysis has been shown to outperform differential gene expression analysis when gene interactions cannot largely be assumed to be independent. Here we reanalyze influenza A infection of patient-derived epithelial cell lines that include treatment with a sex hormone, estradiol. We show that network analysis results are largely divergent from differential analysis; network analysis enriches for cell cycle and estrogen signaling pathways whereas differential gene expression enriches for methylation, programmed cell death and meiosis pathways. Half the transcription factors we uncover were previously unstudied in viral infection and only one was previously been implicated in coronavirus replication. Finally, our network analysis significantly identifies relevant host factors in viral replication screens. Thus, we reveal the role of hormones in influenza A viral infection by identifying key signaling proteins and 9 transcription factors using our network modeling approach.

Speaker: Jason E. Shoemaker (Department of Chemical and Petroleum Engineering, University of Pittsburgh)

3:00 PM → 4:20 PM Structural Approaches to the Dynamics of Chemical Reaction Networks

3:00 PM Manifold robust perfect adaptation and structural limits on steady-state reachability

Biochemical reaction networks often display robust responses to persistent perturbations despite high dimensionality, feedback, and uncertain kinetics. Classical robust perfect adaptation (RPA) captures one important mechanism: after sustained input changes, a designated output returns to a fixed steady state independent of perturbation magnitude. However, many cellular systems do not relax to a single adapted point. Instead, their steady states lie on lower-dimensional sets such as lines or planes, indicating regulation of relations between species rather than fixed absolute levels.

We introduce manifold robust perfect adaptation (manifold RPA), a framework in which persistent perturbations drive the system to an invariant manifold in steady-state concentration space. We show that manifold RPA can arise as a structural property of biochemical reaction networks and derive sufficient conditions for it without assuming specific kinetic forms. This yields a rigorous characterisation of adaptive behaviour that preserves ratios or linear relations among molecular species while allowing absolute concentrations to vary.

Our results extend the classical notion of adaptation and reveal structural constraints on steady-state reachability imposed by network architecture. This provides a principled explanation for non-pointwise steady-state responses in metabolism and signalling, and suggests a design principle for synthetic biological circuits requiring adaptive behaviour under relational, rather than fixed, targets.

Speaker: Ankit Gupta (ETH Zürich)

3:20 PM Biological functions and functional modules originated in structure of chemical reaction network.

In living cells, numerous chemical reactions are interconnected by sharing substrates and products, forming a reaction network. Various functions of cells emerge from dynamics of such interconnected system. Cells regulate amount of key chemicals by controlling amount/activity of enzymes, thereby achieving control of cellular functions. However, in such an interconnected system, can different chemicals responsible for different biological functions be controlled independently? We mathematically demonstrate that “modularity”, where parts of a system are controlled independently of others, arises solely from network topology. We found that the qualitative response of chemical concentrations to changes in enzyme amount/activity are localized to finite ranges in a network, and each range is determined by a subnetwork called a “buffering structure”, that is defined by the equation $\chi≔-$(# of chemicals)$+$(# of reactions)$-$(# of cycles)$+$(# of conserved quantities)$=0$ from local topology of a network. Using the cell cycle system as an example, we show that buffering structures actually exist in living organisms, performing important roles. In the cell cycle, the G1-S and G2-M transitions are strictly controlled by distinct protein complexes, requiring the activation of different complexes at different phases. Analysis of the cell cycle network revealed that the two complexes belong to different buffering structures. Moreover, by comparing theoretical predictions with experimental verification, we theoretically predict the necessity of an unknown reaction and experimentally confirm it.

Speaker: Atsushi Mochizuki (Kyoto University)

3:40 PM Monomial parametrizations and absolute concentration robustness in reaction networks

In this talk I will share recent results on how to detect whether a reaction network with mass-action kinetics admits a monomial parametrization or displays absolute concentration robustness. When requiring that either property arises in an open subset of parameter space, both problems can be approached by an initial check using linear algebra, and a second check where a more detailed analysis of the steady state variety is required. The linear algebra check provides a necessary condition, and therefore lack of both properties can be easily detected in many cases.

Speaker: Elisenda Feliu (University of Copenhagen)

4:00 PM Cycling Reaction Network Robustness Analysis

Cycling reaction networks are ubiquitous in nature,
underpinning key processes such as the Krebs and Kelvin
cycles. In this talk, we analyze the robustness of such networks.
Under the regularity assumption—that all supplied species are
subject to degradation—we show that the dynamics converge to
a consensus state, where all external and internal flows equalize
while species concentrations remain bounded. Our proof relies
on a suitably constructed piecewise–linear Lyapunov function
in the reaction rates. The non-regular case is substantially more
delicate, since concentrations of external species may diverge.
We show that all internal reaction rates still converge to a consensus
value. If the concentration of the minimal-input node remains bounded,
the consensus value coincides with the minimal input. Otherwise,
the rates converge to a common value that does not exceed it

Speaker: Franco Blanchini (University of Udine)

3:00 PM → 4:20 PM Newtonian and non-Newtonian Biofluidmechanics: Integrating Theory, Experiments, Modeling, and Simulations

3:00 PM The Immersed Boundary Single-Layer (IBSL) method for reaction-advection-diffusion systems

The Immersed Boundary Method (IBM) is widely used in the simulation of systems involving fluid-structure interaction [1]. The ability to simulate problems involving complex, moving geometry using a simple, Eulerian grid has led to the use of the IBM for the study of many biomechanical and biophysical systems. However, the study of chemical systems often necessitates the ability to impose Neumann or Robin boundary conditions at irregular locations on the Eulerian grid. Here, we present a method for imposing Neumann and Robin boundary conditions within an IBM framework. The method leverages the single-layer formulation of boundary integral equations, and we therefore refer to it as the Immersed Boundary Single Layer (IBSL) method. It requires solving a larger, augmented linear system. However, this system is well-conditioned and can be solved with a small number of iterations of a standard Kylov method without preconditioning. We also present some convergence results, limitations, and use cases of our methodology.

Speaker: Owen Lewis (University of New Mexico)

3:20 PM Suppression of upstream swimming in shear flows by memory-mediated chemotaxis

Elongated microswimmers such as E. coli exhibit run-and-tumble dynamics that bias motion in response to chemical gradients. In confined pressure-driven flows, elongated swimmers also reorient along Jeffery orbits, spending extended periods oriented near the upstream or downstream direction. Near boundaries, this alignment leads to upstream swimming, contributing to contamination and surface colonisation [1,2].

In this work, we investigate the competition between shear-induced reorientation and finite memory chemotactic responses in confined flows. We show that strong chemotactic sensitivity amplifies temporal comparisons in chemical signalling, fundamentally altering the orientation phase space associated with shear-induced dynamics of near-wall swimmers. In particular, strong chemorepulsive cues at channel surfaces lead to the loss of longer upstream trajectories, inducing a transition from positive rheotaxis to downstreamdominated transport.

Chemotactic memory, when coupled with chemorepulsive surface cues, inhibits upstream contamination by progressively reducing the number of swimmers occupying upstream-oriented states. These results identify a general mechanism by which memory-driven chemotactic responses can be used to control microswimmer transport in flow, offering new design principles for limiting surface colonisation in microfluidic and biomedical environments, complementing existing studies of microswimmer–surface interactions and suspension dynamics [3,4,5].

[1] Rachel N. Bearon and Andrew L. Hazel. “The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel.” Journal of Fluid Mechanics 771 (2015): R3.
[2] Tolga Kaya and Hur Koser. “Direct upstream motility in Escherichia coli.” Biophysical Journal 102.7 (2012): 1514-1523.
[3] Smitha Maretvadakethope, et al. “The interplay between bulk flow and boundary conditions on the distribution of microswimmers in channel flow.” Journal of Fluid Mechanics 976 (2023): A13.
[4] Roberto Rusconi, Jeffrey S. Guasto, and Roman Stocker. “Bacterial transport suppressed by fluid shear.” Nature Physics 10.3 (2014): 212-217.
[5] Barath Ezhilan and David Saintillan. “Transport of a dilute active suspension in pressure-driven channel f low.” Journal of Fluid Mechanics 777 (2015): 482-522.

Speaker: Smitha Maretvadakethope (Imperial College London)

3:40 PM Mechanical Interactions between a Contact Lens and the Eye

Contact lenses are worn by millions of people worldwide to correct vision impairments. The mechanical interactions between the lens and the ocular surface are difficult to access in the clinic. We developed a mathematical model of the mechanical interactions between the lens and the eye to predict the ocular stress load due to contact lens wear.

The lens is modeled as a thin, axially symmetric, linear elastic material that conforms to the eye [1]. The eye is modeled as an axially symmetric, linear elastic material with spatially varying material properties. The eye and lens models are coupled non-linearly via the suction pressure under the lens [2]; we assume the thin tear film layer between the lens and the eye has a constant thickness. The coupled problem is solved by an iterative numerical algorithm using finite difference methods to approximate the lens mechanics and f inite element methods to approximate the eye. We have extended the model to account for the effect of intraocular pressure (IOP) on lens-eye interactions.

The model predicts that the center of the cornea (center of the eye) is negatively displaced (toward the inside of the eye), while the edge of the cornea is positively displaced and experiences the highest stresses. The final aim of this work is to improve contact lens design and the fitting process by predicting ocular deformations and ocular stress load before wearing a lens.

[1] Ross D.S., Maki K.L., Holz E.K., Existence theory for the radially symmetric contact lens equation, SIAM J. Appl. Math., Vol. 76(3), 827-844 (2016). https://doi.org/10.1137/15M1036865.
[2] Carichino L., Maki K.L., Ross D.S., Supple R.K., Rysdam E., Quantifying Ocular Surface Changes with Contact Lens Wear, Mathematical Biosciences and Engineering, Vol. 23(1), 172209 (2026). https://doi.org/10.3934/mbe.2026008.

Speaker: Lucia Carichino (Rochester Institute of Technology)

4:00 PM An immersed boundary model for fluid membrane interaction in the cochlea

The mammalian ear has a remarkable ability to distinguish sounds that differ only slightly in frequency, while at the same time amplifying these signals so that they can be converted into neural impulses. This fine-frequency tuning phenomenon is commonly attributed to some form of mechanical resonance within the fluid-filled cochlea (or inner ear), and more specifically to resonant oscillations in the basilar membrane (BM) that runs along the cochlear duct [2]. We extend a well-known immersed boundary model for fluid-structure interaction in the cochlea [1, 4] by incorporating a small-amplitude periodic internal forcing due to contractions of outer hair cells that are embedded within the BM structure and induce parametric resonance through periodic variations in the BM stiffness. A Floquet stability analysis demonstrates the existence of resonant (unstable) solutions for physical parameters typical of mammalian cochleas, and also exhibits travelling wave solutions that are consistent with other models and experiments [3]. We then describe more recent efforts to include the influence of Reissner's membrane, which is another much more flexible elastic structure that is typically ignored in other cochlear models. Numerical simulations validate the analytical results and support the hypothesis that fluid-mediated resonance may be a significant contributing factor in the active process that drives cochlear mechanics [5].

[1] Richard P. Beyer, Jr. A computational model of the cochlea using the immersed boundary method. Journal of Computational Physics, 98:145162, 1992.
[2] A. J. Hudspeth. Mechanical ampli cation of stimuli by hair cells. Current Opinion in Neurobiology, 7:480486, 1997.
[3] William Ko and John M. Stockie. An immersed boundary model of the cochlea with parametric forcing. SIAM Journal on Applied Mathematics, 75(3):10651089, 2015.
[4] Randall J. LeVeque, Charles S. Peskin, and Peter D. Lax. Solution of a two-dimensional cochlea model with uid viscosity. SIAM Journal on Applied Mathematics, 48(1):191213, 1988.
[5] Tobias Reichenbach and A. J. Hudspeth. The physics of hearing: Fluid mechanics and the active process of the inner ear. Reports on Progress in Physics, 77:076601, 2014.

Speaker: John Stockie (Rochester Institute of Technology)

3:00 PM → 4:20 PM Epidemiological-behavioural modelling to address health challenges

3:00 PM Integrating human behaviour and epidemiological modelling: unlocking the remaining challenges

The SARS-CoV-2 pandemic highlighted that epidemic models fail to incorporate data-driven and theoretical knowledge of behavioural response to pandemics. This gap is partially driven by the lack of quantitative models that can predict the adoption of behaviours across individuals and populations, particularly in new social contexts. Hence, there is a need to improve behavioural realism in integrated "epidemiological-behavioural" models.

We will first summarise our involvement in related events around epidemiological-behavioural modelling. That includes an upcoming Isaac Newton Institute Satellite programme on ‘Maths of Human Behaviour: modelling sociality, mobility and protectionism’ taking place during 20 July – 14 August 2026 at the University of Nottingham, UK (https://www.newton.ac.uk/event/mhb/).

Ed will discuss a perspective paper \cite{hill2024} highlighting: (i) the key role of interdisciplinary collaboration for integrating dynamic human behaviour into epidemiological models; (ii) interdisciplinary challenge areas in epidemiological-behavioural modelling; (iii) recommendations to make progress in each of the challenge areas.

Matt will then present work that investigates behavioural trends in testing behaviour for COVID-like illness \cite{ryan2025}. Matt will briefly describe how dynamic testing behaviour can be included into compartmental models and highlight key results from this modelling.

Speakers: Edward Hill (University of Liverpool), Matthew Ryan (Commonwealth Scientific and Industrial Research Organisation (CSIRO))

3:20 PM Epidemics Don’t Just Spread - People React: Modelling Behaviour in Real Time

Standard epidemic models tend to assume that human behaviour is fixed, rational, or slow to change. Reality is messier. During COVID-19 and beyond, behaviour has proven fast-moving, socially contagious, and often emotionally driven. People respond to risk, to each other, and to policy - sometimes amplifying interventions, sometimes undermining them. We present a modelling framework that treats behaviour as part of the epidemic system itself, not an external input. Transmission dynamics are coupled to time-varying behavioural indices (e.g. trust, adherence), which evolve through feedback from incidence, peer influence, and bounded policy responses. This creates a two-way interaction: epidemics shape behaviour, and behaviour reshapes epidemics. Using structured perturbations of behavioural drivers under realistic “policy budgets,” we generate ensembles of counterfactual scenarios and quantify uncertainty in outcomes such as peak incidence and healthcare demand. Even small shifts in behavioural response can produce large and nonlinear differences in epidemic trajectories, particularly around critical periods such as pre-peak intervention timing. The key message is simple: identical policies can lead to very different outcomes, depending on how people respond. By embedding behaviour directly into mechanistic models, we move towards a more realistic and policy-relevant understanding of epidemic dynamics - one where human response is not noise, but signal.

Speaker: David Haw (University of Liverpool, UK)

3:40 PM Modelling social influence through discussion-based contacts in coupled behaviour-epidemic models

Peer influence can act as an invisible force that promotes or hinders the adoption of health-protective behaviours. While traditional epidemiological models focus on physical contacts driving transmission, they often overlook the social interactions through which opinions and behaviours spread.

We use contact data from a multinational survey of over 22,000 respondents across six European countries to construct age-stratified matrices for disease transmission and social contagion \cite{offeddu2025advancing}, distinguishing physical from discussion-based interactions. We develop a stochastic SIR model in which adoption and abandonment of protective behaviours are mediated by discussion contacts and modulated by infection and recovery levels through non-linear responses.

Incorporating empirical discussion mixing into the model produces an earlier and sharper epidemic peak due to rapid behavioural uptake, followed by heterogeneous relaxation across age groups that generates a secondary wave absent under fixed adoption. Assuming the age structure of physical contacts for discussion yields epidemic trajectories that generally diverge from the empirical case, with more pronounced effects in some countries than others.

This data-driven framework captures peer-mediated behavioural contagion and shows how age-specific social influence can reshape both adoption and epidemic dynamics, underscoring its importance in fostering the uptake of protective behaviours.

Speaker: Elisabetta Colosi (Bocconi University, Italy)

4:00 PM Feedback loops in multi-season influenza vaccinations strategies

Annual vaccination remains the most effective intervention in reducing the burden of seasonal influenza epidemics. Considering vaccination strategies over multiple seasons could allow the identification of more effective interventions than those designed for a single season. The effect of vaccination depends on and changes both the immunological memory of the host population and the evolutionary pressure driving antigenic drift, creating a multi-season feedback loop in which current interventions influence future disease dynamics and vaccine performance.

In this talk, we explore such a multi-season feedback loop by considering how vaccination strategies targeting groups with different social contact patterns perform across multiple seasons. We explore if and when the dependence of vaccine efficacy on prior infection and vaccination history can change the relative effectiveness of targeting each group, as well as some structural trade-offs that emerge in long-term vaccination dynamics.

Speaker: Joel Winterton (University of Cambridge, UK)

3:00 PM → 4:20 PM Novel Approaches in Mathematical Biology

3:00 PM Hybrid Mechanistic-Machine Learning Frameworks for Personalized Oncology

Mathematical modeling in oncology frequently encounters a trade-off between the structural interpretability of mechanistic equations and the flexible predictive power of data-driven algorithms. While mechanistic models provide essential biological constraints, they are often subject to structural misspecification when faced with the high dimensionality of clinical heterogeneity. Conversely, purely statistical machine learning (ML) approaches lack the inductive biases necessary to generalize from the sparse and noisy datasets typical of clinical practice. This work presents a methodological framework that treats mechanistic models and ML as complementary components of a unified architecture. The use of ML to learn mechanistic model residuals is discussed, thereby augmenting the predictive accuracy of first-order mechanistic approximations. Hierarchical Bayesian modeling is examined as a robust approach for parameter estimation across patient cohorts, facilitating the personalization of mechanistic dynamics. Operator learning is investigated to map high-dimensional clinical data to patient-specific dynamics. Finally, the integration of reinforcement learning (RL) with mechanistic simulations is demonstrated, where the latter provides a biologically grounded environment for optimizing sequential treatment policies. By formalizing these hybrid methodologies, this work aims to contribute to the ongoing development of decision support tools in oncology.

Speaker: Alvaro Köhn-Luque (Oslo Centre for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo)

3:20 PM Deciphering antibody repertoire evolution using protein language models and B cell lineage inference

B cell selection and evolution are key processes in regulating successful adaptive immune responses. Recent advances in single-cell sequencing and deep learning strategies have unlocked new potential to study affinity maturation of B cells at unprecedented scale and resolution. To unravel the complex dynamics of B cell repertoire evolution during immune responses and to facilitate Protein Language Model (PLM)-guided antibody engineering, we created the R package AntibodyForests \cite{van_ginneken_delineating_2025}. AntibodyForests encompasses pipelines to infer B cell lineages, quantify inter- and intra-antibody repertoire evolution, and analyze somatic hypermutation (SHM) using PLMs and protein structure. Using AntibodyForests, we explore how general and antibody-specific PLM-generated likelihoods relate to features of in vivo B cell selection, evolution, antigen specificity and binding affinity \cite{van_ginneken_protein_2025}. We find that PLM likelihoods correlate with biologically relevant features including isotype and V-gene usage, mutational load, and SHM patterns. Additionally, we observed that mutating residues along evolutionary trajectories tend to have lower PLM likelihoods than conserved residues. These results indicate that PLMs could predict to what amino acid SHM will most likely mutate and at which position. Interestingly, our findings challenge in vitro observations \cite{hie_efficient_2024} by revealing a negative correlation between PLM likelihoods and antigen binding affinity in in vivo repertoires. In our exploitation of these discoveries using six different PLMs and varying sequence regions, we uncovered that the region of antibody sequence (Complementarity-Determining Region (CDR3) or full-length VDJ) provided to the PLM, as well as the type of PLM used, influences the resulting likelihoods. These comparisons emphasize the importance of PLM long-range interaction, potential training data biases, and pairing heavy and light chains. Together, these studies highlight the power of combining repertoire-wide phylogenetic inference with PLMs to better understand the principles governing antibody evolution and selection, and offer new tools for therapeutic antibody discovery and engineering.

Speaker: Daphne van Ginneken (Center for Translational Immunology, University Medical Center Utrecht)

3:40 PM Establishing a Taxonomy of Computational Modeling as the Foundation Towards Certifying Trustworthy Artificial Intelligence

There is a 30-year history and leadership in verification, validation, and uncertainty quantification (VVUQ) established by the U.S. Department of Energy National Nuclear Security Administration (NNSA) Labs to evaluate the credibility of computational models used in high consequence applications. Today, the U.S. National Institute of Standards and Technology has established the building blocks for trustworthy artificial intelligence (AI) in response to the advancements in machine learning (ML). In this presentation we describe ongoing work to certify the trustworthiness of ML models by establishing the credibility evidence for an epidemiology example that leverages hybrid models, that include neural network model-form error corrections, as a novel diagnostic to elucidate global versus local trends in complex dynamical systems. We will introduce the variability in trustworthiness evidence and credibility in ML models is based on their datasets, inference goals, and training algorithms. As new emerging AI technology continues to revolutionize advancements in scientific discovery and
computational modeling, we articulate the importance in establishing a taxonomy of computational models. Prioritizing a taxonomy of AI algorithms, we establish the principles of AI trustworthiness for a class of algorithms that are well suited to the application context and provide a framework for establishing a certification process.

Speaker: Erin Acquesta (Sandia National Laboratories)

4:00 PM Exploring the Spatial Dynamics of the Immune Response to Viral Infections

Respiratory viruses, such as influenza and SARS-CoV-2, pose significant global health threats. Mathematical models have been instrumental in understanding epidemiological spread and within-host viral dynamics. These are typically compartmental models that neglect spatial structure. In contrast, agent-based models (ABMs) enable the representation of localized, single-cell interactions and spatial structure within infected tissues. We developed a multiscale, spatial agent-based model in PhysiCell to investigate viral spread and immune dynamics within the lungs following influenza infection. In our model, cells are represented as off-lattice agents capable of migrating, proliferating, and exchanging substrates within the microenvironment. Viral propagation
and immune interactions are resolved at single-cell resolution, with diffusive transport coupled through BioFVM. We coupled viral dynamics to the spatiotemporal dynamics of immune cells, including macrophages, neutrophils, CD8+ and CD4+ T cells, dendritic cells, and key inflammatory mediators (i.e., cytokines, chemokines, IFN, ROS), to
quantify infection control and tissue damage. Using this framework, we characterized how inhaled virus spreads within lung tissue and how immune responses shape spatial infection patterns. By integrating spatial structure and cellular-level interactions within a
multiscale ABM framework, this work advances mechanistic understanding of within-host viral dynamics. Overall, spatially resolved modeling provides a computational platform for dissecting infection control mechanisms and supporting preparedness against emerging respiratory viruses, with potential applications in the pre-clinical
evaluation of therapeutic strategies.

Speaker: Fatemeh (Azade) Beigmohammadi (University og Montreal)

3:00 PM → 4:20 PM Cell Growth & Division: Connecting Phenomenology to Mechanisms

3:00 PM Effects of molecular noise on bacterial size control

Exponentially growing cells employ control strategies to maintain a stable size in the presence of noise. Phenomenological models provide important insights into these strategies, revealing classes such as "timer", "adder", and "sizer" control. However, these models necessarily ignore the molecular mechanisms needed to implement the strategy. I will describe our work showing that incorporating these mechanisms can change the model conclusions in important ways. For example, the sizer strategy is thought to minimize the noise in cell size. But using a mechanistic model where division is triggered at a molecular abundance threshold, we find that the adder strategy minimizes noise in cell size. The reason is that cell size noise inherits the molecular noise of the division mechanism. We derive a lower bound on size noise that agrees with publicly available data from six microfluidic studies on Escherichia coli bacteria. Our work connects molecular mechanisms to phenomenological modeling and reveals the consequences of noise propagating across scales.

Speaker: Andrew Mugler (University of Pittsburgh)

3:20 PM Cell growth under high antibiotic concentrations drastically reshapes the bacterial transcriptome

Bacteria exhibit remarkable phenotypic heterogeneity upon antibiotic exposure, induced by complex feedback mechanisms mediated by interactions between drug action, metabolism, gene regulation, and expression of resistance. However, how global transcriptional programs are rewired under drug stress in these different phenotypes remains poorly understood. In Escherichia coli, exposure to the translation inhibitor tetracycline was shown to produce distinct phenotypes with a range of growth rates, whose underlying transcriptional states have not been fully characterized. Here, we use RNA sequencing across nutrient and drug conditions to show that increasing tetracycline concentration leads to a progressive breakdown of transcriptional organization and the emergence of a disordered gene expression state. We find that exposure to intermediate tetracycline concentrations induce coordinated transcriptional changes consistent with the maintenance of homeostasis under the drug. In contrast, high drug levels trigger widespread dysregulation marked by increased transcriptional entropy, and the upregulation of stress and resistance functions at the expense of metabolism and growth. This work combines environmental perturbations with bulk transcriptomics to develop models explaining the progression of heterogeneous cellular states, providing insight into how bacteria persist in growth-limited, clinically relevant conditions.

Speaker: Daniel Schultz (Geisel School of Medicine)

3:40 PM Cell Size Regulation from Bacteria to Mammalian Cells

How cells regulate their size remains an open question. Cell-size regulation is commonly characterized by the Pearson correlation between birth and division sizes, with the corresponding regulation parameter α defined as one minus this correlation coefficient. Single-cell experiments provide generation-resolved measurements of birth and division sizes along individual lineages, typically across many lineages of varying lengths. The parameter α is usually inferred either by estimating it
separately for each lineage and averaging across lineages, or by fitting a single effective parameter to the pooled data across lineages. These two approaches are affected by distinct systematic errors: the lineage-wise estimator is biased for finite lineages, whereas the pooled estimator is biased by lineage-to-lineage variability arising from extrinsic noise. Moreover, both estimators are affected by different kinds of measurement errors. Here, we quantify the above-mentioned effects and develop a Bayesian framework to overcome these biases. Applied to synthetic and experimental cell-size data, this approach yields more reliable estimates from short and heterogeneous lineages and provides a principled way to distinguish among different size regulation strategies.

Speaker: Kuheli Biswas (Weizmann)

4:00 PM Essential Role of Extrinsic Noise in Models of E. Coli Division Control

Our understanding of cell division control still relies largely on interpreting correlations between phenomenological variables, with limited connection to the underlying molecular mechanisms.

In this talk, I present an analytically tractable stochastic threshold–accumulation model in which a size-dependent divisor protein triggers division upon reaching a noisy, autocorrelated threshold. This framework disentangles, within a unified theory, the roles of intrinsic and extrinsic noise, as well as key mechanistic features such as threshold reset and threshold memory. We show that these ingredients generate a much richer spectrum of behaviors than the commonly assumed adder, spanning continuously from timer to sizer-like strategies while modulating size fluctuations.

Comparison with single-cell E. coli data indicates that extrinsic noise and additional mechanistic ingredients are required to reproduce the observed variability. However, mechanisms that control fluctuations typically reshape the underlying division strategy. Strikingly, we identify a regime in which size fluctuations can be tuned independently of division control, preserving adder-like behavior even in the presence of extrinsic noise. This regime emerges from a balance between threshold correlations and threshold reset, extending the prevailing view that full reset is required for adder control. Altogether, this provides a direct mechanistic link between molecular noise and the emergent division laws observed in data.

Speaker: Mattia Corigliano (IFOM)

3:00 PM → 4:20 PM Mathematical and AI-enhanced computational models for sexually transmitted diseases and other public health threats

3:00 PM Development of agent-based modelling of STI’s: Can we use AI methods for improving implementation of partnership dynamics?

With the recent increase in computing power, agent-based simulations have become progressively more complex. There is a growing tendency to include greater detail of sexual networks, disease progression, and targeted interventions into STI models to answer relevant public health questions. However, increasing model complexity also amplifies data requirements, and often necessitates the integration of data from different sources for model parameterization. One key challenge in STI transmission modeling is the accurate representation of the dynamic partnership network. Formation and separation of partnerships depend on many factors, including demographics (age, sex), partnership history, infection status, and an individual’s perceived risk of acquiring infection. AI models offer a promising avenue to better integrate data analysis with agent-based modelling to link partnership dynamics directly to underlying determinants. In a first step to explore such a hybrid model, we integrated an XGBoost algorithm—trained on behavioural survey data—into a static network model to inform decisions of agents to engage in protective behaviour during an outbreak of a respiratory infection. We find that epidemic trajectories are influenced by underlying network structure as well as the adaptive behaviour of agents. For agent-based models of STI our approach may provide a flexible way to incorporate determinants of partnerships, predicting their formation or separation from behaviour surveys.

Speaker: Mirjam Kretzschmar (University Medical Center Utrecht)

3:20 PM Early-warning signals for infectious diseases with a social-media compartment

Early-warning signals (EWSs) are crucial tools for anticipating disease emergence and guiding public-health responses, but uncertainties in transmission and incomplete data can limit their reliability. Additionally, the performance of EWSs is rarely evaluated when disease emergence is delayed, and their use in the context of interactions between disease transmission and communication through social-media platforms has largely not been considered. We evaluate the relative performance of EWSs in predicting disease emergence under varying noise conditions and explore the use of EWSs with social-media dynamics to predict disease emergence. We develop a mechanistic model coupling infectious disease and social-media dynamics, introduce stochasticity and generate simulated time series. We detect changepoints, quantify delays relative to the bifurcation point and assess the performance of EWSs across different segments of the time series. The ``reporting" infected compartment proves most reliable, and variance outperforms autocorrelation in high-noise scenarios. However, in the social-media compartment, variance and autocorrelation have weak predictive power. Our work provides a framework to advance understanding of how EWSs can be applied to forecasting disease emergence, contributing to improved disease preparedness and response.

Speaker: Stacey Smith? (University of Ottawa)

3:40 PM Mathematical Modeling of Post-Infection Mortality and Transmission Structure: Implications for Persistent Infections and Public Health Dynamics

Post-infection mortality is an important yet often overlooked factor in epidemiological modeling, as it directly influences both disease prevalence and long-term population structure. In this work, we revisit and analyze compartmental models that explicitly incorporates post-infection mortality along with partial immunity, and we investigate how disease outcomes depend on the choice of incidence function. Under mass-action incidence, the inclusion of post-infection mortality can generate complex dynamics, including bifurcations that lead to recurrent outbreaks. In contrast, when standard incidence is used, such oscillatory behavior is greatly reduced or eliminated, and the system typically converges to a stable endemic state. Our results show that modeling post-infection mortality in combination with different transmission assumptions leads to markedly different qualitative and quantitative outcomes, underscoring its significance for understanding persistent infections and for guiding more realistic epidemiological predictions.

Speaker: Zhisheng Shuai (University of Central Florida)

4:00 PM Qualitative impact of political and economic decisions on PrEP users under HIV epidemic control

In this work, we explore the dynamics of a hybrid differential–difference system with delay describing a HIV SI-model with protected compartment (PrEP treatment) and a nonmonotonic recruitment rate. The limited protection duration offered induces a delay in the system. First, we study the existence of equilibria. Under our assumption, we show that the system exhibits several steady states without infection which challenges the study. After a local stability analysis of each equilibrium, we study the existence of Hopf bifurcation around the endemic equilibrium. Our results show that the delay may destabilize the endemic steady state and lead to the existence of recurrent periodic epidemic waves. Each situation is illustrated illustrate each situation.

Speaker: Gregoire Ranson (Claude Bernard University Lyon 1)

3:00 PM → 4:20 PM Modeling of protein dynamics with applications to Neurodegenerative Diseases

3:00 PM Mathematical models of brain networks: propagation of diseases and of brain activity

My talk will focus on developing mathematical and computational models that use the brain’s structural connectivity to predict the development of neurodegenerative diseases like Alzheimer’s. I will first describe our original proposal that Alzheimer's and other dementias are underpinned by misfolded pathologies that spread in the brain's structural connectome. This process can be mathematically captured by the so-called "Network Diffusion Model". Several examples from AD, ALS, Huntington's, Parkinson's, and other dementias will be demonstrated.
I will then present new extensions of this model in many meaningful ways, incorporating protein aggregation, clearance, active axonal transport, and mediation by external genes, cells, and neuroinflammation. Recent work on interactions between microglia, inflammatory signals, and cytokines will be presented. Deep neural network implementations of these complex and computationally prohibitive models will be motivated, and exciting new work on physics-informed neural networks that utilize neural operator learning will be presented.
I will also briefly describe recent work in modeling brain electrophysiology using similar graph spectral models. All above models centrally involve the brain’s complex network Laplacian eigen-spectrum and “graph harmonics.” Through this work, we have found significant differences in the model’s parameters that relate healthy brains to Alzheimer’s disease, sleep, epilepsy, and infant brain maturation. The related papers will be briefly highlighted.

Speaker: Dr Ahsish Raj (University of California, San Francisco)

3:20 PM Non-Linear Dynamics and Catalytic Exchange Govern Prion Assembly and Spreading

Prion fibril assemblies exhibit a strong structural and dynamical heterogeneity that cannot be described by classical linear polymerization models.
Using single-assembly imaging and bulk kinetic measurements, we show that fibrillar and oligomeric subpopulations coexist and continuously exchange material through catalytically mediated processes. At the population level, this exchange generates spontaneous depolymerization, damped oscillations, and multi-timescale relaxation dynamics, indicating that prion assemblies evolve far from equilibrium and form a non-linear dynamical system with multiple interacting species. These experimental observations provide quantitative constraints for a minimal kinetic framework based on catalytic feedback and exchange between subpopulations. Embedded in a reaction–diffusion setting, this framework was used to explore how non-linear replication dynamics shape prion spreading in tissue. The model reveals the emergence of attractor states, strain-dependent propagation regimes, and non-trivial strain interference and co-propagation, arising solely from kinetic non-linearities and feedback rather than tissue-specific templating. Overall, this work illustrates how experimentally grounded non-linear dynamics at the assembly level can control large-scale spreading and strain behavior.

Speaker: Dr Human Rezaei (INRAE)

3:40 PM A perinuclear crown of proteins as a biomarker for neurodegeneration syndromes

Since 10 years, our lab has been developing a mechanistic model of the individual stress response based on the nucleo-shuttling of the ATM protein kinase. First, the stress triggers the monomerization of the ATM protein proportionally to the stress dose. Second, the ATM monomers diffuse to the nucleus to trigger the DNA repair pathways. Any delay caused by some environmental molecules or overexpressed proteins that interact with ATM may lead to a well-described pathology. Interestingly, we have observed that perinuclear interactions of ATM lead systematically to syndromes related to aging or neurodegeneration. Indeed, a crown of complexes made of ATM and some other specific proteins or molecules may forbid the entry of the nucleus to ATM: as a consequence, DNA breaks are neither recognized nor repaired, and progressively, cells die via senescence. A mathematical model describing the formation of ATM crowns and the senescence of cells is proposed.

Speaker: Dr Nicolas Foray (INSERM)

4:00 PM ATM-ApoE crown formation in Alzheimer’s disease

Alzheimer’s disease (AD) is a neurodegenerative disorder, with current therapies primarily focused on symptom management. Recent studies have proposed the Radiation-Induced ATM NucleoShuttling (RIANS) response as a mechanism that involves the formation of a perinuclear crown (PC) and may impair DNA repair.
We present a mathematical framework to investigate this process. First, an ordinary differential equation (ODE) model is developed to analyze PC dynamics under constant and periodic oxidative stress. This model is used to simulate the effects of combined radiation and antioxidant/statin treatments. Second, we formulate a spatial model using partial differential equations (PDEs) that incorporates protein diffusion and advection. For this system with quadratic reactions, we prove the global existence and uniqueness of a non-negative solution, extending well-posedness results for non-autonomous reaction-diffusion-advection systems. Numerical simulations in two dimensions illustrate the behavior of the model.

Speaker: Felipe Olivares (Lyon 1 University)

5:00 PM → 6:20 PM Reaction Networks in Modern Mathematical Biology

5:00 PM Genetic recombination, deterministic reaction systems, stochastic partitioning, and Markov embedding

We consider the system of differential equations describing genetic recombination, which is well known to be equivalent to the law of mass action of a chemical reaction network \cite{Mueller_Hofbauer_15,Alberti_21}. It is equally well known that this nonlinear system can be solved via its dual process backward in time (see \cite{Baake_Baake_21} for a review). This dual process is a (linear) Markov chain in continuous time, which describes how an individual's genes are partitioned across its ancestors when looking back into the past.

We find an explicit representation of the semigroup of the partitioning process, and thus an explicit solution of the recombination equation, both for the simple case of single crossovers and for general recombination distributions. The latter works by representing the realisations of the partitioning process as trees and establishing an inclusion-exclusion principle for the decomposition of these trees into subtrees.

Based on the semigroup, we attack the embedding problem for recombination in discrete time, where the partitioning is described by a discrete-time Markov chain.
The embedding problem of Markov transition matrices into Markov semigroups is a classic problem that goes back to Kingman \cite{Kingman_62}; the question is whether a discrete-time Markov chain may be represented as the semigroup of a continuous-time Markov process. We solve the problem for short gene sequences and give an outlook to the general case.

Speaker: Ellen Baake (Bielefeld University)

5:40 PM A Graph grammar view on chemical reaction networks

I will introduce a graph grammar-based formalism to handle (bio)chemical reaction networks. The formalism provides a set of powerful techniques to specify, construct and analyze chemical reaction spaces. A chemical space is defined by a set of compounds and a "reaction chemistry" defined as a collection of graph transformation rules. This algebraic model of chemical transformation in combination with mathematical optimization techniques makes it possible to explore the bio-synthetic design space in a systematic manner. Questions such as "Does a specified chemical space harbor multiple, possibly competing, routes to a target molecule or harbors reaction motifs of interest?" is rephrased in the mathematical language of integer hyperflows on hyper-graphs offering an efficient way to identify functional networks in the chemical space, such as auto-catalysis, that conform to a formal flow specification. I will briefly touch the question of randomization of chemical reaction networks, and what needs to be preserved to remain during randomization in the realm of chemical reaction networks. If appropriate thermodynamic and kinetic parameterization is available, questions concerning the cost of maintaining pathways that run at a constant throughput can be asked. Finally, rule-base stochastic simulations of closed and open reactive system can be performed, allowing to discover mechanistic ideas how an event of interest, e.g. the construction of a particular molecule is achieved by the concurrent dynamic system.

Speaker: Christoph Flamm (University of Vienna)

A Software Package for Chemically Inspired Graph Transformation

Chemical Transformation Motifs - Modelling Pathways as Integer Hyperflows

Graph-based stochastic simulations of chemical reactive systems

Thermodynamic ranking of pathways in reaction networks

What makes a reaction network "chemical"?

6:00 PM From Mean Control to Variability Control in Biological Systems

Biological systems must maintain stable functions despite environmental perturbations and intrinsic molecular noise. Robust perfect adaptation (RPA) enables biological networks to restore their output to a desired level after disturbances. While antithetic integral feedback can guarantee adaptation of the mean output, it often amplifies stochastic fluctuations and therefore fails to control single-cell variability. In this talk, I present a mathematical framework that achieves noise-robust perfect adaptation, enabling simultaneous control of both the mean and variability of molecular outputs. The key idea is to combine a classical mean controller with a newly developed noise controller that regulates the second moment of the output species. This architecture allows stochastic biochemical networks to maintain both their mean and noise levels even after perturbations. We demonstrate how this framework stabilizes gene-expression dynamics and reduces failure rates in a model of the DNA damage response in E. coli. These results illustrate how mathematical modeling and stochastic control theory can provide new principles for regulating cellular variability in biological systems.

Speaker: JaeKyoung Kim (KAIST)

5:00 PM → 6:20 PM Behaviour and Individuality in Population Level Epidemiological Models

5:00 PM Qualitative impact of political and economic decisions on PrEP users under HIV epidemic control

The HIV/AIDS epidemic remains a major global health challenge, with no definitive cure currently available. Following the World Health Organization’s 2014 recommendations, a preventive treatment known as Pre-Exposure Prophylaxis (PrEP) has been adopted worldwide, introduced in France in 2016, to curb HIV transmission. We propose here a new compartmental epidemiological model that explicitly accounts for the limited duration of PrEP’s protective effect. The PrEP compartment is described by an age-structured hyperbolic equation, while initiation of PrEP use is governed by a differential equation. Together, these lead to a nonlinear differential–difference system with discrete delays. We analyze both local stability and global dynamics of the system. Using numerical simulations informed by data from the French population of men who have sex with men (MSM), we validate the accuracy of our model. In particular, we show that combining logistic time dynamics with a Hill-type function yields an excellent fit to the available data. The model is further extended by incorporating a variable force of infection among PrEP users, influenced not only by the size of the infected population but also by political and economic factors. This reflects the reality that socioeconomic constraints can restrict access to PrEP for part of the population. Finally, we investigate epidemic dynamics under a non-monotonic recruitment rate. Altogether, these results provide new insights into the potential trajectory of the HIV epidemic in France, under the assumption of sustained PrEP uptake within the population.

Speaker: Laurent Pujo-Menjouet (Lyon 1 University)

5:20 PM A Basic Reproduction Number for Pair Formation Models with Co-Infection

The basic reproduction number is a standard tool in disease modelling for determining the conditions under which a disease free equilibrium goes unstable and produces an epidemic. One popular procedure for determining this is the next generation matrix method. When this method is applied to models with pair formation, it is able to determine the stability threshold for the disease free equilibrium, but does not accurately compute the basic reproduction number. In this talk we show how to reconcile this by adapting the method to pair formation models. We extend this to the case where there are multiple diseases to consider via co-infection. We demonstrate that our modified next generation method recovers the basic reproduction number in a mathematical model of coinfection with mpox and HIV.

Speaker: Iain Moyles (York University)

5:40 PM Instabilities in a disease model incorporating compliance

Management of the COVID-19 pandemic required in its early stages the deployment of non pharmaceutical interventions (NPIs) [social isolation, physical distancing, mask-wearing, hand-washing]. We analyse a simple model to illustrate the consequences, for the evolution of the disease, of variable, dynamic individual compliance to these measures: the model divides a population in uninformed, informed-compliant and informed-noncompliant subpopulations. Conditions for the existence of multiple stable equilibria will be discussed as well as the consequences for the control of the infection.

Speaker: Jacques Bélair (Université de Montréal)

6:00 PM From within-host to between-hosts models via a virtual cohort

I will present a methodology that maps within-host dynamics of infection into an age-of-infection model. The one-directional link is achieved using a virtual cohort of individuals through which we gather information about disease characteristics at the population level namely, age-of-infection dependent transmission, recovery and death rates.

Speaker: Julien Arino (University of Manitoba)

5:00 PM → 6:20 PM Complexity Science for Biological and Medical Problems

5:00 PM Simplicity in complexity: A probabilistic view microbial ecology

Combining RNAseq data and models in microbial ecology aims to reveal species interactions and improve health outcomes. However, data is often noisy, and inferred "interactions" are merely model-dependent correlations rather than direct biological mechanisms. This raises a crucial question: when inferring models from data, are complex models better, or is simplicity more effective?

We argue that minimal models generally outperform complex ones. Using information geometry and Bayesian inference, we demonstrate that simple models maximize reliable information extraction, making them information-theoretically optimal \cite{castro2025scarce}. Furthermore, many widely reported microbial macroecological patterns may simply result from data aggregation \cite{castro2026} or lack the robustness required to be genuine laws \cite{camacho2025microbial}.

Speaker: Mario Castro (Instituto de Investigación Tecnológica (IIT), Universidad Pontificia Comillas de Madrid)

5:20 PM An evolutionary approach to ecological transitions in population dynamics

Population dynamics has traditionally focused on the study of what occurs in ecological regimes that only change their relationships quantitatively. However, populations that transition from one ecological regime to another, such as predation or parasitism shifting to mutualism, or vice versa, have been extensively documented in diverse ecological contexts. When population dynamics has addressed those transitions, it usually follows ad hoc mechanisms or uses different dynamics for each regime. Here, we present a model that combines adaptive dynamics with a generalized population dynamics model \cite{stucchi2020general} in an integrated way, which allows the transition between ecological regimes. We use a microbial toy-model that despite its simplicity shows that such transitions might occur naturally \cite{stucchi2022prevalence} for different set of parameters and serves as a proof of concept. We also show a few simulations that resemble empirical cases of ecological transitions driven by evolution.

Speaker: Luciano Stucchi (Universidad del Pacífico)

5:40 PM Species interactions do matter in microbial dynamics

During the last decades, macroecology has identified broad-scale patterns of abundances and diversity of microbial communities and put forward some potential explanations for them. However, these advances are not paralleled by a full understanding of the dynamical processes behind them. In particular, abundance fluctuations of different species are found to be correlated, both across time and across communities in metagenomic samples. Reproducing such correlations through appropriate population models remains an open challenge. The present paper tackles this problem and points to species interactions as a necessary mechanism to account for them. Specifically, we discuss several possibilities to include interactions in population models and recognize Lotka–Volterra constants as a successful ansatz \cite{camacho2024sparse, camacho2024nonequilibrium}. For this, we design a Bayesian inference algorithm to extract sets of interaction constants able to reproduce empirical probability distributions of pairwise correlations for diverse biomes. Importantly, the inferred models still reproduce well-known single-species macroecological patterns concerning abundance fluctuations across both species and communities. Endorsed by the agreement with the empirically observed phenomenology, our analyses provide insights into the properties of the networks of microbial interactions, revealing that sparsity is a crucial feature.

Speaker: Aniello Lampo (Departamento de Matemáticas, Universidad Carlos III de Madrid)

6:00 PM Robust time-independent metrics for evaluating drug efficacy

Traditional drug efficacy assessment relies on cell viability and the IC$_{50}$ index. This index represents the concentration of drug required for cell viability to be 50%, i.e. the population of treated cells is half that of the control population. However, since early-stage cell populations follow Malthusian growth, viability is inherently time-dependent. This makes IC$_{50}$ a transient metric that fails to distinguish between different proliferation dynamics.

In this work, we propose a robust mathematical framework to analyze cell viability assays by focusing on effective growth rates rather than endpoint populations. Assuming exponential proliferation, we employ bootstrap resampling method to achieve precise exponential fits. This approach allows for the discovery of two new time-independent parameters: IC$_{\text{r}0}$, corresponding to a zero-growth rate, and IC$_{\text{rmed}}$,corresponding to a growth rate half that of the control \cite{sanchez2025assessment}.

Both indices provide a more biologically meaningful evaluation of drug efficacy. This methodology offers a standardized, mathematically based alternative to classical pharmacodynamics, ensuring that efficacy measurements reflect the real impact of a drug on cell proliferation regardless of the experimental timeframe.

Speaker: Marta Sánchez-Díez (Center for Biomedical Technology, Universidad Politécnica de Madrid)

5:00 PM → 6:20 PM Modeling Collective Dynamics in Heterogeneous Cell Populations

5:00 PM Life & death in a tight spot: how bacteria grow and confront their foes in crowded 3D environments

Bacteria inhabit nearly every ecosystem, with critical implications for biogeochemistry, agriculture, and health. Many bacterial habitats are complex 3D environments, e.g., soils, hosts, and bodies of water, where they form spatially structured multicellular communities. This spatial organization is pivotal for community growth, cross-feeding, and diversity, and for withstanding challenges such as competing species, toxins, and bacteriophages—viruses that infect and kill bacteria. However, laboratory studies of well-mixed cultures and surface-attached colonies miss key spatial arrangements, ecological interactions, and defensive strategies that emerge in such environments. As a result, the collective dynamics and defensive capabilities of 3D bacterial colonies remain largely unknown, despite their prevalence in nature.

In this talk, I will first discuss how bacterial colonies acquire their shape in complex 3D environments. By integrating experiments with biophysical modeling, I will show how colonies growing in 3D transparent granular environments develop distinct architectures—driven by differential access to nutrients—that fundamentally differ from their flat-culture counterparts and are generic across species and environmental conditions. I then turn to phage–bacteria interactions in 3D and ask how anti-phage defense systems operate in such 3D-structured populations. Focusing on abortive infection systems, in which infected cells undergo programmed cell death to halt viral spread, I will show that spatial structure itself provides an additional layer of protection: anti-phage defense systems are significantly more effective in 3D structured communities than in well-mixed or flat-culture conditions.

Together, these findings show how spatial structure governs bacterial collective dynamics and function—from growth to anti-phage defense—and provide a quantitative framework for predicting and ultimately controlling microbial communities in realistic 3D environments, bridging simplified laboratory settings and natural ecosystems.

Speaker: Alejandro Martinez-Calvo (Princeton University)

5:20 PM Multi-phase field approach towards modelling mechanical heterogeneity in tissues

Biological tissues exhibit heterogeneity across multiple scales, from genetic to non-genetic. In epithelial layers, variability in mechanical properties such as adhesion and motility, together with differences in cell–cell interactions, strongly influences collective dynamics and tissue organization.

We present a 3D multiphase-field model \cite{monfared2025multiphase} of confluent cell monolayers in which each cell is described by a phase field whose evolution is governed by motility, interfacial tension, adhesion, and volume constraints. Mechanical heterogeneity is introduced through cell-dependent parameters controlling passive and active contributions. We apply this framework to investigate cell extrusion in epithelial monolayers \cite{balasubramaniam2025dynamic}. Combining simulations with experiments on epithelial cells with different levels of E-cadherin–mediated adhesion, we show how mechanical properties determine whether extrusion is apoptotic or live and whether it occurs apically or basally, leading to cell invasion into soft collagen gels.

Hence, by incorporating cell heterogeneity at various levels, our model provides a more comprehensive framework for understanding the role of mechanical heterogeneity on collective behaviour in tissues..

Speaker: Aleksandra Ardaševa (Institute of Biosciences, École polytechnique fédérale de Lausanne and Niels Bohr Institute, University of Copenhagen)

5:40 PM Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods

The coexistence of diverse phenotypic traits within a population - such as variations in cell movement, growth, or signalling - can profoundly shape collective dynamics of cell populations. To capture these complexities, classical PDE models for cell migration can be extended to include phenotypic structuring, giving rise to a powerful class of non-local models: phenotype-structured partial integro-differential equations (PS-PIDEs). In this talk, I will present a tutorial-style review paper dedicated to this growing field \cite{lorenzi2025phenotype}, offering both a pedagogical foundation for teaching and a roadmap for advancing research. We will first explore the current state of the art of how PS-PIDEs can be formally derived from agent-based models, analysed with semi-classical asymptotic methods, and solved numerically, in order to investigate the emergence of spatial sorting of the population at the tissue-scale due to the interplay between cell adaptive dynamics and environmental feedback. Finally, we will discuss open mathematical and interdisciplinary challenges expected to shape the future of this field.

Speaker: Chiara Villa (CNRS & MAP5 (UPC))

6:00 PM A multiscale discrete-to-continuum framework for structured population models

Population models commonly use discrete structure classes to capture trait heterogeneity among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions can improve analytical tractability and scalability of numerical solutions. Common upscaling approaches based solely on Taylor expansions may, however, introduce ambiguities in truncation order, uniform validity and boundary conditions. To address this, we introduce a discrete multiscale framework to systematically derive continuum approximations of structured population models. Using multiscale asymptotic methods applied to discrete systems, we identify regions of structure space for which a continuum representation is appropriate. The leading-order dynamics are governed by nonlinear advection in the bulk, with diffusive boundary-layer corrections near wavefronts and stagnation points. We also derive discrete descriptions for regions where a continuum approximation is fundamentally inappropriate. This multiscale framework can be applied to other heterogeneous systems with discrete structure to obtain appropriate upscaled dynamics with asymptotically consistent boundary conditions.

Speaker: Eleonora Agostinelli (University of Oxford)

5:00 PM → 6:20 PM Integrating machine learning into mathematical oncology

5:00 PM LLM-Guided Mechanistic Model Discovery in Population Pharmacometrics

Structural model selection for pharmacokinetics (PK) and tumor dynamics (TD) is iterative and expert-driven, requiring ODE formulation, nonlinear mixed-effects fitting, and biological plausibility assessment. We present an LLM-agent framework for automated population ODE model discovery, fit locally via SAEM (Monolix).

The workflow iterates: a builder agent proposes candidate ODE systems in MLXTRAN; a diagnostic agent interprets goodness-of-fit metrics (BICc, RSEs, IWRES); a reflection agent selects the best structure. No patient data are sent to the LLM.

For PK discovery (synthetic benchmark, n=10), 7/10 ground-truth structures were identified, including 4/4 one-compartment models. On real clinical data (Theophylline, Warfarin, Docetaxel, Irinotecan), AI-selected models matched or outperformed published references.

For TD (synthetic and real preclinical/clinical datasets), canonical growth models (exponential, logistic, Gompertz) were recovered alongside drug-effect structures. Exact model recovery occurred in 50% of six PK-TD scenarios; biologically plausible alternatives emerged otherwise.

Runtimes remained under 20 minutes. This framework offers a tractable, reproducible assistant for mechanistic model discovery in mathematical oncology, complementing expert judgment.

Speaker: Sébastien Benzekry (1. COMPutational pharmacology and clinical Oncology, Centre Inria d'Université Côte d'Azur 2. Cancer Research Center of Marseille, Institut Paoli-Calmettes, Inserm UMR1068, CNRS UMR7258, Aix Marseille University UM105, Marseille, France)

5:20 PM Deep Reinforcement Learning for Sequential Decision-Making in a Polytherapeutic Cancer Landscape

Drug resistance remains a primary obstacle in oncology, transforming clinical management into a complex, sequential decision-making problem. While Reinforcement Learning (RL) has shown promise in optimizing adaptive dosing for single agents, its application to large polytherapeutic panels—where clinicians choose from numerous drugs with overlapping resistance profiles—remains underexplored. This gap is exacerbated by the lack of mechanistic models capturing how drug sensitivity is shared across diverse agents due to cell subpopulation overlap.

In this talk, I will present a deep RL framework designed to optimize treatment strategies within a broad therapeutic panel. Inspired by the cyclic response-and-relapse dynamics of multiple myeloma, a mathematical model of tumor evolution is developed to track the competition between sensitive and resistant subpopulations. Crucially, a statistical model is integrated to encode correlations in drug sensitivity profiles, offering a conceptual approach to account for the biological reality of cross-resistance. Using these environments, a Proximal Policy Optimization (PPO) agent is trained to navigate the high-dimensional decision landscape. The agent learns to select drug sequences that adaptively respond to the evolving virtual tumor, aiming to minimize long-term tumor burden. Results demonstrate that RL can identify non-intuitive sequencing strategies that outperform standard clinical heuristics, providing a promising proof-of-concept for the future of AI-driven personalized medicine.

Speaker: Alvaro Köhn-Luque (1 Oslo Centre for Biostatistics and Epidemiology, Faculty of Medicine, University of Oslo 2 Department of Medical Genomics, Oslo University Hospital)

5:40 PM Towards personalized glioblastoma radiotherapy using growth modeling and recurrence prediction

Glioblastoma remains one of the greatest challenges in oncology, with near-universal recurrence largely driven by diffuse tumor infiltration beyond radiologically visible tumor margins, yet current radiotherapy planning relies on uniform geometric expansions that ignore patient-specific tumor biology and anatomy. Computational growth models and machine learning approaches have the potential to estimate these invisible tumor extensions and guide personalized radiotherapy planning, but their clinical translation has been limited by a lack of standardized benchmarking datasets and evaluation frameworks.

In this talk, I present current approaches to tumor growth modeling and recurrence prediction, including a novel U-Net-based model, and compare their performance against the current standard of care for radiotherapy planning. To this end, I introduce PREDICT-GBM, an end-to-end platform and curated dataset for evaluating computational models of glioblastoma growth and recurrence prediction. The results demonstrate that both biophysical and deep-learning approaches significantly outperform standard-of-care protocols in predicting future recurrence. Finally, I discuss what these comparisons reveal about the strengths and limitations of biophysical and data-driven approaches for guiding personalized radiotherapy, and outline the next steps toward clinical integration.

Speaker: Lucas Zimmer (1AI for Image-Guided Diagnosis and Therapy, Technical University of Munich, Germany)

6:00 PM Image-based prediction of skin cancer evolution for clinical decision support through machine learning

Skin cancer is among the most prevalent cancers worldwide, and current monitoring relies on biweekly image-based follow-ups that visually compare lesion changes over time. Although effective, this strategy is reactive and offers limited ability to anticipate future lesion behavior. To address this gap, we propose a predictive framework that leverages routinely collected clinical images to forecast lesion evolution. The approach combines a convolutional autoencoder, which encodes lesion images into a compact latent representation capturing key visual features, with a machine learning model that models temporal changes within this latent space. The decoder reconstructs images from latent vectors, enabling generation of future lesion appearances. Analysis of the latent space revealed structured, interpretable representations of lesion dynamics. From these, quantitative metrics such as trajectory length, progression speed, and cluster transition frequency were derived. Notably, these descriptors effectively differentiated stable lesions from rapidly evolving ones and captured patient-specific progression patterns. Lesions with higher latent speeds and more frequent cluster transitions showed greater morphological change over time. Overall, this framework provides a quantitative basis for anticipating lesion progression, supporting more proactive and personalized treatment decisions, including therapy initiation, adjustment, and response prediction.

Speaker: Daniel Camacho-Gomez (Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center, Tampa, FL 33612)

5:00 PM → 6:20 PM Stochastic Modelling for Inference with Gene Expression data: Methods and Applications

5:00 PM Statistical inference of chromatin- and transcription dynamics in living cells

Recent live-cell microscopy techniques allow the simultaneous tracking of distal genomic elements and transcription activity, offering new ways to study chromatin dynamics and gene regulation. However, drawing robust conclusions from such data is statistically challenging due to substantial technical noise, intrinsic fluctuations and limited time resolution. In this talk, I will present a method to infer the statistical relationship between transcription activation and enhancer-promoter distance from live-cell measurements. The problem is formulated as a generalized state-space model, accounting for chromatin dynamics, stochastic transcription activation as well as technical noise. Based on this model, we develop a path-space variational inference scheme, which reveals posterior densities over gene promoter states, polymerase loading events and enhancer-promoter distance. This allows us to quantify the spatiotemporal relationship between enhancer-promoter interactions and gene activation events. We applied the approach to experimental data in mESCs where enhancer-promoter distance and nascent transcription have been quantified across a broad range of conditions. I will conclude the talk by discussing potential implications and future work.

Speaker: Christoph Zechner (SISSA)

5:20 PM When Trajectory Inference Fails: The Challenges of Inferring Dynamical Models from Single-Cell RNA-seq Data

Single-cell RNA sequencing (scRNA-seq) enables inference of cellular trajectories from snapshots of differentiating cells. However, in many cases the inferred "pseudotime" does not have a clear mechanistic interpretation. We developed a principled trajectory inference framework based on biophysical models that can estimate interpretable parameters including process time and transcriptional rates \cite{f}. Based on this model, we demonstrate that trajectory inference from scRNA-seq data faces fundamental limitations. Through systematic analysis of simulated and real datasets, we characterise specific failure scenarios where insufficient dynamical information is embedded in the data. Key challenges include unmatched time scales, high measurement noise, and sparse sampling of intermediate states—limitations inherent to the static nature of scRNA-seq measurements. Our findings reveal critical gaps between the promise of trajectory inference and its practical limitations, emphasising the need for careful experimental design and rigorous model assessment.

Speaker: Meichen Fang

5:40 PM Deep learning for the Analysis and Reconstruction of Transcriptional dynamics from live-cell imaging data

Quantifying transcriptional bursting from live-cell imaging data is critical for understanding stochastic gene regulation. Here, we present DART (Deep learning for the Analysis and Reconstruction of Transcriptional dynamics) \cite{m}, a deep learning framework that infers promoter-state trajectories from fluorescence intensity traces, enabling the estimation of activation and inactivation rates and the selection of the most appropriate promoter-switching model. Using extensive synthetic datasets spanning a wide range of transcriptional bursting levels, we demonstrate that DART outperforms current binarization methods, including conventional and augmented hidden Markov models, in both accuracy and robustness. Furthermore, a reanalysis of published experimental data using DART reveals a strong linear coupling between activation and inactivation rates, contradicting previous claims of independence. By integrating machine learning with stochastic modelling, DART provides a powerful and generalizable tool for quantitative analysis of transcriptional kinetics from live-cell imaging data.

Speaker: Muhan Ma (University of Edinburgh)

6:00 PM Quantifying the impact of cell division and size control on stochastic auto-regulatory gene expression

Gene expression is inherently stochastic, leading to fluctuations in protein levels that can influence cellular function. Negative autoregulatory feedback is a common regulatory motif that can suppress these fluctuations and stabilize gene expression, but its effects can depend strongly on additional cellular processes. We investigate how cell-cycle dynamics influence the noise-reduction properties of negative feedback loops by first considering a framework where cell growth and division are modeled through the effective dilution of proteins. We then extend this framework by introducing an explicit model of the cell cycle that accounts for cell growth, division, and molecular partitioning. Our results demonstrate that explicitly modelling the cell cycle can qualitatively alter noise behavior: depending on parameter regimes, the cell cycle can either amplify or further suppress fluctuations compared to the effective model. These results highlight how model structure influences the relationship between underlying biochemical mechanisms and measurable variability, with direct implications for inference from gene expression data. Finally, we explore how different cell-size regulation strategies—such as sizer, timer, and adder mechanisms—affect noise in protein expression.

Speaker: Abigail Kushnir (University of Edinburgh)

5:00 PM → 6:20 PM Multiscale perspectives on cancer resistance: from intracellular networks to population dynamics

5:00 PM Modeling phenotypic switch in cancer drug response to identify new drug combinations

The emergence of drug-tolerant cells in clonal cancer populations is the main cause of reduced cytotoxic drug efficacy. But these tolerant cells can also be used as a specific target to design drug combinations. In this study (\cite{peyre}), we investigate the response of clonal cancer cells to pro-apoptotic and pro-necroptotic drugs. In both cases, fractional killing increases upon repeated administration. However, transcriptomic analysis reveals that pro-apoptotic-tolerant cells resemble pro-necroptotic-sensitive cells — suggesting that alternating treatments could mitigate this effect, which we validate experimentally. We then present a population model of drug response phenotypic switch, based on ODEs, to understand the re-sensitization of tolerant cells. The model is calibrated independently for each drug then coupled into a unified system simulating transitions between the tolerant, apoptosis-sensitive and necroptosis-sensitive states. We demonstrate that cells adapt to treatment by modulating drug retention time via regulation of drug degradation rates and reveal that the majority of pro-apoptotic-tolerant cells are in fact sensitive to necroptosis; pro-apoptotic treatment only accelerating the transition from the tolerant state toward necroptotic sensitivity.

Speakers: Benjamin Bian, Bernard Mari, George Vassaux, Jérémie Roux, Ludovic Peyre, Marielle Pere (Marseille Medical Genetics), Marina Moureau-Barbato, Mickael Meyer, Walid Djema

5:20 PM From Black Board, to Plate, to Patient: Dissecting Resistance Dynamics to Personalise Cancer Treatment Scheduling

Systemic therapies have revolutionised our ability to treat metastatic cancer. However, improvements are all too often temporary due to compounding toxicity and the emergence of drug-resistance. Most drugs are given according to a one-size-fits all approach and only changed upon toxicity or progression. In this talk, I will present work across two different spatial-temporal scales in which we ask: can we improve outcomes by personalising treatment scheduling?
In the first part, I will discuss integration of in vitro experiments and mathematical modelling to study the impact of drug scheduling on cancer evolution. By treating fluorescent co-cultures of sensitive and resistant cells with four different treatment schedules (Continuous Therapy, Intermittent Therapy, Low-Dose Continuous Therapy), we show that intermittent scheduling can slow drug resistance and that cell plasticity plays an important role in shaping the treatment dynamics. In the second part, I will present recent work in which we are asking what we can learn about resistance dynamics in patients from routinely collected tumour burden data. I will present a Bayesian model selection framework with which we dissect the response dynamics of metastatic colorectal cancer patients by comparing different evolutionary hypotheses. Optimising drug scheduling is a key aim of mathematical oncology, and I hope to convince you of the opportunities – and importance - of studying this problem at multiple scales.

Speaker: Maximilan Strobl (The Institute of Cancer Research and Imperial College London)

5:40 PM How Modulation of the Tumor Microenvironment Drives Cancer Immune Escape Dynamics

Metastatic disease is the leading cause of cancer-related death, despite recent advances in therapeutic interventions. Prior modeling approaches have accounted for the adaptive immune system's role in combating tumors, which has led to the development of stochastic models that explain cancer immunoediting and tumor-immune co-evolution. However, cancer immune-mediated dormancy, wherein the adaptive immune system maintains a micrometastatic population by keeping its growth in check, remains poorly understood. Immune-mediated dormancy can significantly delay the emergence (and therefore detection) of metastasis. An improved quantitative understanding of this process will thereby improve our ability to identify and treat cancer during the micrometastatic period.
Here, we introduce a generalized stochastic model that incorporates the dynamic effects of immunomodulation within the tumor microenvironment on T cell-mediated cancer killing. This broad class of nonlinear birth-death model can account for a variety of cytotoxic T cell immunosuppressive effects, including regulatory T cells, cancer-associated fibroblasts, and myeloid-derived suppressor cells.
We develop analytic expressions for the likelihood and mean time of immune escape. We also develop a method for identifying a corresponding diffusion approximation applicable to estimating population dynamics across a wide range of nonlinear birth-death processes. Lastly, we apply our model to estimate the nature and extent of immunomodulation that best explains the timing of disease recurrence in bladder and breast cancer patients. Our findings quantify the effects that stochastic tumor-immune interaction dynamics can play in the timing and likelihood of disease progression. Our analytical approximations provide a method of studying population escape in other ecological contexts involving nonlinear transition rates.

Speakers: Jason T. George (Texas A&M University, Houston, TX, USA ; Rice University, Houston, TX, USA), Pujan Shrestha (Texas A&M University), Zahra S. Ghoreyshi (Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843 Translational Medical Sciences, Texas A&M Health Science Center, Houston, TX 77030)

6:00 PM Integrating glioblastoma plasticity into combination therapy strategies to overcome therapeutic resistance: a quantitative systems pharmacology approach

Glioblastoma (GBM) is the most aggressive primary brain tumor in adults, with a median survival between 14-21 months and no curative treatment currently available [1]. To investigate resistance mechanisms to temozolomide (TMZ), the standard-of-care chemotherapy, we generated perturbed proteomic data (with and without TMZ) for 12 patient-derived cell lines (PDCLs). Pathways enrichment and independent component analysis revealed a high inter-patient heterogeneity. Proteins linked to TMZ response were identified and matched to pharmacological compounds using a new pipeline, leading to 40 promising drugs from an initial screening. These candidates are currently evaluated in a second screening to assess synergistic effects. The next step is to build a digital twin for each PDCL, enabling personalized prediction of combination therapies. A previously developed quantitative systems pharmacology (QSP) model of TMZ pharmacokinetics-pharmacodynamics serves as a foundation [2]. To initiate model individualization, we developed a method to personalize model parameters using publicly available multi-omics and TMZ cytotoxicity data. Current work focuses on integrating proteomics-derived key species into the core model to obtain PDCL-specific digital twins and infer personalized treatment by combining QSP and machine learning. This integrative approach, combining data analysis, network reconstruction, and mechanistic modeling, opens the path for efficient patient specific therapies in GBM.

Speakers: Ahmed Idbaih (Sorbonne Université, AP-HP, Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Hôpitaux Universitaires La Pitié Salpêtrière - Charles Foix, DMU Neurosciences, Service de Neurologie 2-Mazarin, France), Annabelle Ballesta (Institut Curie, INSERM U1331, Cancer Systems Pharmacology team), Maité Verreault (Paris Brain Institute, Inserm UMR 1127, Hopital Pitié Salpetrière AP-HP, France), Sergio Corridore (Servier, data science and data management unit, France), Thibault Delobel (Institut Marie Curie)

5:00 PM → 6:20 PM Population level models of bacterial processes and interaction

5:00 PM Mathematical Modeling of Microbial-Induced Corrosion of Bioplastic in Marine Environments

Microbial-induced corrosion (MIC) and biodegradation in marine environments are driven by complex microbial consortia whose metabolic activity controls chemical transformations at material surfaces. In this presentation, we present a mathematical framework describing the interaction among microbial functional groups and their role in degradation processes. The model is applied to the biodegradation of biodegradable plastics in deep-sea conditions, accounting for microbial attachment, biofilm formation, enzyme secretion, polymer breakdown, and uptake of soluble compounds.

The system is formulated as a set of nonlinear differential equations, combining hyperbolic equations for microbial populations, parabolic equations for enzymes and degradation products, and an ordinary equation for biofilm thickness. To capture spatial effects, a one-dimensional two-layer diffusion model with double free boundaries is introduced, describing the interaction between biofilm growth and corrosion layer formation.

Numerical simulations highlight the key role of microbial metabolism in regulating degradation rates and shaping microbial community dynamics. The results provide insights into MIC mechanisms and offer a predictive tool for assessing bioplastic fate in marine environments.

Speaker: Luigi Frunzo (Univ Naples)

5:20 PM Bacterial Biofilm Growth Modelling in a Counter-Diffusion System, Coupled with Biozone Formation in the Aqueous Phase by Planktonic Bacteria, driven by Directed Movement.

In marine environments,bacterial biofilm formation occurs on the surface of plumes of marine snow that serve as moving nutrient hotspots.We develop a mathematical model on bacterial biofilm study that accounts for biomass growth,surface attachment-detachment,diffusive and directed movement of planktonic bacteria and perform a numerical simulation study.The biomass density controls the spatial expansion of biofilm,whereas biomass growth depends on the concentration of two counter-diffusive substrates,carbon and oxygen.Carbon diffuses from surface of marine snow into the domain,while oxygen enters from the opposite boundary.Planktonic bacteria, driven by directed movement,accumulate in regions with favorable growth conditions.The system is described by a one-dimensional set of four highly nonlinear PDEs.The flux-conservative finite volume method is used for space discretization of transport terms corresponding to biomass in biofilm and suspension.Substrate equations are discretized and numerically solved using a time-adaptive method from ‘ReacTran’ library in ‘R’.Simulation results show biofilm expansion toward the aqueous phase and dynamic migration of suspended bacteria toward optimal nutrient zones.A comparative study on uniform and non-uniform grid refinement using the Shishkin mesh and graded mesh is conducted.The interplay between directed movement,attachment-detachment and counter-diffusion is shown to significantly influence biofilm maturation dynamics.

Speaker: Rachana Mandal (Univ. Guelph)

5:40 PM Modelling accumulation of toxic substances in bacterial cells: a route to suppressing antimicrobial resistance

The global rise in antimicrobial resistance levels, coupled with the downturn in discovery of new antibiotics, has resulted in an urgent need for novel ways to tackle bacterial infections. Most antibiotics work by accumulating inside bacterial cells, but bacteria have evolved mechanisms to prevent prolonged intracellular exposure to toxic substances including by limiting the permeability of their membrane (to prevent substances entering the cell) and activating efflux pumps (to secrete substances outside of the cell). Understanding how these processes are regulated under different conditions presents a route for us to manipulate them for therapeutic gain. We will present a variety of mathematical modelling approaches, integrated with experimental data where possible, to investigate the dynamics of toxic substance accumulation in bacteria cells. This computational framework enables the generation of experimentally-testable predictions on the optimisation of accumulation.

Speaker: Sandeep Shirgill (University of Birmingham)

6:00 PM Ecological interactions and spatial dynamics in microbial aggregates: A novel modelling framework

We present a mathematical model based on a system of partial differential equations (PDEs) with cross-diffusion and reaction terms to describe ecological interactions between multiple bacterial species and substrates within microaggregates, where bacteria proliferate in response to substrate availability and undergo passive dispersal driven by population pressure gradients. The ecological interactions include interspecific competition for shared substrates, and commensalism, whereby one species benefits from the metabolic by-products of another. The main motivation comes from individual-based models (IBMs) of microbial aggregates, where simulations reveal that substrate-limited conditions can give rise to rich spatial patterns. Our numerical experiments demonstrate that our PDE-based model captures the key qualitative features of three verification scenarios that have previously been investigated with IBMs. Moreover, we formally derive a competition system from an on-lattice biased random walk, and establish local well-posedness for a parameter-symmetric subcase of it. We then formally analyse the travelling wave behaviour of this case in one spatial dimension and compare the minimal travelling wave speed with the wave speed measured in the simulations.

Speaker: Viktoria Freingruber (TU Delft)

5:00 PM → 6:20 PM Introduction to chemical reaction network modelling and simulation with Catalyst.jl

5:00 PM Parameter Identifiability and Inference with Catalyst.jl and PEtab.jl

In this second part of the session on Catalyst.jl, we focus on inverse problems, i.e. estimating parameters in models via fitting to data. Using Catalyst models as examples, we will demonstrate how Julia packages can be composed to generate complete model fitting pipelines.

First, we will show how structural identifiability can be assessed for any model using StructuralIdentifiability.jl. Next, we will demonstrate how Catalyst.jl integrates with PEtab.jl to define and solve inverse problems by fitting models to time-series data. This includes showing how PEtab.jl can be used to create parameter problems with a wide range of features, such as events/callbacks, simulation conditions (where the model is simulated under different control parameters for different measurements), complex observable models linking model output to data, and steady-state initialization. We will then show how to fit models using robust global optimization methods such as multistart parameter estimation, and how to assess practical identifiability using profile likelihood analysis.

Finally, we will cover how to define and perform parameter estimation for scientific machine learning (SciML) models that combine mechanistic and data-driven components using Catalyst.jl and PEtab.jl. As these models are often challenging to train, we will also demonstrate how to leverage state-of-the-art training strategies implemented in PEtab.jl to improve parameter estimation performance.

Speakers: Sebastian Persson (Francis Crick Institute), Torkel Loman (University of Oxford)

5:00 PM → 6:20 PM Progresses in Mathematical and Computational Immunobiology and Infections

5:00 PM Inside the wavering mind of an NK cell: Mathematical modeling of NK cell activation in health and disease

The paradigm of NK cell activation is the “Missing-Self Hypothesis”; NK cells kill cells that lack MHC. When considering a single interaction between an NK cell and a target cell, the “Missing-Self Hypothesis” offers a plausible explanation for NK cell activation. However, an NK cell’s interaction with a target cell is not an isolated event. Experimental studies have shown that NK cells in an MHC-deficient environment fail to lyse cells lacking MHC. Curiously, a study by the Yokoyama lab (Washington University in St. Louis) found that when 10% of cells in a well-mixed environment lacked MHC, the NK cells failed to lyse most of the cells. Our hypothesis is that target cell recognition is less about the balance of the presence or absence of markers, and more so about detecting outliers in an environment. We developed mathematical models of how NK cells assess and learn from their environment under static and dynamic MHC suppression. Our results suggest NK cells may be vulnerable to “slow growing danger” which makes detecting outliers challenging. We are collaborating with the Weis lab (Huntsman Cancer Institute) to experimentally test our model predictions.

Speaker: Montana Ferita (Department of Mathematics, School of Biological Sciences)

5:20 PM From binding to neutralization: A mathematical model for flavivirus antibody responses

Flaviviruses such as Dengue, Zika, Yellow Fever and West Nile virus represent major global public health threats. Envelope (E) proteins on the viral surface mediate host-cell attachment and membrane fusion. These 180 E proteins are arranged in a highly ordered geometry that shapes epitope accessibility and antibody binding.

Neutralization of flaviviruses is primarily mediated by monoclonal antibodies (mAb) targeting the E protein in an interplay between mAb affinity, epitope accessibility, and the number and organization of bound mAb.

We present preliminary results on a mathematical model of seroneutralization. We model virus–antibody interactions as a stochastic binding process that accounts for epitope spatial organization and occupancy on the viral surface. We include conformational transitions of the E protein and viral “breathing” dynamics, which modulate epitope accessibility and constrain binding kinetics. By introducing these structural and dynamical constraints, our approach aims to provide a mechanistic interpretation of neutralization curves grounded in the geometry and physics of the virion.

In parallel, we have developed a database of seroneutralization data for many measurements from mAbs, cells and flaviviruses. Using this resource, we explore mechanistic links between microscopic binding parameters and the shape of neutralization curves. Our framework aims to account for key features observed experimentally, including partial neutralization and neutralization by antibody mixtures.

This approach is designed to bridge quantitative modeling with practical questions in public health, including antibody-dependent enhancement (ADE) and the interpretation of polyclonal immune responses.

Speaker: Nathanael Hoze (Institut national de la santé et de la recherche médicale)

5:40 PM MS32-7 (Talk confirmed)

Awaiting abstract.

Speaker: Elissa Schwartz (Department of Mathematics and Statistics, Washington State University)

6:00 PM Decoding Influenza Transmission from Ferret Contact and Viral Dynamics

The determinants of influenza transmission at the level of individual contacts remain poorly understood. We analyze a unique dataset of controlled ferret transmission experiments in which one or two infected donors interact with four susceptible recipients for varying durations (typically 1–4 hours), combining high-resolution video and longitudinal viral load measurements to link time-resolved behavior with infection outcomes.

Our approach integrates machine learning–based behavioral tracking using Social LEAP Estimates Animal Poses (SLEAP) with statistical and mechanistic modeling to quantify how contact patterns influence infection risk. We reconstruct individual-level exposure histories and relate them to infection outcomes to estimate associations between specific contact patterns and transmission, and to explore parsimonious transmission-kernel formulations.

The primary objective is to determine which features of behavior and infectiousness are identifiable from these data, and which are fundamentally confounded. More broadly, this work asks a general question: given realistic behavioral and biological data, what can we actually learn about transmission mechanisms?

Speaker: Veronika Zarnitsyna (Emory University School of Medicine)

5:00 PM → 6:20 PM Structural Approaches to the Dynamics of Chemical Reaction Networks

5:00 PM Structural properties and biological oscillators: ideas from strongly 2-cooperative systems

Fundamental properties and emergent behaviours of biochemical systems often depend exclusively on the system structure (the graph topology along with qualitative information), regardless of parameter values. We first provide an overview of the parameter-free assessment of important properties, including the stability of equilibria and the sign of steady-state input-output influences. Then, we focus on the emergence of sustained oscillations via convergence to periodic orbits, a complex question with important applications in systems biology, including the understanding of biomolecular oscillators that rule cell life cycle and metabolism, as well as circadian rhythms in hormone secretion, body temperature and metabolic functions. The study of sustained oscillations in a dynamical system requires first showing that at least one periodic orbit exists and then assessing the stability of periodic orbits and characterising the initial conditions from which the solutions converge to periodic trajectories. For a class of strongly 2-cooperative nonlinear dynamical systems, leveraging results from the theory of cones, the spectral theory of totally positive matrices and Perron-Frobenius theory, we show that every solution emanating from an explicit set of initial conditions of positive measure converges to a periodic orbit. The result applies to well-known biological systems, including the n-dimensional Goodwin oscillator and biological oscillators based on RNA-mediated regulation.

Speaker: Giulia Giordano (University of Trento)

5:20 PM The structural concept(s) of cores in reaction networks

In recent years, there have been a few uses of the word ‘core’ in the context of chemical reaction networks, all related to some idea of minimality. Based on stoichiometric considerations alone (i.e. no dynamics nor kinetic considerations involved), Alex Blokhuis with co-authors identified autocatalytic cores as minimal structures carrying autocatalysis, a fundamental biochemical concept related to self-amplification. To effectively connect stoichiometric intuitions to dynamical conclusions, I introduced with Peter Stadler the framework of parameter-rich kinetics, which allows disentangling parametric dependence from the structural analysis of the Jacobian matrix. Widely used kinetics in biochemistry, such as Michaelis–Menten or generalized mass action, are naturally parameter-rich. Within this framework, we investigated minimal stoichiometric structures whose presence guarantees the possibility of dynamical instability (that is, the capacity for a locally unstable steady state). Since the autocatalytic cores sensu Blokhuis form a strict subset of these structures, we named them unstable cores. Finally, with both Peter Stadler and Alex Blokhuis, we addressed periodic oscillations, introducing the concept of oscillatory cores, i.e. minimal structures that guarantee periodic oscillations in any network containing them, again under parameter-rich kinetics. In this talk, I will give an overview of these and related results.

Speaker: Nicola Vassena (University of Leipzig)

5:40 PM Non-monotonic dose-response curve in biochemical systems

A response curve measures the output of a biological system at equilibrium against an input parameter $u$, which could be a rate constant, or amount of a stimulus (poison, drug, ligand, etc.). Of interest is the shape of a response curve: does it have a plateau region (homeostasis); is it monotonic? In T-cell's response to antigen, a non-monotonic (i.e., biphasic) response has been observed. For systems where $u$ directly affects one variable, we previously proved that either an incoherent feedforward loop, or a combination of positive and negative feedback loops, is necessary for biphasic response. In this talk, we consider the case where $u$ impacts multiple variables, for example if $u$ is the rate constant of a reaction. Finally, we comment more generally on translating motifs between the influence diagram and the reaction network.

Speaker: Polly Yu (University of Illinois Urbana-Champaign)

6:00 PM A Structural Approach to Identifying Indicator Species in Chemical Reaction Networks

Cellular phenotypes exhibit remarkable diversity, reflecting the complex functional states of individual cells. Although phenotypic diversity has traditionally been assessed at the transcriptomic level, recent advances in single-cell technologies have shifted attention toward metabolomic phenotyping, which provides a more direct reflection of cellular function. Nonetheless, the high dimensionality of the metabolome poses significant challenges for both measurement and computational classification. A fundamental question therefore arises: which subset of species in a reaction network suffices to represent the system's overall state? To address this, we develop a novel theory that relies solely on the structural topology of chemical reaction networks to identify indicator species—those whose concentrations uniquely determine all others and thereby distinguish multistable equilibria. An efficient algorithm implementing this theory is applied to biochemical pathway databases. Numerical experiments show that phenotypic classification using only these indicator species achieves accuracy that matches or exceeds that of the full metabolite set, while demonstrating superior robustness to measurement noise. These results establish a rigorous, topology-based foundation for indicator species identifications, advancing metabolomic phenotyping and biomarker discovery.

Speaker: Yong-Jin Huang (Kyoto University)

5:00 PM → 6:20 PM Models and Methods for the Analysis of Cancer Treatment

5:00 PM Assessing the Role of Model Complexity in Virtual Clinical Trial Outcomes

Virtual clinical trials (VCTs) hold significant promise for improving the drug development process, yet their predictive reliability depends on design decisions that remain poorly understood. This presentation investigates how model complexity, prior parameter distributions, and virtual patient (VP) inclusion criteria interact to shape VCT outcomes.

Using oncolytic virotherapy in murine tumors as a case study, we compared three models of varying complexity using different parameter priors and methods for including/excluding a parameterization in a virtual population. Our results demonstrate that while the simplest model inadequately spans the feasible trajectory space, potentially missing critical interpatient heterogeneity, there are diminishing returns beyond intermediate complexity. Both intermediate and complex models captured similar ranges of patient responses across various dosing protocols.

Further, we show that methods that simply reject “out-of-bound” parameterizations can generate posterior distributions that overly resemble the chosen prior, artificially reducing variability in treatment responses. In contrast, patient generation methods that instead perturb “out-of-bound” VPs to make them feasible produced results less sensitive to prior assumptions. These findings suggest that VCT design should prioritize intermediate-complexity models to capture key biological mechanisms, paired with perturbation-based inclusion criteria that prevent unrealistic prior assumptions from overconstraining the virtual population. [Joint with Dr. Joanna Wares]

Speaker: Jana Gevertz (The College of New Jersey)

5:20 PM Cellular kinetics of drug response: are they conserved when altering experiment and biological context?

Sometimes! Gleaning insight from a model independent of data is (understandably) rarer and rarer in mathematical biology, and determining parameters from biological data has become an established practice of modern mathematical modelling. Once parameters are estimated (ideally with bounds), an important question remains: whether (and to what extent) are biological parameters conserved? For example: do cells grow at the same rate in a dish and in an organoid? Are enzyme kinetics in a beaker the same as within a cell? Is the dose-response curve the same for a cell in and out of the body?

Often, biological parameters are implicitly assumed to be conserved - but this is an assumption we should examine and grapple with. In this talk, I will present our recent work examining conservation of biological parameters that describe the kinetics of cellular response to targeted therapeutics (i.e., drugs that have been engineered to preferentially interact or avoid specific types of cell) – specifically, to lipid nanoparticles (LNPs). We have investigated to what extent these cellular kinetics are conserved when changing experimental details or biological contexts. This work may be of particular interest to those developing targeted therapeutics or lipid nanoparticles, or to those interested in mathematical oncology (as one of the primary expected uses of targeted therapeutics is in the treatment of cancer).

Speaker: Matt Faria (University of Melbourne, Pneumatica Bio)

5:40 PM Mechanistic Learning of Engineered Immune Cell-Tumor Cell Interactions and Heterogeneity

Chimeric Antigen Receptor (CAR) T-cell therapy has emerged as a promising option for relapsed or refractory lymphoma patients and acute leukemias. Mathematical modeling offers a valuable tool for investigating the interactions among these living drugs, tumors, and heterogeneous patients' immune or inflammatory context. Using longitudinal data from experiments and the clinic, we examine how diverse CAR T cell phenotypes interact with heterogeneous tumors, how these interactions can be inferred, and how they impact outcomes.

Speaker: Philipp Altrock (Cancer Modeling & Evolution UKSH Campus Kiel)

6:00 PM An Agent Based Modelling Framework for the Role of Tumour-Stroma Dynamics in Metastatic Colorectal Cancer

Metastasis to the liver remains a leading cause of mortality in colorectal cancer patients, due largely to the difficulty of treating established metastatic lesions. Spatial transcriptomic (ST) imaging provides highly detailed, spatially resolved data on the cellular composition and interactions within these lesions, offering new insights into how metastases are established and evolve in the liver. Upon arrival, tumour cells interact with hepatic cells and actively remodel the surrounding tissue to form a supportive metastatic niche \cite{li_understanding_2025}. These early processes, which can be resolved through spatial analysis of ST images, determine whether lesions can successfully form and expand. Here, we develop an agent-based multiscale model using a PhysiCell framework to investigate colorectal metastases in the liver \cite{ghaffarizadeh_physicell:_2018, ghaffarizadeh_biofvm:_2016}. To bridge experimental data and model development, we employ a spatial analysis pipeline using tools such as Muspan \cite{bull2024muspan} to quantify cellular neighbourhoods, interactions, and tissue architecture from the ST images. This approach enables the construction of a data-driven, spatially informed agent-based model that captures the mechanistic processes underlying metastatic colonisation. By validating the model against experimental observations, we establish a framework to predict disease progression and potentially improve future therapeutic strategies.

Speaker: Sam Oliver (University of Oxford)

5:00 PM → 6:20 PM Past, Present, and Future of Reaction Networks Theory

5:00 PM An Invitation to Reaction Networks

This is an introductory talk, and does not assume that you have any previous knowledge about the theory of reaction networks.

We will introduce and discuss reaction networks and reaction systems, especially as they are used in Mathematical Biology.

We will also emphasize the history of the development of key results and ideas about reaction systems, starting with ideas from thermodynamics and the Boltzmann equation from the 19th century, and followed by steady progress which culminates in 1972 with three key achievements: the stability of vertex balanced systems by Horn and Jackson, the deficiency zero theorem of Horn and Feinberg, and the connection between deterministic and stochastic models by Thomas Kurtz.

Among the more recent developments we will mention results on existence and uniqueness of positive steady states, as well as persistence (i.e., non-extinction), and global stability (i.e., the existence of globally attracting states).

Many examples will illustrate these ideas and results.

Speaker: Gheorghe Craciun (University of Wisconsin-Madison)

5:40 PM Multi-scale Models Arising in Chemical Reaction Networks

Biochemical reaction networks are characterized by varying orders of abundance for different species types, as well as varying orders of magnitude for different reactions.
This feature allows one to reduce a complex model to a simpler one without losing the salient features of the dynamics. The model reduction can also lead to novel models that incorporate both stochastic and deterministic dynamics. I will present some examples of both finite-dimensional and infinite-dimensional (spatial) systems where new processes arise in the multi-scale limit of reaction networks.

Speaker: Lea Popovic (Concordia University)

6:00 PM Making Sense of Reaction Networks via Atoms and Inheritance

Let's imagine "CRN space", the set of all finite chemical reaction networks (CRNs), which can be visualised as an infinite set of digraphs. We can stratify CRN space in various ways: by molecularity, by number of species or reactions, by rank, by various equivalences, and so forth. Much of CRN theory consists of theorems linking network structure and network dynamics. Many classical and modern results tell us that, under some kinetic assumptions, some dynamical behaviour is permitted or forbidden by a given set of networks. In this sense, CRN theory provides tools which bring order to CRN space. The theory of "inheritance" provides another powerful tool for this purpose: it tells us how dynamics propagates through CRN space. Its results provide partial orders on CRN space, with A <= B implying that some behaviour of network A must also occur in network B. The theory is most useful when combined with results on "atoms" - minimal networks with a given behaviour. Each atom immediately defines an upper set of networks which must have this behaviour and a lower set of networks which forbid this behaviour. I'll describe some elements of this story, and what I see as the most important missing pieces.

This talk is based on joint work with Balázs Boros (University of Szeged), Josef Hofbauer (University of Vienna), and Casian Pantea (West Virginia University).

Speaker: Murad Banaji (Lancaster University)

5:00 PM → 6:20 PM Newtonian and non-Newtonian Biofluidmechanics: Integrating Theory, Experiments, Modeling, and Simulations

5:00 PM Drag on Microtubule Asters

Microtubule asters–dynamic microtubules anchored at a centrosome–form the spindle poles during cell division. Utilizing the method of regularized Stokeslets, we prescribe the motion of microtubule asters in a confined geometry and compute the resulting hydrodynamic drag on the aster. Moving beyond classical asymptotic approximations, we characterize the drag on a single aster inside a spherical cell as a function of its positions and microtubule distribution. We then extend this to study drag on several interacting asters, corresponding to cellular aster configurations prior to division.

Speaker: Sarah Olson (Worcester Polytechnic Institute, USA)

5:20 PM How do glioma cells infiltrate the narrow gap between astrocytes endfeet and blood vessel through ion-exchange and physical deformation for the critical cellular infiltration?

Malignant gliomas are devastating, aggressive tumours that frequently kill patients with a low survival rate (1 year after diagnosis). Diffuse invasion of glioma cells after surgical resection in brain tissue is a major obstacle for effective therapy. Glioma cells use the tortuous extracellular routes of migration, using blood vessels as guides. These cells manipulate ion channels in the local microenvironment to dynamically adjust their cell volume to accommodate to narrow spaces and breach the blood-brain barrier through disruption of astrocytic endfeet, that support blood vessels. We investigated the cell-mechanical aspect of glioma cell migration along the blood vessels by using an immersed boundary method without volume convervation. This involves many intercellular interactions and biochemical reactions. We illustrate that the viscoelastic properties of the glioma cell and ion-induced reduction in volume enable them to penetrate the narrow gap. The unique biology of glioma invasion provides unexplored brain-specific therapeutic targets for this devastating disease with little effective treatment options.

[1] V.A. Cuddapah, S. Robel, S. Watkins, and H. Sontheimer. A neuro-centric perspective on glioma invasion. Nature Reviews Neuroscience, 15(7):455-465, 2014

Speaker: Yangjin Kim (Konkuk University)

5:40 PM The Method of Regularized Stokeslets as an Introduction to Fluid-Structure Interactions

Mathematical and computational modeling plays an important role in understanding biological fluid mechanics. Even though the fluid motion is governed by partial differential equations, there are many projects in this field that can be made accessible to undergraduate students. The Method of Regularized Stokeslets (MRS) [1] is a popular technique used in modeling low Reynolds number flows. In this talk, I discuss the development of an introductory guide to the MRS designed for undergraduate students with a background in linear algebra and multivariable calculus. This framework can be adapted for high-impact research projects for undergraduates at any level.

[1] Cortez, Ricardo. The Method of Regularized Stokeslets. SIAM Journal on Applied Mathematics, 23(4):1204-1225, 2001.

Speaker: Amy Buchmann (University of San Diego)

5:00 PM → 6:20 PM Epidemiological-behavioural modelling to address health challenges

5:00 PM Modelling the adoption of Integrated Pest Management (IPM) by UK crop growers

Reducing the harmful impact of pesticides is a key challenge faced by the agricultural industry globally. In many countries, policies have been introduced to discourage the use of pesticides, while encouraging the use of alternative methods of crop disease control. One such method is Integrated Pest Management (IPM), a set of holistic and sustainable measures for the prevention, monitoring and control of crop diseases \citep{pesticidenationalactionplan}. While many IPM measures are acknowledged to offer effective control, their implementation has thus far been limited in the UK.

To explore the potential impact of policy on the adoption of IPM by crop growers in the UK, we developed a joint epidemiological-behavioural model \citep{vincent2025modelling,vincent2026modelling}. Within a simulated outbreak of Septoria tritici blotch (STB), growers could choose to switch between two disease control strategies based on their relative profitability: IPM, and a conventional fungicide regime. In these simulations, we found that the projected rate of IPM adoption would not meet the UK's pesticide reduction targets for 2030. We also found that policies addressing behavioural barriers among crop growers had the greatest potential to increase adoption trends, compared to other forms of incentive.

Speaker: Elliot Vincent (University of Warwick, UK)

5:20 PM Memory mechanisms in Bayesian behavioural change epidemic models

Accurately capturing epidemic dynamics requires accounting for how individuals adjust behaviour in response to perceived infection risk. Recently models have been developed to incorporate behavioural feedback \cite{ward_bayesian_2023}, but they currently rely on simplified, ad hoc representations of memory. For instance, many emphasize only recent case counts, neglecting the lasting influence of earlier epidemic experiences on current risk perception.
Here, we introduce a framework of Memory Mechanism Enhanced Behavioural Change (MEBC) models within a Bayesian SIR setting. Five memory formulations -- memoryless, sliding window, power-law, exponential, and reciprocal -- are considered, each reflecting a distinct way past epidemic information shapes present behaviour. A fully Bayesian data-augmented MCMC approach jointly estimates transmission and behavioural parameters while accounting for uncertainty in infectious periods.
Simulation results show that the MEBC framework provides accurate parameter recovery and remains robust under misspecified memory assumptions. Applications to the early COVID-19 outbreak in Miami-Dade County and the 2023–2024 influenza season in Manitoba demonstrate that incorporating an interpretable memory mechanism significantly improves model fit, underscoring the importance of collective memory in behavioural adaptation and disease transmission.

Speaker: Rob Deardon (University of Calgary, Canada)

5:40 PM Oscillatory epidemic dynamics driven by non-linear behavioural feedback

Spontaneous behavioural changes in response to an outbreak can significantly alter transmission dynamics. Recent studies \cite{ Omori2024JTB} have explored how the human perception of risk, and the subsequent reduction in contact rates, can be modelled as a function of epidemiological indicators. This study aims to provide a qualitative understanding of how such perception-based feedback shapes the emergence and characteristics of multi-wave epidemics.

We analyse an SIR-type model where the transmission rate depends on a non-linear function of past infection levels, reflecting the diminishing sensitivity of human behaviour to increasing incidence. To evaluate the oscillatory potential of the system, we employ a quasi-stationary approximation for the susceptible population. By linearizing the dynamics using logarithmic perturbations around the quasi-equilibrium, we derive the characteristic equation and analytically identify the conditions under which the interaction between the disease and behaviour leads to self-sustained oscillations. Our findings elucidate how the non-linear scaling of risk perception, combined with information lag, governs the fundamental frequency and damping of epidemic waves.

This analysis offers a theoretical basis for understanding the mechanisms by which behavioural-epidemiological interactions generate complex, multi-modal epidemic trajectories.

Speaker: Ryosuke Omori (Hokkaido University, Japan)

6:00 PM Predicting contact rates in response to control measures: a validated protocol for generating contact matrices relevant to transmission modelling of respiratory diseases

Transmission models are used to predict the course of epidemics and inform policy makers. For respiratory diseases, many models incorporate rates of contacts within and between age groups, summarized in contact matrices. Contact rates may change due to control measures. To forecast transmission, contact matrices should reflect this impact before measures are introduced. We present a protocol to predict future contact matrices using data on time-use, contacts, and demographics, collected before an epidemic.

For each set of control measures, we identified activities on which less time will be spent. The protocol assumes that reductions in time lead to proportional reductions in numbers of contacts made during these activities. School and work time were stratified by educational level and profession based on demographics. We validated the protocol by applying it to measures against COVID-19, comparing predicted to observed matrices.

Predicted matrices agreed with observed matrices. By age, predicted contact rates matched observed rates, especially for contacts involving adults. For child-child contacts, predicted rates were lower than observed rates, with observed school contacts likely overreported. Predicted workplace contact rates matched office occupancy data.

The protocol uses pre-epidemic data, providing consistent and transparent contact matrices for transmission models. It is suited for future epidemics when data are periodically collected.

Speaker: Willem Frederiks (National Institute for Public Health and the Environment (RIVM), The Netherlands)

5:00 PM → 6:20 PM Novel Approaches in Mathematical Biology

5:00 PM MS71-5

Speaker: Jason Hartford (University of Manchester)

5:20 PM A Hybrid Networked SEIR Model with Generative-AI Driven Agents for Behavioral Heterogeneity in Epidemics

Human behavioral responses play a central role in shaping epidemic dynamics, yet they remain difficult to model mechanistically due to their heterogeneity and context dependence. We develop a hybrid, networked SEIR framework that integrates generative AI-driven agents to capture individualized protective behavior. Each agent is characterized by demographic and socioeconomic attributes, and a large language model (LLM) generates daily willingness-to-comply scores from prompts that encode personal traits, occupation and income, local and global epidemic conditions, social influence, and policy strength. These AI-generated behavioral states modulate edge-level infection risk on dynamic physical contact networks, linking individual decision-making to population-level transmission outcomes. The framework offers a generalizable approach for integrating generative agent simulation into epidemic modeling and evaluating targeted, context-aware non-pharmaceutical interventions.

Speaker: Jia Zhao (University of Alabama)

5:40 PM Generation of Model-Based Virtual Patient Cohorts Using Neural Networks

Limitations of human data in cancer research poses significant challenges for accurately predicting tumor growth and treatment outcomes. To address this, virtual patient cohorts are created to facilitate in silico exploration of new treatments. We propose a novel framework that integrates mathematical modeling, statistical data augmentation, noise reduction, and neural network-based trajectory tailoring to create a virtual patient cohort. Starting from 10 initial simulated patients, we apply a bootstrap technique with added noise to generate a cohort of 200 candidate patients. We then apply denoising techniques and process the candidate patients through a neural network, to sculpt the tumor growth trajectories to match the statistics of our simulated data. To benchmark our method, we compare it against cohort generation via Bayesian inference and sampling of posteriors, demonstrating that our framework is not only more computationally efficient but also more robust in handling noisy data. Finally we apply the pipeline to a dataset for oncolytic virotherapies and recapture the Kaplan Meier survival curves accurately. Our framework effectively handles noisy data, produces suitable virtual patient cohorts, and offers a scalable, computationally efficient solution for virtual patient cohort generation.

Speaker: Kathleen Wilkie (Toronto Metropolitan University)

6:00 PM Equation Learning and Distributional Inference for Modeling Mitochondrial Inheritance in Yeast

Mitochondrial inheritance during cell division is a fundamental biological process that ensures daughter cell viability, yet its governing mechanisms remain incompletely understood. In budding yeast (Saccharomyces cerevisiae), experimental observations reveal substantial variability in how mitochondrial content is partitioned between mother and daughter cells, raising key questions about the relative roles of deterministic regulation and stochasticity. In particular, we investigate whether inheritance can be explained by simple proportional rules or whether it depends on a higher-dimensional cellular state immediately prior to division. To address these questions, we develop a data-driven modeling framework that combines equation learning with
distributional inference. We analyze high-resolution live-cell imaging data that track mitochondrial content, cell size, and additional molecular markers (e.g., Ime1, Erg6, Vma1) across thousands of cell division events, enabling the reconstruction of lineage relationships and pre-division cellular states. We first apply equation learning techniques, including sparse regression and biologically informed neural networks, to infer interpretable relationships between pre-division cellular features and post-division mitochondrial allocation. To account for inter-cellular variability, we further incorporate a distributional calibration framework based on the Prohorov metric, which enables comparison between empirical and model-generated distributions of inheritance outcomes. Together, these methods provide a unified framework for learning interpretable models of mitochondrial inheritance. More broadly, this work illustrates how combining equation discovery with distributional inference can be used to investigate mechanistic hypotheses in complex biological systems where both structure and population heterogeneity play essential roles.

Speaker: Kevin Flores (Department of Mathematics, North Carolina State University)

5:00 PM → 6:20 PM Mathematical and AI-enhanced computational models for sexually transmitted diseases and other public health threats

5:00 PM MS76-5

5:20 PM An agent-based platform for simulating the impact of chlamydia vaccine in the US population

Chlamydia trachomatis (CT) remains the most reported bacterial sexually transmitted infection in the United States (US), underscoring the urgent need for an effective vaccine. An agent-based model calibrated to the US National Health and Nutrition Examination Survey (NHANES) datasets was developed and used to study the impact of vaccine on the CT and all-cause pelvic inflammatory disease (PID) burden. Model simulations predicted a conventional vaccine with 50% efficacy and 60% coverage can achieve a 64.2% [95%CI: 43.0–68.1] reduction in chlamydia prevalence and a 14.3% [95%CI: 10.1–29.4] reduction in the prevalence of women with one or more lifetime episodes of all-cause PID. In addition, in some countries, the testing policy for asymptomatic chlamydia has been changed. In Netherlands, from 2025, CT testing at Centers for Sexual Health is indicated only for individuals with symptoms or partner notification. No test means no diagnosis and no treatment. However, studies have shown that around 2%-5% untreated CT will develop PID. Following PID, around 15%-20% individuals will develop infertility. Thus we also applied the ABM platform to simulate the natural infection history of Chlamydia infection and testing the impact of removing asymptomatic tests, as well as the impact of limiting the screening to patients with symptoms on the incidence of CT, the incidence of PID, the incidence of longer-term sequelae, and on transmission.

Speakers: Qi Deng (York University), Edward Thommes (University of Guelph and Sanofi)

6:00 PM Decision-making, epidemiological dynamics, individuals, and societies

The COVID-19 pandemic highlighted the importance of individual decision-making for adherence to an intervention. In this talk, I will use simple mathematical models to examine the dynamics of individual adherence to an intervention, and examine when tensions might arise between individuals and societies. I will also examine the effects of adherence to a nonpharmaceutical intervention on epidemiological dynamics (and vice-versa).

Speaker: Chadi Saad-Roy (University of British Columbia)

5:00 PM → 6:20 PM Modeling of protein dynamics with applications to Neurodegenerative Diseases

5:00 PM Modeling the Prion Aggregation Process During Polymerization Experiments Using Delay Differential Equations

Prion proteins are notorious for their ability to induce neurodegenerative diseases by forming long fibrillar aggregates that accumulate in the brain. While the aggregation of these proteins and their fragmentation by oligomeric species are central to disease progression, the underlying mechanisms remain poorly understood. To better interpret experimental data, mathematical models have been developed to translate the key chemical reactions governing this process. In this talk, I present a novel modeling approach based on delay differential equations (DDEs), designed to capture the time-dependent features of prion polymerization dynamics. I will demonstrate how this framework aligns with experimental observations from polymerization assays in which prion monomers are thermally induced to aggregate. The model not only fits the data well but also suggests an alternative perspective on the interplay between aggregation and fragmentation, offering a new theoretical lens on prion dynamics.

Speaker: Mr Theo Loureaux (University of California, Merced)

5:20 PM An optimal control problem for anti-inflammatory treatments of Alzheimer’s disease

We present and analyze an optimal control problem to model anti-inflammatory treatment strategies for Alzheimer’s disease, using a system of differential equations that captures interactions between ABeta-peptides, microglial cells, interleukins, and neurons. These interactions operate through mechanisms such as protein polymerization, inflammation processes, and neural stress responses. In particular, inflammation is highlighted as a key factor in the onset and progression of Alzheimer’s disease, driven by a hysteresis effect related to the degradation rate d of monomers and the initial concentration of interleukins. This implies a critical inflammation threshold that determines whether the disease persists over the long term. The optimal control problem we propose seeks to minimize the concentration of toxic oligomers by modulating interleukin production and degradation rates, representing potential anti-inflammatory treatment effects. Under natural constraints on treatment dose efficacy and cumulative exposure, our goal is to assess whether it is possible to shift the system from a persistent disease state to a disease-free equilibrium. We provide the necessary conditions of the optimal solution and supplement our theoretical findings with numerical simulations, which illustrate the system’s behavior under different parameter settings and the imposed constraints of the optimal control problem.

Speaker: Dr Nicolás Torres Escorza (Université Côte d’Azur)

5:40 PM Fragmentation vs. Trimming: A Mathematical Framework for Resolving the Mechanism of Hsp104 Action on [PSI+] Aggregates

The molecular chaperone Hsp104 is essential for the propagation of the yeast prion [PSI+], yet the precise mechanism by which it remodels prion aggregates remains contested. A leading alternative to the fragmentation model - in which Hsp104 internally severs amyloid fibers to generate new seeds - is the trimming hypothesis, which proposes that Hsp104 acts as a distinct enzymatic activity that removes monomers exclusively from fiber ends. We present a combined deterministic and stochastic modeling framework to critically evaluate these competing mechanisms. Our deterministic models allow systematic exploration of parameter space to identify regimes consistent with observed prion dynamics, while our stochastic framework captures population-level heterogeneity in aggregate inheritance across cell divisions. We show that if trimming represents a qualitatively distinct Hsp104 activity selectively activated under guanidine treatment, this mechanism is inconsistent with observed data. In contrast, interpreting end-proximal breakage as a modest positional bias within a general fragmentation framework remains fully consistent with all observations. Our results support the conclusion that reduced fragmentation activity under guanidine, rather than a separate trimming mechanism, is the parsimonious explanation for existing experimental evidence.

Speaker: Dr Suzanne Sindi (University of California, Merced)

6:00 PM Study of a bi-monomeric Becker-Döring-type model

In order to provide an explanation for the damped oscillations surprisingly observed in Prion depolymerization experiments, a bi-monomeric variant of the seminal Becker-Döring system is proposed. In this talk, we look in detail at the mechanisms leading to these oscillations. We characterize the dynamics of the system in different kinetic phases: from the initial phase of high amplitude oscillations to progressive damping and convergence towards the unique stationary solution. This result is based on quantitative approximations of the main quantities of interest: the period of oscillations, the damping of oscillations corresponding to an energy loss, and the number of oscillation cycles characterizing each kinetic phase.

Speaker: Dr Mathieu Mezache (INRAE)

5:00 PM → 6:20 PM Modelling the mechanical behaviour of cells

5:00 PM Alignment processes in cells: From individual interactions to collective behaviour

How do many groups of organisms, ranging in size from micro-meter scale bacteria, to meter scale birds, form highly co-ordinated groups? One commonly observed dynamic is that of directional alignment of individuals. In this talk I will focus on alignment of elongated cells, with a focus on fibroblasts, which show particularly strong alignment in certain type of scars (keloid scars). To obtain a mechanistic, interpretable, model for the dynamics of cell position, cell orientation and cell shape we use an energy minimization approach. We analyse the resulting dynamics from two points of view: Computationally via a collective dynamics simulation, and analytically in a two cell setting. The combined insights shed light on the role of cell speed, cell deformability and supracellular actin cables in alignment dynamics.

Speaker: Angelika Manhart (University of Vienna)

5:20 PM A Phase-field Model for multi-nucleated myofiber formation through cytoplasmic fusion

Myotube creation and subsequent maturation into myofibers enables skeletal muscle to maintain the size, structure, and function required for contraction and regeneration. A single muscle fibre contains hundreds of nuclei within a large cytoplasmic volume, which is key in generating the necessary force for muscle contraction. Muscle growth throughout the lifespan of an adult is primarily through hypertrophy, where the fibres enlarge. This process is dependent on the recruitment of additional myoblasts, which fuse with pre-existing myofibers, thus enabling adaptation to exercise and mechanical loading. To understand this fundamental process of myoblast fusion in the development of skeletal muscle biology, we aim to develop a mathematical framework which can simulate and replicate these dynamics. Thus, we develop a phase-field framework simulating the fusion of cytoplasm while maintaining intact nuclei, allowing for the investigation of cell fusion of many single cells to form large multicellular structures. We confirm cell fusion through the merging of phases in 1D and identify key parameters. Further numerical simulations are then generated in 2D to observe the cell fusion in multi-cell scenarios, thus supporting the framework's ability to simulate such dynamics for myofiber formation. Finally, we simulate a scenario of 100 single-cell myoblasts forming a myofiber and compare it with microscopy images to validate the simulation through a qualitative comparison.

Speaker: Daniel A. Vaughan (Centre for Human & Applied Physiological Sciences, King's College London, Guy's Campus, United Kingdom)

5:40 PM A geometric surface PDE framework to model cell migration

Cell migration is a ubiquitous and complex process in biology, spanning embryonic development to cancer metastasis. During migration, cells undergo high deformation as they explore the medium or as they traverse narrow pores. Over the last decades, there has been an increasing interest in mathematical models for cell migration, with the particular challenge of integrating dynamic bio-chemo-mechanical processes within an evolving domain. Here, we present a biophysical model of cell migration grounded in the theory of curvature-elastic energetic biomembranes. We develop the model systematically, progressing from equilibrium in the absence of external loads to migration through confined environments. We study diverse migration scenarios, emphasising the mechanical coupling between the cell plasma membrane and the nuclear envelope, and the role of size constraints in cell squeezing. These size constraints arise from the finite availability of lipids to constitute the plasma membrane and the nuclear envelope, combined with osmotic pressure, together restricting surface area and volume. While the elastic stiffness of the nucleus has been thought to be the main obstacle for cell migration in confinement, our results suggest that size constraints and the membrane-to-nucleus mechanical coupling also play a critical role. This suggestion aligns with recent experimental studies tracking the evolution of the nucleus during cell migration.

Speaker: David Hernández-Aristizábal (Université Côte d'Azur, LJAD UMR CNRS 7351, Nice, France)

6:00 PM Modeling active cell migration in complex confined environments: The interplay between nuclear mechanics, chemotaxis, and obstacle geometry

Understanding how cells navigate through dense and heterogeneous microenvironments is a fundamental challenge in biomechanics, with direct implications for cancer metastasis, immune surveillance, and tissue morphogenesis. In confined spaces, the nucleus, the largest and stiffest cellular organelle, acts as the primary physical bottleneck, limiting deformability and determining the success of migration through narrow gaps.

In this work, we present an advanced computational framework based on geometric surface partial differential equations (GS-PDE) to simulate active cell migration. Our approach treats the plasma membrane and the nuclear envelope as evolving, energetic closed surfaces governed by force-balance equations, integrated with a chemotactic signalling mechanism that drives autonomous motion. We investigate various migration scenarios by systematically varying the mechanical properties of the cell and its nucleus, as well as the geometric features of the surrounding environment. Our results highlight how the interplay between nuclear properties and obstacle morphology dictates the efficiency of the migration process. In general, this framework provides a robust and flexible tool for dissecting the biophysical strategies cells employ to bypass physical barriers, offering new insights into the mechanobiology of invasive cellular behaviour.

Speaker: Francesca Ballatore (Laboratoire Jean Alexandre Dieudonné, CNRS UMR7351, Nice, France)

6:30 PM → 8:30 PM Poster Presentations

6:30 PM How do bee’s smell? The multi-physics of honeybee olfaction

The sense of olfaction (smell) in honeybees occurs through sensory receptors along their antennae. We study one type of sensor called a placode, which densely covers each antenna in a regular formation. Sitting close the antennae’s surface, each placode is covered by hundreds of innervated pores that capture olfactory particles. We seek to understand how the morphology and configuration of placodes along the antenna affect the flow of air and how this fluid-structure interaction impacts a bee's ability to smell.

The precise role of the placode's morphology in olfaction is unknown. Two candidate shapes have been identified, which we shall examine. Each is of distinct morphology presenting as either a pit (with an initial sharp ring and smooth inner) or a mound (with a small divot on top).

We model the fluid-structure interaction of the airflow and placodes considering their morphology and configuration to assess their role in volatile capture. Due to the depth and relative length of the placodes, the so-called condensed flow equations apply. Initially, we consider two and three-dimensional configurations for a single placode to investigate the local influences of its morphology on the fluid flow. We later extend this scenario to that of a three-dimensional periodic case, whereby the streamwise and crosswise interactions of many placodes is considered. Finally, we compare these results to FEM models and assess the potential role of electrostatics in this olfactory process.

Speaker: Dr Ryan Palmer (University of Bristol, UK)

6:50 PM An Individual-Based Numerical Modelling Framework for Cancer Cell Invasion and Metastatic Spread

The dynamic behaviour of cancer cells within human organs and tissues has long been a topic of significant interest in cancer research. Understanding these behaviours is essential for gaining insight into the mechanisms underlying tumour growth, invasion, and metastasis within the human body.
In this work, we adopt an individual-based mathematical modelling framework combined with numerical simulation techniques, in which each cancer cell is explicitly represented and tracked in space and time. The model incorporates a range of biologically relevant cellular processes, including cell movement mechanisms such as random walk, chemotaxis, and haptotaxis, as well as cell proliferation, death, and biochemical interactions with substances in the surrounding microenvironment. These interactions play a key role in shaping tumour evolution and spatial invasion patterns.
By numerically simulating these coupled processes, we aim to capture the spatio-temporal spread of cancer cells within the human body, with particular emphasis on the transition from a primary tumour site to potential secondary organs. The proposed framework allows for the investigation of how local cellular behaviours and microenvironmental cues can collectively give rise to large-scale invasion dynamics.
This study provides a computational platform for exploring cancer progression from a mechanistic perspective and will be presented in the form of a poster.

Speaker: Jim Yang (University of St Andrews)

7:10 PM Differentiated Tuberculosis Care: Supervision-Dependent Thresholds and Bifurcation Structure

A novel mathematical model is developed that links the tuberculosis (TB) care cascade with the dynamics of healthcare worker adherence. The model extends standard TB compartmental frameworks by incorporating a health-worker supervision parameter and an evolutionary game for adherence to treatment protocols. We derive an analytic expression for the basic reproduction number $R_0(z)$ as a function of supervision intensity $z$, and we prove conditions for disease invasion and stability. In particular, we show that health-worker supervision alters the epidemic threshold and can induce a backward bifurcation: even if $R_0 < 1$, a stable endemic equilibrium may persist under weak supervision. We obtain an explicit inequality for backward bifurcation involving the cascade and relapse parameters. Combining behavioural and epidemiological thresholds, we identify a composite control criterion ($z > \max\{zc, ze\}$) that guarantees disease elimination. Numerical simulations (bifurcation diagrams and time-series) validate the analysis and illustrate how increasing z drives the system to a disease-free equilibrium. Our results highlight how implementation fidelity fundamentally changes TB transmission dynamics and provide quantitative guidance for achieving elimination.

Speakers: Palak Goel (BML Munjal University Gurugram), Shagun Panghal (IILM University, Gurugram)

7:30 PM ABM–Deep Gaussian Process Virtual Patient Population Reveal Interferon-Dependent Efficacy of Sirolimus in SARS-CoV-2 Infection

Early SARS-CoV-2 infection is governed by nonlinear and often antagonistic interactions among immune cells, cytokines, and intracellular signaling pathways. We developed a mechanistic agent-based model (ABM) of early lung infection integrating pneumocytes, macrophages, natural killer (NK) cells, type-I interferon (IFN) signaling, and the mTORC1 inhibitor sirolimus. To enable large-scale analysis, we trained a Deep Gaussian Process (DGP) surrogate on ABM simulations and generated a virtual patient population spanning physiologically plausible parameter ranges. Using Morris and functional ANOVA sensitivity analyses, we identified regime-dependent drivers of infection outcomes at 48 hours post-infection. When IFN-mediated viral inhibition spans a wide range, viral replication kinetics dominate system behavior, and sirolimus strongly reduces viral load and inflammation despite immunosuppressive effects. In contrast, when IFN inhibition is highly effective, IFN secretion rate becomes the primary determinant of viral load, and sirolimus has diminished impact. The model further predicts context-dependent roles for macrophage polarization, reconciling conflicting experimental findings. These results highlight how immune–viral feedback structure determines therapeutic efficacy and underscores the value of surrogate-assisted ABM sensitivity analysis for interpreting heterogeneous treatment responses.

Speaker: Henrique de Assis Lopes Ribeiro (Univeristy of Florida)

7:50 PM Mathematical Modeling of Learning Behavior (Habituation) in True Slime Mold Based on a Spatially Discretized Reaction–Diffusion System

Habituation is a form of learning characterized by a decrease in response following repeated stimulation and has been observed in a wide range of organisms, from mammals to unicellular organisms. The true slime mold, Physarum polycephalum, is an amoeba-like unicellular organism renowned for its sophisticated adaptive responses to environmental stimuli. Boisseau et al. (2016) reported habituation features in the time required to cross the bridge when slime molds repeatedly cross an agar bridge containing a chemical repellent. This study focuses on the habituation to chemical stimuli reported in slime molds \cite{boisseau2016}.
We developed a mathematical model to describe the slime mold's tip expansion on a straight line. The expansion is driven by internal viscous fluid flow. The flow is generated by spatial gradients in fluid pressure. Accordingly, we formulated a system of ordinary differential equations with three variables: the position of the slime mold tip, $\ell(t)$, and the fluid pressures at the front and rear parts, $p_\mathrm{f}(t)$ and $p_\mathrm{r}(t)$. Our model reproduces the experimental results well. Through a variable transformation and a model approximation, we find that the total amount of chemical species controlling the fluid pressure encodes the history of external stimulation. In addition, the spatial difference in the chemical decomposition rate is important for the emergence habituation behavior in the slime mold.

Speaker: Kota Nishi (Kyushu University)

8:10 PM A Mathematical Approach for Enhancing Tumor Drug Delivery via Collagen Normalization

The tumor microenvironment (TME) presents significant physical barriers, such as elevated interstitial fluid pressure (IFP) arising from disorganized and leaky vasculature together with a dense extracellular matrix (ECM). These barriers limit the effectiveness of systemic therapies by restricting drug penetration into the tumor core \cite{N20}. We develop a coupled mathematical model to investigate how ECM remodeling influences drug delivery within solid tumors. The model is formulated as a system of nonlinear partial differential equations describing the spatiotemporal interactions among tumor growth, vasculature, IFP, and drug concentration \cite{Y17}. To capture the structural role of the ECM, the model explicitly incorporates key constituents, including collagen, hyaluronic acid, and elastin, which together regulate interstitial hydraulic resistance and fluid pressure.

We focus on collagen normalization as a therapeutic priming strategy by modeling collagenase-mediated degradation of collagen fibers prior to chemotherapy administration. Simulations demonstrate that partial collagen degradation substantially enhances drug penetration throughout the tumor domain, resulting in improved therapeutic exposure compared to chemotherapy alone. Furthermore, the model enables systematic investigation of treatment schedules, providing a predictive computational framework for optimizing combination strategies involving ECM-targeted therapies and cytotoxic agents.

Speaker: Onur Kerem Özmen (Özyeğin University)

8:10 PM A Mathematical Framework for Per-Read and Per-Sequence Error Characterization in Single-Molecule Sequencing

We present a mathematical framework for quantifying basecalling error at multiple scales in single-molecule (nanopore) sequencing, from individual bases to whole-sequence classification.
We define hierarchical Phred-like quality scores — per-base, per-read, and per-sequence — and prove via Jensen's inequality that averaging in the Phred domain systematically overestimates accuracy relative to the Phred transform of the mean error. This concavity-driven bias has direct consequences for quality reporting. We address it with an alignment-based correctness score incorporating predicted basecaller confidence and empirical accuracy into a single Phred-scale summary.
We then lift the analysis to sequences by constructing a confusion matrix indexed by true targets and basecaller assignments. Row-normalization produces a stochastic matrix of pairwise misclassification probabilities; its Frobenius distance from the identity yields a Phred-like scalar of classifier fidelity. Clopper–Pearson confidence intervals from the multinomial row structure, with minimum read-count bounds, ensure reliable estimation of rare confusions. A bridge between scales is provided by per-base reliability zones: under conditional independence, the product of position-specific error rates at discriminating sites predicts which off-diagonal entries dominate, enabling anticipation of sequence-level misclassification from basewise profiles

Speaker: Mr Pranjal Srivastava (University of Michigan)

8:10 PM A mathematical framework for quantifying T cell expansion in acute and chronic regulatory contexts

A fast and pathogen-specific supply of effector T cells is essential in the mammalian immune response to acute and chronic infections, as well as cancer. While the basic principles of T cell activation and differentiation are well established, the mechanisms that control the balance between proliferation and differentiation remain incompletely understood.
Motivated by the observation that simple T cell differentiation motifs where proliferation competes against differentiation fail to explain clonal expansion, we developed a mathematical framework to quantify desirable expansion-related properties. Specifically, we defined measures for the potential of controlled expansion, the efficiency of the expansion, and the chronicity under persistent antigen exposure. Within this framework, we systematically analyzed different regulation mechanisms of the proliferation, involving cytokine- and antigen-mediated feedback, under acute and chronic conditions.
Subsequently, we compared the best-performing motifs to a published T helper cell differentiation motif in the context of LCMV infection in mice \cite{burt_2023} and to a tumor-immune interaction model \cite{rob_2012}. In both cases, we fitted the dynamics of the derived motifs to the dynamics in the published models and then compared proliferative potential and chronicity.
Our framework provides a foundation for exploring how circuit-level mechanisms influence T cell population dynamics in acute and chronic scenarios.

Speaker: Joanna Schnorr (Institute for Experimental Oncology, University Hospital Bonn)

8:10 PM A mathematical framework to accurately reconstruct cell lineage from single cell transcriptomics on barcoded cells: application for therapeutics optimization

Introduction: Quantifying tumor plasticity is essential for understanding resistance in glioblastoma (GBM). A mathematical pipeline is presented for the joint analysis of time-resolved single-cell (sc) transcriptomics and lineage barcoding to characterize cancer cell states and quantify their dynamics (proliferation, death, state transitions) in control or temozolimide-treated conditions. This model is used to design interventions targeting specific cell states to maximize drug efficacy.
Methods: Cell states are identified through clustering and enrichment analysis of known signatures . An ordinary differential equation (ODE)-based model is utilized to infer cell state dynamics by integrating both sc barcoding and transcriptomics. Existing work \cite{1} was extended through the incorporation of exponential growth, improved parameter optimization via the CMA-ES algorithm, and relaxation of sparsity constraints.
Results: In GBM lines, lineages are reconstructed across three time points into a hierarchical tree that chieved a close fit to data. Estimating parameters in control or temozolomide-treated conditions revealed key resistance mechanisms . The pipeline was benchmarked against the original model. Strategies to maximize efficacy were designed bt predicting optimal interventions on cell state death or transition rates. Identifying corresponding molecular targets remains the next challenge to allow for clinical translation.

Speaker: Bence Hajdu (Institut Curie)

8:10 PM A non-autonomous continuous mathematical model for the Alzheimer biomarker cascade

This work presents a mathematical study of the progression of Alzheimer’s disease through a dynamical model based on ordinary differential equations. A detailed analysis is carried out on a biomarker cascade model which describes the sequential interaction between beta‑amyloid accumulation, tau hyperphosphorylation, neurodegeneration, and cognitive decline, in the line of the models introduced in \cite{Hao2022, Petrella2019}. A new causal model is proposed, introducing a time‑dependent growth rate for amyloid accumulation, providing greater flexibility to represent genetic factors, therapeutic interventions, and cognitive reserve. A theoretical analysis is developed, including analytical properties, equilibrium points, and stability of the resulting non‑autonomous system. Simulations show the model’s ability to fit diverse clinical patterns and highlight the usefulness of the model as a predictive tool and its potential for future personalized clinical applications based on real patient data.

Speaker: Antonio Baeza (Department of Mathematics, University of Valencia, Spain)

8:10 PM A parallel asymmetric particle Gaussian mixture filter for state-space estimation of highly nonlinear oscillators

Understanding biological oscillators often requires reconstructing internal states from measurement time series. This becomes difficult when dynamics contain slow–fast manifolds that produce strongly nonlinear trajectories. Under such conditions, common state estimation methods face fundamental limitations. In particular, the Kalman–Bucy filter assumes system dynamics can be locally approximated by a single Gaussian distribution, which fails in strongly nonlinear regimes. Particle filtering can capture such dynamics but often incurs high computational cost due to Monte Carlo sampling. To address these limitations, we introduce an asymmetric particle Gaussian mixture filter (AP-GMF) for nonlinear oscillatory systems. The posterior distribution is represented by Gaussian particles whose structure adapts dynamically. Particles are split based on local nonlinearity and combined using the Kullback–Leibler divergence, enabling efficient approximation. Compared with the asymmetric particle population density method, AP-GMF achieves comparable or higher accuracy with fewer particles. We evaluate AP-GMF on the van der Pol oscillator, a general nonlinear oscillator, across multiple parameter regimes. The method consistently outperforms existing filters, including the level-set Kalman filter and the continuous–discrete cubature Kalman filter. We also provide a parallel implementation enabling accurate state estimation at practical computational cost.

Speaker: San Kim (KAIST)

8:10 PM A Scalable Network-Based Parameterization of Positive Steady States for Dynamical Analysis of Biochemical Systems

Understanding how the structure of biochemical reaction networks determines their long-term dynamical behavior remains one of the core problems in systems biology. Analysis of these models becomes increasingly challenging as network size and complexity grow. In this work, we present an enhanced framework for parameterizing the positive steady states of biochemical systems using the structural properties of the associated reaction network. The approach integrates network decomposition with a graph-theoretic network translation method based on elementary flux modes, enabling for an efficient derivation of positive steady states while significantly reducing computational overhead and addressing the various issues encountered in existing approaches. By benchmarking across a diverse set of biochemical models, we demonstrate the improved scalability of the resulting procedure. Finally, we apply the method to illustrate how steady state parameterizations can be used to investigate important biological properties of multistationarity and absolute concentration robustness in the EnvZ-OmpR signaling pathway and a large-scale CRISPRi toggle switch model. These results highlight how the newly developed framework enables a scalable analysis of larger, more complex biochemical systems and provides deeper insights into the long-term behavior of such models.

Speaker: Exequiel Jun Villejo (Institute of Mathematics, University of the Philippines Diliman)

8:10 PM A Water Transfer Experiment Linking Physical Systems and Mathematical Models

This poster presents a hands-on laboratory activity that introduces students to modeling water transfer processes across physical systems. Using simple experimental setups, students collect data on flow and transport, develop mathematical models to describe observed behavior, and test model predictions against measurements. The lesson connects concepts from biology, environmental science, and differential equations while emphasizing data analysis, parameter estimation, and model validation. Adaptable for undergraduate courses and secondary classrooms, the activity provides an accessible entry point to interdisciplinary modeling grounded in real-world environmental phenomena.

Speaker: Brynja Kohler (Utah State University)

8:10 PM Advance Prediction of Immunotherapy Outcomes Using Deep Learning

Immunotherapy has varied results and how to predict whether a patient will respond is an open question. It is crucial to closely monitor a patient’s response once immunotherapy begins, and to potentially change to an alternate treatment if needed. Using a mathematical model, Creemers et al. argued that a patient’s tumor growth rate and immune cell killing rate are the primary parameters affecting response \cite{Creemers et al.}. These can be difficult to estimate as they vary stochastically over time. We tackle this by training a deep learning model that takes in noisy time series data of a patient’s tumor growth during treatment, and predicts whether or not they will recover during the next five years. We use a CNN-LSTM architecture designed to detect time series transitions far in advance\cite{Bury et al.}. This model uses CNN layers to extract important features and then uses LSTM layers to detect patterns over time. Heterogeneous patients are generated using a mathematical model with noisy, realistic parameters. The deep learning model is trained on these synthetic patients, and then a reserved test dataset is used to investigate how far in advance the model can accurately predict outcomes. We propose that frequent tumor measurements of an immunotherapy patient can be fed to the model to help assess whether or not to continue treatment, thus improving the patient's quality of life and chances of survival.

Speaker: Juliette Sinnott (University of Waterloo)

8:10 PM An agent-based model to investigate the dynamics of HIF, TGF-𝛼, and EGFR signalling under hypoxic conditions in cancer spheroids

Cancer spheroids capture the hallmark intratumoral heterogeneity of solid tumours, including phenotypic diversity and spatially distinct gene expression patterns, making them invaluable tools for studying therapeutic resistance. Differential receptor expression across tumour subpopulations remains a major challenge in cancer therapy, yet most computational models treat receptor proteins as a uniform, population-wide property, overlooking the functional consequences of mixed receptor populations within a single tumour. Here, we present a multi-scale agent-based model of a two-dimensional cross-section of a cancer spheroid, implemented in the Chaste framework, that resolves heterozygous Epidermal Growth Factor Receptor (EGFR) expression at the single-cell level. By coupling hypoxia-inducible factor (HIF)-driven transforming growth factor-α (TGF-α) autocrine and paracrine signalling, we show that the ratio of wild-type to mutated EGFR governs emergent spheroid phenotypes - proliferation in normoxic zones, quiescence under hypoxia, and necrosis under anoxia. We envision our modelling framework will provide a foundation for designing therapeutic strategies by accounting for the heterozygous receptor landscapes observed in clinical tumour samples.

Speaker: Vaishnudebi Dutta (University of Bristol)

8:10 PM Analysis of the Role of Network-Plasticity-Related Proteins in Molecular Networks

Cellular plasticity – the ability of cells to adapt to environmental changes by producing diverse phenotypes – plays a vital role in the reprogramming of cells across a broad spectrum of diseases, including cancer, diabetes, and neurodegeneration. It is also a key component of embryonic development and tissue remodelling. Targeting this plasticity is a promising therapeutic approach, as demonstrated by sequential and differentiation therapies, drug holidays, and alternating treatments \cite{kerestely_modulation_2026}.
An effective way to model complex cellular processes like plasticity is through network representations, such as protein–protein interaction (PPI) networks, signalling networks, and gene regulatory networks, whose network plasticity reflects cellular plasticity.
We aim to identify proteins that modulate network plasticity and elucidate their roles within the molecular networks of diseased cells. From the literature, we have gathered multiple regulators of network plasticity and cross-referenced these with existing drug targets. Our analysis indicates that intrinsically disordered proteins, a source of molecular-level plasticity, are enriched among regulators of network plasticity. The results of the network analysis suggest that direct signalling interactions involving network plasticity regulators are generally transient or causational, such as phosphorylation and transcriptional activation.

Speaker: Dr Mark Kerestely (Department of Molecular Biology, Semmelweis University, Budapest, Hungary.)

8:10 PM Autonomous and Nonautonomous Dynamics of an SIRS Model: An Application to Seasonal Influenza in the Congo

This study develops and analyzes an SIRS epidemic model with convex incidence and saturated treatment under both autonomous and nonautonomous frameworks. For the autonomous system, we characterize the disease-free and endemic equilibria and perform a detailed bifurcation analysis, revealing backward and saddle-node bifurcations, as well as Hopf bifurcations that generate endemic bubbles. Furthermore, the bifurcation structure uncovers a codimension-two double-zero bifurcation arising from the interaction between saddle-node and Hopf bifurcations. The nonautonomous extension incorporates seasonal variations in transmission
and recovery rates, capturing realistic periodic forcing observed in infectious diseases such as influenza. Using epidemiological data from the Democratic Republic of the Congo, we identify December as the peak influenza season. Analytical results establish conditions for the existence and global stability of a positive periodic solution, while numerical simulations demonstrate that seasonality can induce complex dynamics, including multiperiodic and chaotic oscillations. Low seasonal intensity sustains disease coexistence, whereas strong seasonal forcing may lead to population extinction. The emergence of quasiperiodic (torus) and chaotic (strange) attractors highlights how seasonal forcing can transform regular epidemic cycles into irregular outbreaks, providing new insights into the role of seasonality in infectious disease dynamics and control.

Speaker: Arun Kumar (Indian Institue of Technology Mandi, Himachal Pradesh India)

8:10 PM Benchmarking temporal causal discovery for fully and partially observed biochemical kinetic models

Systems of intracellular biochemical reactions are highly complex, usually involving parts that cannot be directly measured. Representing these systems as networks, with nodes for biochemical species and edges, their reactions help to quantitatively characterize their function and the effects of dysregulation. Causal discovery methods can uncover interactions within these networks from observational data, detecting hidden effects from partial observations.
We benchmark state-of-the-art temporal causal discovery methods on time series data from simulations of biochemical kinetics models. Our results demonstrate good performance on toy models for this task, particularly when data is sampled in a way that is consistent with the timescales of the system. By omitting data, we consider the problem of reconstructing these networks in the presence of latent confounders and unobserved species participating in reactions. Causal discovery indicates time-uncorrelated confounders with bidirected edges and unobserved species through time-delayed edges, locating hidden effects, and estimating their typical timescales. Finally, we extend these benchmarks to the reconstruction of a model of the epidermal growth factor receptor signalling network, a well-studied system frequently dysregulated in cancer.
Altogether, our work showcases the feasibility and usefulness of causal discovery methods as part of the data-driven mathematical modelling pipeline for systems of biochemical reactions.

Speaker: Holly Chambers (Imperial College London)

8:10 PM Calcium Signalling in Glioblastoma Networks of Different Topologies and Possible Treatments

Glioblastoma cells can form connected networks using tumor microtubes. Recently, it was discovered that through these connections glioblastoma cells can form a cell network which allows propagation of calcium waves. Additionally, there is a rare cell type called “periodic cell” which can sustain consistent intracellular calcium transients and is likely to have KCa3.1 pumps. In this work, we adapt an ordinary differential equation model for intracellular as well as intercellular calcium signaling. We also test three main hypotheses for the mechanism behind the sustained calcium oscillations in periodic cells. We find that all three hypotheses yield similar calcium oscillation patterns resembling the ones seen in the data of Hausmann et al. 2023. We apply our model to small-world, scale-free and random networks and test how communication is inhibited through removal of cells, removal of tumor microtubes, and inhibition of KCa3.1 pumps. All three network types were more vulnerable to random cell damage than to random TM damage. We find that inhibition of KCa3.1 pumps can have a significant impact on the inhibition of network communication, however, to fully degrade the calcium signalling network, all periodic cells must be eradicated confirming experimental observations.

Speaker: Alexandra Shyntar (University of Alberta)

8:10 PM Considerations on Model Complexity with respect to Parameter Sensitivity and Identifiability: A case study of cell invasion

Cell invasion is a process in which cells degrade surrounding tissue and start populating the newly created space. It occurs in healthy and ill cells, during wound-healing but also during cancer. There are many mathematical models of different modalities and complexity levels that aim to describe and quantify this phenomenon. In this work, we compare the outputs of two partial differential equation (PDE) models \cite{Crossley, Colson} and a hybrid model based on \cite{vanOers} using a naïve data fit, and the relationships of their parameters with a variance-based sensitivity analysis to see how different parameter interactions can or cannot produce similar results. We observe rather superficial parameter relationships in the PDE models, and more deeply intertwined relations in the hybrid model. Despite these differences on a deeper level, we find that the PDE models are suitable to describe the behavior of the hybrid model when restricted to the same, one-dimensional domain. We conclude with a parameter identifiability analysis with the simplest model to understand whether it is reduced enough to allow for a confident parameter estimation. We find that only half of the parameters are practically identifiable, and justify this discovery with the findings from the sensitivity analysis.

Speaker: Veronika Hofmann (Technische Universität München)

8:10 PM Contrastive Self-Supervised Learning for Decoding Physical Parameters in Stochastic Gene Expression Dynamics

Cells encode environmental information through the nuclear localisation dynamics of transcription factors (TFs) - stochastic time-series governed by physical parameters: mean expression (μ), coefficient of variation (CV), and autocorrelation time (T_ac). Labelling these is costly, motivating a foundational self-supervised model generalisable across TF localisations and biological contexts cite{zhang2022tfc, yue2022ts2vec}.

Benchmarks reveal no single approach generalises: raw SVMs achieve 86% on full-length trajectories by exploiting transient bursts, but collapse to chance (49%) on truncated series. Catch22 cite{lubba2019catch22} - 22 interpretable time-series features - scores 67% on truncated but only 61% on full-length data. Dataset design governs apparent performance.

To learn dataset-agnostic representations, we train a SimCLR-style cite{chen2020simclr} contrastive Transformer cite{vaswani2017attention} on Gillespie-simulated trajectories via InfoNCE loss. The Transformer acts as a feature extractor whose embeddings feed a downstream SVM used for classification.

We uncover a fundamental paradox: normalisation is essential for stable contrastive training, yet destroys absolute scale. Consequently, μ - trivially recoverable by a raw SVM - collapses to chance (~50%) across all SSL variants, while CV (87%) and T_ac (63%) are well-encoded. This exposes a hard incompatibility between SSL stability and scale preservation in stochastic biological time-series.

Speaker: Xi (Ian) Yang (University of Edinburgh)

8:10 PM Decoding Nonequilibrium Dynamics in Biological Systems with Horizontal Visibility Graphs

Fluctuations in red blood cell (RBC) membranes and chromatin domains encode key information about cellular mechanical properties and metabolic activity, which are often linked to physiological states and pathological alterations \cite{di_pierro_anomalous_2018}. Quantitative analysis of these fluctuations provides access to the underlying dynamics that characterize living systems as stochastic systems operating far from equilibrium. Here we transform experimental time series into complex networks using the Horizontal Visibility Graph (HVG) method \cite{luque_horizontal_2009} and exploit their topological properties as quantitative descriptors of active dynamics. We show that, without requiring additional preprocessing beyond the time-series-to-network conversion, graph-based metrics discriminate metabolic states across different cellular groups. Furthermore, the analysis reveals the presence of the precision–efficiency uncertainty principle in biological systems \cite{gnesotto_broken_2018}, whereby reductions in dynamical uncertainty occur at the expense of system efficiency. Together, these results indicate that the HVG framework provides a sensitive and robust approach to characterize active biological dynamics and to detect physiological alterations from fluctuation patterns.

Speaker: Lucía Benito Barca (Universidad Francisco de Vitoria)

8:10 PM Development of a computational microscopy pipeline for the inference of the subcellular and population-scale mechanome of red blood cells

Abstract

This work presents an automated pipeline designed for the inference of the subcellular and population-level mechanome in red blood cells (RBCs). The system utilizes high-resolution spatial (65 nm/px) and medium-resolution temporal (30 Hz) video microscopy to capture the dynamics of cell membrane thermal fluctuations (flickering).

From a mathematical and data-driven perspective, the computational framework integrates deep learning models (YOLO/ResNet) for cell localization. Membrane quantification is performed by searching for the maximum intensity gradient within the polar-transformed bounding box of the selected cell, achieving subpixel contour tracking. This architecture allows for modeling membrane fluctuations as stochastic processes, from which fundamental biophysical properties constituting the mechanome—such as viscoelasticity, mechanical power, and entropy production—are derived.

The pipeline demonstrates real-time performance levels, having processed a total population of approximately 5,000 individual cells. The method was tested by evaluating the effect of quercetin on membrane stiffness, yielding results consistent with established literature and demonstrating high sensitivity for detecting molecular modulations and subcellular mechanical heterogeneities. This advancement provides a robust statistical and computational framework for large-scale analysis in cellular mechanobiology.

Speaker: Jorge Barcenilla González (Computational Biophysics and Biological Data Analysis, Institute for Biosanitary Research, Faculty of Experimental Sciences. Francisco de Vitoria University (UFV))

8:10 PM DNA Strand Displacement Sequential Release Circuit for Scheduled Therapeutic Interventions

HIV remains a major global health challenge because antiretroviral therapy (ART) suppresses active virus but cannot eliminate the latent reservoir of infected CD4+ T cells, which can persist for years and reignite infection if treatment stops. New strategies are therefore needed to address viral latency. This theory project explores the use of DNA strand displacement (DSD) circuits to autonomously control the timing and sequence of drug delivery for chronic infections such as HIV. Using simulations, we couple a programmable ten-stage molecular release circuit to a mechanistic HIV disease model that tracks uninfected, infected, and latently infected CD4+ T cells, free virus, and drug concentrations. The model incorporates both ART and latency-reversing agents (LRAs). We integrate a sequential DSD circuit that acts as a molecular controller, releasing payloads that activate latent virus, deliver ART, or pause treatment based on therapeutic effectiveness. In simulation, this system can implement a “shock and kill” strategy by activating latent reservoirs, evaluating multiple drug options, and continuing the most effective treatment until the reservoir is reduced, after which the circuit remains dormant but responsive. These results suggest that programmable DSD timing circuits could enable autonomous, patient-specific therapies for HIV and other diseases requiring long-term, staged interventions.

Speaker: Alivia Behnke (Washington State University)

8:10 PM Dynamical System Model Discovery from Sparse Data with GFlowNets and PINNs

Discovering differential equations governing dynamical systems is a fundamental challenge in mathematical biology, where mechanistic models are used to study complex processes such as gene regulation, cell fate decisions, and tumor dynamics. This becomes particularly difficult when experimental data is sparse. Generative Flow Networks (GFlowNets) are a probabilistic framework for generating diverse candidate solutions using a reward function \cite{Bengio2021}, and recent work has shown that GFlowNets can be applied with symbolic regression for mechanistic model discovery \cite{Li2023}. However, biological data are often sparse and noisy, making the derivative estimates required for this approach unreliable.

We present a method that combines GFlowNets with physics-informed neural networks (PINNs) to discover differential models from sparse time-series data. The GFlowNet sequentially generates candidate symbolic expressions for a differential equation; each expression is then fit using a PINN, which learns trajectories consistent with both sparse/noisy observations and the proposed differential equation. The resulting PINN loss defines the reward used to train the GFlowNet. We demonstrate this approach on synthetic biological data from gene regulatory networks, and evaluate whether the method can recover governing equations under sparse data conditions.

Speaker: Saranya Varakunan (University of Waterloo)

8:10 PM Early Detection of Malaria Outbreaks Using Incubation Period Distributions and Machine Learning

Malaria remains a major global health concern. In the Republic of Korea, Plasmodium vivax is the dominant parasite and is characterized by both short- and long-incubation periods. Climate change has altered the mosquito habitats and expanded outbreak areas. However, the current malaria warning system in Korea is activated only when Plasmodium parasites are detected in captured mosquitoes. This study aims to improve the early detection of malaria outbreaks.
We utilized malaria case data from the Korea Disease Control Prevention and Control Agency (KDCA) and meteorological data from the Korea Meteorological Administration (KMA). First, we estimated infections at the time of infection using a back-calculation approach based on incubation period distributions. Second, we compared random forest, XGBoost, and LSTM models using meteorological variables from 2012 to 2020 and selected the best-performing model to predict infections. Finally, we identified outbreak periods using change point detection methods.
The XGBoost model showed the best performance in predicting infections. The outbreak onset estimated from long-incubation cases was detected earlier than the time when cases started to rise sharply. These findings suggest that change points derived from estimated long-incubation cases can serve as an effective tool for the early detection of P. vivax outbreaks. Overall, this approach may serve as a useful basis for determining the timing of preventive interventions.

Speaker: Ms Jeonghwa Seo (Department of Statistics, Kyungpook National University, Daegu, 41566, Korea)

8:10 PM Evolution of drug resistance under experimental vs within host adaptation

Experimental adaptation is widely used to study antibiotic resistance in bacteria. However, mutations identified during experimental adaptation are not always present in clinical strains \cite{waller_evolution_2023} \cite{chauhan_evolutionary_2025}. Ideally, repeating experimental adaptation multiple times can help estimate the probabilities of different evolutionary pathways towards resistance \cite{sakenova_systematic_2025}. This is particularly relevant when certain genotypes exhibit collateral sensitivity to a drug other than the one to which they were initially adapted. In our simulation study, we model a bacterial population with access to multiple mutations, each conferring some level of resistance, modelled as a shift in MIC but a decrease in maximal growth rate without drug. Mutations can be combined within one individual. This creates a dynamic fitness landscape as the drug concentration changes. The initially wild-type population is allowed to adapt to either a drug concentration that doubles every day or two or to a typical within-patient drug concentration time trajectory. This stochastic simulation is repeated many times for different levels of resistance per mutated locus. We hypothesise that if the time between drug increases in experimental adaptation is too long or bottlenecks are too drastic, selective sweeps can occur and trap the population on a specific evolutionary pathway. This would be contrary to within-host adaptation.

Speaker: Maya Louage (EAWAG & ETH)

8:10 PM Exploring the Neuroblastoma Microenvironment Using Cellular Automata: Insights into Celyvir Therapy.

Neuroblastoma is a significant health concern in children, as it is one of the most common types of cancer among this age group and is associated with poor survival rates. Currently, there are no effective therapies that significantly improve outcomes for these patients. This study explores the efficacy of Celyvir – an advanced therapy comprising mesenchymal stem cells carrying the oncolytic virus against neuroblastoma, by means of an individual-based model. A probabilistic cellular automaton was developed to implement the dynamic interactions between neuroblastoma cells, T lymphocytes, and the treatment Celyvir. The model examines various sizes, shapes, and positions of the tumour within a lattice, along with different infection probabilities associated with the action of Celyvir and various treatment schedules. This analysis identifies the most influential infection probabilities according to the model, and demonstrates that different treatment regimens can effectively eradicate the tumour, in contrast to standard clinical approaches. Additionally, Kaplan–Meier curves have been generated to assess different treatment schedules under specific tumour scenarios, highlighting the importance of precise treatment scheduling to optimise therapeutic outcomes. This study provides insights into the potential of Celyvir in neuroblastoma treatment, emphasising the need to understand tumour dynamics and strategically implement treatment schemes to improve clinical outcomes \cite{1}.

Speaker: José García Otero (Mathematical Oncology Laboratory (MOLAB), University of Castilla-La Mancha)

8:10 PM Extracting Hidden Cellular Dynamics: A Bayesian Approach to Estimating Time-varying Growth Rates from Noisy Microscopy Data

Estimating time-varying cellular growth rates from time-lapse microscopy remains computationally challenging \cite{1}. Image segmentation errors propagate into size measurements, and because traditional methods rely on finite-difference approximations, they amplify this noise. This obscures biological fluctuations and forces reliance on moving averages that artificially flatten true dynamics.
To address this, we propose a continuous state-space model uncoupling biological growth from observation noise. The unobservable cellular growth rate is modeled as a mean-reverting Ornstein-Uhlenbeck (OU) process. Cell area is modeled as the exponential of the integral of this growth rate, subject to multiplicative segmentation noise. We deployed a Bayesian inference pipeline, combining MCMC parameter estimation with a RTS Kalman Smoother, to retroactively extract the hidden time-varying growth rate from noisy area measurements \cite{2}.
Validation on simulated data demonstrates our Bayesian approach significantly outperforms moving-average techniques. By leveraging the exact cross-covariance between area and growth rate, the model successfully suppresses noise without sacrificing temporal resolution.
Currently being tested on raw experimental data, this model will subsequently be extended to jointly estimate cell-internal biochemical processes, specifically plasmid copy numbers, to quantify how internal process time-scales correlate with overall growth rate fluctuations.

Speaker: Mr Vishvas Ranjan (Centre INRIA de saclay)

8:10 PM Fluctuations of plasmid copy numbers in a population

Plasmids are extrachromosomal DNA molecules that replicate independently of the chromosome and are widely found in bacteria and other organisms. In nature, plasmids are ubiquitous and can carry various genes that play essential roles in the life of bacteria. In synthetic biology, plasmids are used as the standard tool to equip cells with designed gene circuits. Despite their importance, the theoretical literature on plasmid copy number dynamics remains fragmented, and many models are only described in the supplementary material of experimental studies. This situation often leads experimentalists to rely on models whose mechanistic basis is not fully established. In this poster, I present a new mathematical modeling framework to connect single-cell models of plasmid replication and segregation with experimentally measured plasmid copy-number distributions in growing populations. The approach couples a structured population model with a Markov jump process.

Speaker: Valentine Brulard

8:10 PM Genotoxic Effects of Bacteria and Drugs: Investigation of Hidden Interactions with a Differential Equation-Based Approach

We investigate the genotoxic effects that bacterial infections and antibiotics exert on human cells. Bacteria may induce mutations either by invading cells or by generating extracellular stress, and drugs can also have mutagenic effects. Moreover, complex interactions between the bacteria and the drug take place in the background. We modify the usual in-host pathogen models for chronic infections to create a new model by including self-replication for the bacteria, as well as a pathogen-loss term. We obtain a system of nonlinear differential equations which describes the interactions between healthy and infected human cells, the external bacteria, and possibly drug treatment.
We carried out a detailed analysis of the model. We discovered surprisingly complex dynamical phenomena, including bistability and different types of bifurcations (saddle-node, transcritical, backward). We determined the optimal infection rate from the bacteria’s perspective, and noted that for certain parameter combinations, there is evolutionary risk when striving for this value. Finally, we looked into the cumulative genotoxic effect of different therapies and compared the results of the model with experimental data measuring DNA damage in cells. Our model provides insight and helps to understand how the aforementioned interactions influence the total mutagenic effects on cells.

Speaker: Anna Geretovszky

8:10 PM Global Stability and Existence of Traveling Wave Solutions of the One-Predator-Two-Prey Models

This work investigates the three species of one-predator-two-prey ecological models in Lotka-Volterra type functional response with or without diffusive terms.
Without the diffusive effects and under two essential assumptions, we generically classify all global dynamics completely. The global asymptotically stabilities of three equilibria are shown analytically in each case. Alternatively, with the diffusive term, we establish the existence of traveling wave solutions by the higher dimensional shooting method, the Wazewski principle. In particular, there are two critical wave speeds $0<c_2<c_1$. We show the existence of traveling wave solutions with the wave speed $c$ if $c>c_1$ and the non-existence of traveling wave solutions if $0<c<c_2$. Finally, a brief discussion, biological interpretations, and numerical simulations are given.

Speaker: Mr Yung-Chih Yang (the department of applied mathematics and data science, the college of science, Tamkang University)

8:10 PM Improving Parameter Identifiability of Stochastic Reaction Network Systems Using Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) is a common tool to tackle statistical inference problems for systems where the likelihood function is intractable, a feature common in biological settings due to the inherent complexity of the models under investigation. ABC replaces the likelihood with a comparison of experimental and simulated data, finding parameters which minimise any discrepancy. To improve the efficiency of ABC techniques such as Sequential Monte Carlo (SMC) are typically implemented where the tolerance used in the rejection sampling procedure is gradually reduced over multiple iterations. We have found that designing appropriate tolerance schedules is critical not only for efficiency but also reliability of ABC SMC, with commonly used techniques for schedule selection often leading to inferred parameter values associated with local minima in discrepancy space, rather than the global minima. This problem is particularly acute in stochastic systems. We propose a new procedure to overcome this issue underpinned by reliably choosing the value for the first tolerance to be just below any local minima, with subsequent iterations refining inference around the true parameter values. We have also found that inference of stochastic systems with limit-cycle dynamics is particularly challenging. However, we show identifiability is improved by incorporating reaction-event level stochastic statistics into the discrepancy metric used to compare observed and simulated data.

Speaker: Mr Matthew Brown (University of Strathclyde)

8:10 PM Inferring Intercellular Interaction Rules for HER2+ Breast Cancer Cell Motility Using Equation Learning

Metastasis is a major determinant of survival and treatment efficacy in cancer, yet the mechanisms by which the competition and interaction of heterogeneous tumor cell clones leads to metastasis remains poorly understood. Prior experiments comparing fluorescently barcoded models of human HER2+ breast cancer show that wild-type, d16, and p95 isoforms differ in their invasion and motility (speed, persistence, mean-square displacement) properties. We developed a generative AI-based pipeline that extracts single-cell trajectories from in vitro live-cell timelapse microscopy videos of mixed-isoform cultures of HER2+ breast cancer cells. Then we construct a computational pipeline to infer agent-based model (ABM) rules describing the interactions between different isoforms using the single-cell trajectories. We simulate data from an ABM that recapitulates the motility characteristics of mixed-isoform in vitro HER2+ breast cancer cell populations. We then apply the Weak Sparse Identification of Nonlinear Dynamics (WSINDy) approach to test whether intercellular interactions governing cell movement can be recovered from simulated data, and the degree to which recovery accuracy depends on ABM initial conditions such as initial cell density and the proportion of cells within each isoform subpopulation (wild-type, d16, p95).

Speaker: Allison Introne (Department of Mathematics, North Carolina State University)

8:10 PM Inferring the Interaction Between Circadian Rhythms and Heart Rate Dynamics from Wearable Data

Circadian rhythms regulate a wide range of physiological processes, including core body temperature, hormone secretion, and cardiovascular activity. Among these, heart rate exhibits pronounced diurnal variation arising from endogenous circadian regulation. Despite this close relationship, the dynamical interaction between circadian rhythms and heart rate variation remains poorly understood.
In this study, we investigate the interaction between circadian regulation and heart rate dynamics using long-term wearable device data. We used a mathematical modeling to infer latent dynamics underlying heart rate and circadian variation. This approach enables us to characterize how circadian regulation modulates heart rate dynamics over daily timescales.
Our analysis reveals systematic differences in the inferred interaction patterns across demographic groups and clinical outcomes. These results highlight the importance of studying interactions among multimodal physiological rhythms and demonstrate how wearable data combined with dynamical modeling can provide new insights into the regulation of human physiological systems.

Speaker: Kangmin Lee (KAIST)

8:10 PM Investigating the roles of prior chemotherapy and risk type in bi-specific T-cell engager therapy against B-ALL via mathematical modeling and Bayesian inference

Blinatumomab is a bi-specific T-cell engager that links CD3+ T-cells to CD19+ B-cells, leading to T-cell-mediated B-cell lysis. While it has improved outcomes in relapsed/refractory B-cell precursor ALL (r/r B-ALL), treatment response remains highly variable and the underlying immunological mechanisms are not fully understood.
T-cell exhaustion and impaired immune fitness may contribute to treatment resistance. CD226 (DNAM-1) is a co-stimulatory receptor possibly implicated in anti-tumor immunity and its downregulation may reflect early transitions toward dysfunctional states.
We developed a mechanistic ordinary differential equation (ODE) model distinguishing CD226+ and CD226- T-cell subpopulations during blinatumomab treatment. We incorporate differences in baseline immune fitness between medium- and high-risk pediatric r/r B-ALL patients, reflecting differences in prior chemotherapy exposure. By integrating longitudinal patient cell-count data with Bayesian inference, we characterize patient-specific tumor-immune dynamics under treatment. We further assess parameter identifiability and sensitivity, and evaluate the clinical relevance of inferred immune fitness dynamics. Overall, our modeling, in close collaboration with clinical colleagues, establishes a productive cycle that integrates mathematical modeling and novel data collection strategies at clinically relevant time points to improve bi-specific T-cell engager therapy for pediatric B-ALL.

Speaker: Yifan Chen

8:10 PM Large-Scale Mechanistic Modeling for Patient-Specific Drug Recommendation and Organoid Testing in Colorectal Cancer

Colorectal cancer (CRC) remains a major cause of cancer morbidity and mortality, increasing mostly in adults younger than 50. Precision therapy and drug repurposing approaches may improve outcomes for patients who are ineligible for or do not respond to standard targeted therapy. We describe a computational framework that constructs individualized mechanistic “digital twin” models from patient transcriptional profiles. Proposed in silico drug combinations are then evaluated in patient-derived organoids (PDOs).

To this end, biopsy tissue from CRC patients is used to derive PDO lines and to generate bulk RNA-seq from both original tumor tissue and the established PDOs. Large-scale mechanistic models \cite{frohlich_efficient_2018} of intracellular signaling important for proliferation and survival form the basis of these in silico models, augmented with semi-mechanistic machine-learning components to represent treatment effects not captured by the mechanistic scaffold. Models are trained on transcriptional and cell-viability data from cell lines in CCLE and GDSC. In a second step, these models are individualized by selectively (de-)activating aberrant gene/protein species and parametrizing components using gene expression data. Model construction, parameter estimation and simulation are performed using AMICI, pyPESTO and PEtab \cite{frohlich_amici:_2021}, \cite{schalte_pypesto:_2023}, \cite{schmiester_petabinteroperable_2021}.

Speaker: Moritz Richter (Life and Medical Sciences (LIMES) Institute, University of Bonn, Bonn, Germany, Bonn Center for Mathematical Life Sciences, University of Bonn, Bonn, Germany)

8:10 PM Learning Optimal Adaptive Therapies in Space and Time: Dynamic Threshold Therapy for Prostate Cancer

BACKGROUND: Adaptive therapy delays drug resistance by modulating treatment instead of continuously applying the maximum tolerated dose \cite{1}. While Deep Reinforcement Learning (DRL) can optimize adaptive therapy in non-spatial, well-mixed deterministic tumor models \cite{2}, extending it to spatial models is challenging because tumor dynamics become stochastic and clinically observable data are limited.
METHODS: We combined DRL with an existing spatial Agent-Based Model \cite{3} and addressed the challenge of stochastic spatial dynamics by introducing a memory mechanism based on historical tumor responses to treatment and holiday periods, using clinically observable tumor burden. We also developed a transfer-learning framework to stabilize learning in stochastic spatial environments.
RESULTS: We found that the memory mechanism can significantly improve time to progression relative to memory-free agents. Besides, we show that decision-relevant information is stored in the memory, allowing the agent to infer latent tumor composition and spatial structure from treatment history. Memory therefore provides a biological interpretation for decision-making by acting as a proxy for hidden tumor state. The learned strategies remained robust under treatment perturbations, and dynamic threshold therapy emerged from memory-informed control.
CONCLUSION: Historical response memory provides an interpretable and robust mechanism for controlling tumors under limited access to spatial data.

Speaker: Yunli Qi (Wolfson Centre for Mathematical Biology, University of Oxford, Oxford, UK and Department of Integrated Mathematical Oncology, H. Lee Moffitt Cancer Center & Research Institute, Tampa, FL, USA)

8:10 PM Mathematical Modelling of Antibiotic Diffusion in Bacterial Biofilms

It has been hypothesised that a mechanism for antibiotic tolerance in bacterial biofilms -populations of bacteria embedded in an extracellular matrix - is the failure of the antibiotic to penetrate throughout the biofilm. In P. aeruginosa colonies for example, filamentous viral phages produced by bacterial cells have been shown to provide strong protection against antibiotics. Fluorescence and light microscopy imaging reveal reduced uptake of antibiotics by cells associated with phages, suggesting that they act as a barrier to diffusion. Binding is known to affect diffusion in other biological systems, such as antibody penetration in tumours. This poster presents a mathematical model for antibiotic diffusion in biofilms with binding to phages, and extensions to the model that I aim to work on as part of my PhD, in the hope of further elucidating the mechanisms by which phages protect bacteria in biofilms.

Speaker: Florence WILLIAMS (UCL)

8:10 PM Mathematical Models for the Mechanics of Soft Tissues: From Linear Elasticity to Morpho-Visco-Poroelasticity

Biological tissues are often subjected to forces, and modeling their response is crucial in cases like tumor growth or skin contraction to improve therapies. Linear elasticity is the simplest constitutive law, allowing superposition and fundamental solutions to analyze multiple force points, as illustrated by the immersed interface method \cite{roy2020immersed}. We discuss this principle in terms of convergence using singularity removal \cite{Gjerde_2019}.

However, real tissues are porous and contain moisture, and microstructures change due to cellular activity. To capture this, we use a morpho-visco-poroelastic framework \cite{Hall_2008}, which accounts for elasticity, porosity, and microstructural evolution. This framework is analyzed for stability around equilibria \cite{Sabia2025}. To address spurious oscillations in numerical solutions, we provide monotonicity conditions and propose a numerical stabilization method.

Speaker: Sabia Asghar (HASSELT UNIVERSITY)

8:10 PM Mean Flow Index (Mxa) and Autoregulation Index (ARI): Divergent Calculations, Convergent Conclusions

Cerebral autoregulation can be assessed by several methods in the ICU. Two of the most used methods are the Autoregulation Index (ARI) and mean velocity index (Mxa), but their agreement varies across patient populations. This study aims to evaluate their relationship in critically ill patients.
Transcranial Doppler recordings from 15 patients (46 paired ARI–Mxa measurements; median age 72 years [IQR 61–75], 80% male) were analyzed, and a significant negative correlation between ARI and Mxa was emphasized (r = −0.74, 95% CI [−0.85, −0.57]). A linear regression estimated ARI as Y′ = 5.934 − 4.66 × Mxa, with an Mxa of 0.3 corresponding to an ARI of ~4.5, which is consistent with their respective impaired autoregulation thresholds.
These findings indicate a measurable, albeit variable association between ARI and Mxa, highlighting differences in their responsiveness to cerebral hemodynamic changes.

Speaker: Taylan Ozkaya

8:10 PM MICAL2 expression promotes invasion and metastasis by cell autonomous and non-cell autonomous mechanisms in Pancreatic Cells

Pancreatic ductal adenocarcinoma (PDAC) is a lethal cancer due to its propensity for early metastasis. MICAL (microtubule-associated monooxygenase) proteins, which are highly expressed within PDAC, directly induce actin depolymerization and indirectly cause cytoskeleton reorganization through transcription factors. Despite this knowledge, the holistic impact of MICAL2 on cytoskeleton states of cells remains unknown. Here, we have taken a multi-scale modeling approach to connect cytoskeletal gene expression programs exhibited by pancreatic cancer cells to biochemical signaling networks and extracellular matrix conditions that regulate the cellular mechanical state. Our model allows us to determine how the expression of MICAL2 impacts pancreatic cancer cell migration across soft and stiff substrates. Our preliminary results using our modeling framework indicate that MICAL2 activity confined to its direct interaction with the cytoskeletal actin network does not significantly influence cell migration. However, activation of SRF transcriptional factor downstream of MICAL2 activity towards nuclear actin significantly adds to the cytoskeletal changes and increased migration of cells in 3D environments.

Speaker: Katherine Simms

8:10 PM Minimal Mechanistic ODE Model for Hormetic Dose–Response Dynamics

Hormesis, a biphasic phenomenon of low-dose stimulation and high-dose inhibition, poses a modelling challenge due to nonlinear, history-dependent dynamics. Static curves cannot capture temporal evolution, hysteresis, or recovery. Existing approaches are empirical, high-dimensional, or lack explicit dose-memory, limiting their ability to capture hysteresis and recovery. Here we propose a minimal, interpretable ODE model with explicit dose-memory to address this gap.

The model comprises a biological response and a dose-memory variable, governed by six fitted parameters covering stimulation, stimulation attenuation, adaptation, homeostasis, toxicity, and memory decay; the dose-memory variable enables hysteresis and phase-lagged recovery. Parameter estimation combined Differential Evolution (global) with L-BFGS-B refinement. Validated against weekly intrinsic mitochondrial respiration data from an excessive exercise training study \cite{Flockhart2021}, weeks 1-4 for calibration and week 5 as validation, yielding R2=0.998, RMSE=0.105.

Sensitivity analysis showed toxicity and stimulation parameters dominated model output; memory-related parameters showed negligible sensitivity, an identifiability limitation of weekly resolution, not a structural deficiency. Daily sampling or perturbation protocols are recommended to resolve memory dynamics. The framework generalises conceptually to other repeated-exposure systems exhibiting stimulation, adaptation, and recovery.

Speaker: Aini Fitriyah (University of Birmingham)

8:10 PM Modeling Adult Neural Stem Cells in Zebrafish With Feedback

The zebrafish serves as a powerful model of lifelong neurogenesis in vertebrates. Their Neural Stem Cells (NSCs) persist in specialized niches to generate neurons and glial cells, exhibiting high constitutive neurogenic activity and remarkable regenerative capacity \cite{Labusch2020, Grandel2006}.

Key gaps remain in understanding the molecular and cellular regulators of NSCs quiescence, activation, proliferation dynamics, migration, and fate decisions, particularly in domains like the telencephalon. Filling these gaps could inform strategies for enhancing regeneration in less neurogenic species, such as mice or humans, with implications for regenerative medicine and neurodegenerative disease therapies
\cite{Elkin2025, Kalamakis2019}.

In this poster, I will present a new mechanistic modeling framework, based on experimental data, that capture the spatio-temporal regulation of NSCs located in the adult zebrafish pallium.

Speaker: Theo Andre (Heidelberg University)

8:10 PM Modeling EBV-Driven B Cell Fate Trajectories

Most adults are infected with the Epstein-Barr virus (EBV), which infects B cells and establishes lifelong latency. EBV achieves this by hijacking B cell-intrinsic transcriptional programs, which ultimately promotes B cell survival, including that of atypical memory B cells (ABCs), a population associated with autoimmune disease. Here, we aim to construct an ODE model of B cell fate trajectories following EBV infection, with the goal of quantifying the dynamics of cell state changes that lead to successful infection as well as to the emergence of ABCs. Our approach uses scRNA-seq data collected during the early stages of EBV infection in B cells to quantify how cell state proportions evolve over time. We then apply a SINDy-based model discovery framework to infer interpretable ODEs describing transitions between cell states. Ultimately, beyond the specifics of studying the influence of EBV on B cell fate, we aim to build a generalizable pipeline that translates scRNA-seq data into interpretable, dynamic models of cell fate trajectories.

Speaker: Grace McLaughlin (Duke University)

8:10 PM Modeling the Transient Nature of Immunosenescence in Influenza Infection

The majority of ordinary differential equation models that exist in the literature focus on steady state equilibria or long-term outcomes, with very few emphasizing the transient nature of these systems of equations. In this work, we present a reduced system of ODEs to investigate the kinetics and transient nature of T cell activation in response to acute viral infection. Through an analysis of the system, we identify a T cell threshold that governs how the system solutions behave, as well as whether or not immune control over infection is attained. As a case study, we investigate influenza infection in young (aged 12-16 weeks) and aged (aged 72-76 weeks) mice in order to identify differences in the immune response between the two groups of mice. The results of our case study and analysis show that there is a distinct shift in the T cell threshold between young and aged mice, indicating the existence of a regulatory mechanism by which differences in the immune response due to aging can be explained. These results also highlight the importance of investigating the transient dynamics of ODE systems, especially as they relate to determining the outcomes of acute infection.

Speaker: Havilah Neujahr (Department of Mathematics and Statistical Science, University of Idaho)

8:10 PM Modeling tumor dynamics under PROTAC therapy: a mathematical model for resistance analysis

We present a mathematical framework to describe tumor growth under PROTAC treatment, integrating PK, PD, and tumor growth inhibition. PROTACs are a new class of drugs that promote selective degradation of oncogenic proteins \cite{1}. Although preclinical studies show tumor shrinkage, relapse often occurs, suggesting resistance mechanisms \cite{2}. The model links PROTAC-induced protein degradation to tumor growth inhibition. To account for reduced treatment efficacy, we introduce a cumulative resistance mechanism, allowing a progressive reduction of drug efficacy over repeated dosing \cite{3}. The model combines a two-compartment PK model, a protein turnover module with constant synthesis and drug-stimulated degradation \cite{4}, and classical tumor growth laws (Linear, Exponential, Logistic, Gompertz) \cite{5}. After calibration on in-vivo xenograft data, the model accurately reproduces both initial regression and subsequent regrowth observed experimentally. A key contribution is the mathematical analysis. By treating the remaining protein level as a bifurcation parameter, we identify a critical threshold separating tumor eradication from relapse. Crossing this threshold induces a qualitative change in system stability, marking the transition from regression to tumor outgrowth. This analysis provides a predictive tool to anticipate resistance onset from protein dynamics, supporting adaptive therapeutic strategies aimed at delaying relapse while optimizing drug exposure.

Speaker: Cecilia Torboli (University of Udine, Italy)

8:10 PM Modelling resistance evolution in spatially structured microbial populations

The emergence and spread of drug-resistant microbes is an increasingly pressing problem, fueled by the declining development of new antimicrobials and the rapid adaptation of pathogens. In bacteria, sessile surface-attached biofilms represent the predominant mode of growth. This form of bacterial life not only confers intrinsic tolerance to stressors, including antibiotics, but also introduces spatial structure within the population \cite{flemmingBiofilmsEmergentForm2016}. Limited diffusion into the biofilm matrix, as well as sorption and degradation of antimicrobials, can lead to spatial drug concentration gradients \cite{stewartTheoreticalAspectsAntibiotic1996}. Similarly, nutrient and oxygen limitation in the lower regions of biofilms can create gradients in metabolic activity \cite{coEmergentMicroscaleGradients}. Here, we examine the influence of population spatial structure and spatial gradients in drug concentration and metabolic activity on the dynamics of drug resistance evolution in bacterial biofilms. A stochastic pharmacokinetic/pharmacodynamic population genetic model, that discretises across the depth of a bacterial biofilm, is used to capture population spatial structure. Simulations reveal that spatial gradients can modify evolutionary trajectories and that population spatial structure can increase the likelihood of resistance emergence. Implicating the importance of considering population spatial structure when treating biofilm-associated infections.

Speaker: Basil Vogelsanger (ETHZ)

8:10 PM Modelling the Range Change Dynamics of Host-Macroparasite Systems under Climate Change using Reaction-Diffusion Equations

Macroparasites, such as helminths, mosquitoes, and ticks, can impact host fitness and population dynamics, both directly and through the diseases they transmit. Climate change is expected to lead to macroparasite range shifts as habitats become more suitable towards the poles and less suitable towards the equator. These shifting distributions can have negative consequences on host-macroparasite population persistence and survival; however, mathematical models that can accurately predict such spatiotemporal changes are lacking. Here, we develop trait-based reaction-diffusion equations to model the range change dynamics of environmentally transmitted macroparasites under climate change. Using MATLAB to numerically simulate model solutions over a discrete space-time grid, we focus our analyses on a single-host-single-macroparasite system and track how the macroparasites progress throughout various life stages, die and reproduce; traits which are temperature dependent. We outline in which climate warming scenarios macroparasites and/or their hosts are expected to undergo range contractions vs expansions, as well as which scenarios may lead to increases or decreases in disease burden and extinction risk. Our framework lays the foundation for predicting climate change impacts on the changing spatial distributions of parasites and parasitic diseases and will help managers develop proactive plans for mitigating the subsequent impacts on human, animal and environmental health.

Speaker: Haley Morris (Department of Ecology & Evolutionary Biology, University of Toronto)

8:10 PM Molecular dynamics simulations of epilepsy- associated SCN1A variants for guiding pharmacological treatments

Ion channels play an essential role in brain communication networks. Mutations in the SCN1A gene encoding the alpha subunit of the voltage-gated sodium channel NAV1.1, expressed in the central nervous system, are responsible for severe epilepsy and migraines often resistant to treatments.

We used molecular dynamic simulations to investigate consequences of four clinically relevant SCN1A variants (R1636Q, I1498M, R859H, R946C). Structural models were generated using AlphaFold and subsequently subjected to large-scale atomistic simulations using GROMACS to characterize alterations in channel dynamics.

Our simulations revealed that the gain-of-function mutations R1636Q and I1498M exhibited a more buried IFM binding pocket and altered structural dynamics in domain IV. In contrast, the loss-of-function variant R946C displayed pronounced perturbations in the selectivity filter region. The mixed-function variant R859H showed distributed conformational changes across all four channel domains.

We further simulated the effect of the antiepileptic drugs oxcarbazepine (a sodium-channel blocker), and 8DE (a selective Nav1.1). Oxcarbazepine increased the exposure of the IFM binding pocket in both gain-of-function variants, suggesting a previously unreported mechanism that may partially restore inactivation.

Together, these results show how atomistic simulations link genetic variation to channel dynamics and drug responses, supporting variant-specific therapies in channelopathies.

Speaker: Mistre Bekele (University Of Luxembourg)

8:10 PM Multiscale Simulation of Ovarian Follicle Dynamics: Linking PDE and ODE Descriptions

Follicular phase in the ovarian development involves two key mechanisms: follicle maturation (via cellular growth and mass increase) and competition among follicles. Capturing both remains challenging. Compartmental ODE models (e.g., \cite{Hendrix}) describe maturation through discrete stages and reproduce macroscopic dynamics, but neglect follicular competition and cellular maturation. Conversely, models like \cite{Fischer} include competition but lack maturity structure. Physiologically structured population models (PSPMs) (e.g., \cite{Monniaux}), formulated as transport PDEs, account for both maturity growth and follicular competition; numerical simulations exist (e.g., \cite{Aymard}). Yet, they remain computationally intensive and less directly connected to established ODE frameworks.

We introduce a class of transport equations bridging these approaches via perturbative moment closures. These PDEs allow the application of standard numerical procedures for solving them. We present numerical simulations showing how the resulting PDEs reproduce cellular development and follicular competition consistent with the macroscopic ODE models. The structured PDEs preserve the key nonlinear mechanisms governing recruitment, selection, and atresia, providing a computationally efficient framework for multiscale modelling of ovarian follicle development for different physiological and pathological conditions.

Speaker: Edilbert Christhuraj (Anhalt University of Applied Sciences)

8:10 PM One item per disorder: a cross-disorder optimization framework for simultaneous prediction of six psychiatric conditions

Mental disorders are a major contributor to the global burden of disease and often manifest as overlapping symptom profiles rather than isolated diagnoses. In clinical and digital health settings, this requires simultaneous assessment of multiple psychiatric domains, including depression, anxiety, trauma-related symptoms, substance use, and suicidality. However, current screening frameworks rely on separate disorder-specific questionnaires, producing lengthy assessments that increase response burden and limit scalability for large-scale or longitudinal monitoring. From a systems perspective, this raises the question of whether multi-disorder psychiatric risk signals are distributed across many questionnaire items or concentrated within a smaller set of core symptom dimensions. Here, we investigate structural compression in multi-disorder psychiatric assessment by identifying representative symptoms across six commonly used instruments. Our framework compresses 57 questionnaire items into a six-item representation while preserving strong predictive performance across all disorders (AUROC ≈ 0.90–0.97). Network analysis further shows that the selected symptoms occupy central positions within the symptom interaction network, suggesting that multi-condition psychiatric risk can be captured through a compact set of symptom dimensions.

Speaker: Ms Myna Lim (Graduate School of Data Science, KAIST)

8:10 PM Pan-genome scale metabolic modeling reveals medium dependent metabolic diversity in Sulfolobus

The genus Sulfolobus includes some of the most extensively studied thermophilic Archaea and is notable for its metabolic versatility and relevance to industrial biotechnology. Genome-scale metabolic models (GEMs) enable predictive analyses of metabolism, but their reconstruction is complex, time consuming and sensitive to environmental assumptions, particularly during gap filling.

Here, we reconstructed the Sulfolobus pan-reactome comprising 76 GEMs derived from publicly available genomes. Models were generated using two different growth media to assess how environmental assumptions influence model structure and predictions. While reaction content differed by less than 1% across models, media composition strongly affected growth feasibility, auxotrophic behavior, and predicted growth rates. Predicted growth rates deviated from experimental values by 4–24%, despite minimal differences in global predictive accuracy.

This work presents the first genus-wide Sulfolobus pan-reactome and a curated genome-scale model for S.acidocaldarius, highlighting how reconstruction assumptions can bias inferred metabolic capabilities in archaeal GEMs.

Speaker: Maria Jose Rimon Martinez

8:10 PM Parameter estimation in infectious disease models from infected case data using metaheuristic-tuned PINN

One crucial part of modeling infectious disease dynamics is accurate parameter estimation. This study proposes a framework using physics-informed neural networks with metaheuristic hyperparameter tuning to estimate parameters in infectious disease models. For practical applicability, the method uses only infected case data while enforcing the governing differential equations during training. The results shows that the approach can effectively recover model parameters from limited observations.

Speaker: Arrianne Crystal Velasco

8:10 PM Physics-Informed Neural Networks for Inferring Tumor Glucose–Lactate Metabolic Dynamics

Metabolic reprogramming is a central hallmark of cancer, enabling tumor cells to sustain rapid proliferation and adapt to fluctuating nutrient availability and microenvironmental stress. In particular, the coupled dynamics of glucose consumption and lactate production provide insight into tumor metabolic phenotypes such as the Warburg effect and metabolic switching between glycolytic and oxidative states. Mathematical models have been widely used to study these processes; however, linking experimental metabolite measurements with mechanistic models of tumor metabolism remains challenging due to limited observability, measurement noise, and uncertainty in model parameters. In this work, we present a hybrid experimental–computational framework for identifying tumor metabolic dynamics by integrating multiplexed microfluidic biosensing with physics-informed neural networks (PINNs). We developed a microfluidic bead-based aptamer sensing platform capable of quantifying glucose and lactate concentrations in cancer cell culture media, enabling time-resolved monitoring of metabolic changes during cell proliferation. Experimental data are integrated with a differential-equation model of tumor glucose–lactate metabolism using PINNs, enabling inference of metabolic parameters and reconstruction of metabolic trajectories. Application to glioblastoma and prostate cancer cell lines reveals distinct metabolic behaviors consistent with glycolytic and hybrid phenotypes.

Speaker: Shadi Vandvajdi (University Of Waterloo.Department of Electrical and Computer Engineering, Department of Applied Mathematics)

8:10 PM Physics-Informed Neural Networks for Solving and Calibrating the Fisher-KPP Equation in Spatiotemporal Pathogen Dynamics

Reaction-diffusion equations are central in ecological modeling for describing how biological populations, such as pathogens, propagate through space and time. While standard numerical methods such as finite difference and finite element schemes are well established for solving these equations, they can be difficult to integrate with data-driven inverse problems, particularly when estimating model parameters from noisy experimental observations. In this study, we employ Physics-Informed Neural Networks (PINNs) to solve and calibrate the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation, which models the logistic growth and homogeneous diffusion of biological populations \cite{Raissi_2019, Leclerc_2023}. We specifically investigate the spread of Peyronellaea pinodes on pea stipules using sequential daily imagery obtained from an experimental setup \cite{pea_dataset_2022}. By integrating the Fisher-KPP equation into the neural network’s loss function, our framework enables the simultaneous prediction of the probability of infection and the identification of key biological parameters, including the growth rate and diffusion coefficient, directly from the image dataset. This approach demonstrates the potential of PINNs to provide efficient solutions to both forward and inverse problems in complex biological systems.

Speaker: Jayrah Bena Riñon (Data Science Program, College of Science, University of the Philippines Diliman; Department of Mathematics, College of Science, Bicol University)

8:10 PM Protein-Ligand Affinity Prediction via Topologically-Aware Graph Neural Network

Recent computational methods predict the binding affinity between pairs of proteins and ligands, often applied to evaluate how well a candidate drug might attach to a target protein. In complex-based protein-ligand affinity prediction, binding strength is inferred from the known 3-dimensional structures of protein-ligand complexes. State-of-the-art methods employ neural networks, but certain geometric structures remain difficult to encode as learnable features. To address this challenge, we apply persistent homology cohomology (PCH)\cite{pch}, a mathematical technique that identifies “holes” in data across spatial dimensions. In the protein-ligand complex, PCH identifies 0-dimensional holes, representing clusters of nearby atoms, 1-dimensional holes representing ring-like atomic structures, and 2-dimensional holes representing cavities in the binding pocket. To represent PCH features in a learnable format, we introduce the spatially-aware topological graph. We locate spatial representatives of each n-dimensional PCH feature, and compute the shape-preserving Wasserstein distance between each pair. These distances induce the spatially-aware topological graph, nodes represent n-dimensional holes and edges connect holes sharing a Wasserstein-neighborhood. Embedding nodes and edges with known physiochemical properties, we train a graph neural network on the PDBbind dataset\cite{pdb} of known protein-ligand complexes, achieving accuracy comparable to existing high-end methods.

Speaker: Perry Beamer (North Carolina State University)

8:10 PM Quantifying Relative Contributions of Driving Factors of ILI Incidence Dynamics across Europe

Previous studies have identified several drivers of influenza-like illness (ILI) incidence dynamics in temperate regions, yet it remains unclear whether these associations are reproducible across countries or shaped by local context. This study quantifies the relative contributions of climate and behavioral factors to ILI incidence dynamics across multiple European countries, using weekly incidence data from 2014 to 2025 reported to ERVISS, the surveillance database maintained by ECDC. We compute the weekly effective reproduction number ($R_e$) from incidence data and model them as a function of explanatory variables within a regression framework. These variables include absolute humidity, holiday periods, and the Normalcy Index. The framework separates persistent associations from season-specific baseline components and reporting-related variation, and enables comparison between pre- and post-pandemic periods. We find that absolute humidity shows consistent negative associations with weekly $R_e$ across countries, whereas behavioral factors exhibit greater heterogeneity. This framework provides a way to distinguish between generalizable and context-dependent drivers by comparing cross-regional dynamics, informing interpretation of epidemic trends during both normal and disrupted periods, such as the COVID-19 pandemic.

Speaker: Pauline Bakker (National Institute for Public Health and the Environment (RIVM), the Netherlands)

8:10 PM Quantifying serial killing via multiscale Bayesian comparison of models for sequential NK cell responses

Natural killer (NK) cells eliminate stressed and transformed cells by integrating signals from activating and inhibitory receptors. Although “serial killing” has been widely discussed, two quantitative gaps remain. First, it is unclear whether apparent serial killers reflect stable, intrinsic cytotoxic capacity differences, stochastic encounter dynamics, or both, making the definition ambiguous: how many kills, or how many productive stimulations, are required before a cell is more than a stochastic outlier? Second, the effect of sequential stimulation is unresolved, with repeated engagements potentially reinforcing commitment or inducing exhaustion.

We combine multiscale modelling with Bayesian inference to link intracellular activation to population-level single-cell readouts under sequential stimulation. Using flow-cytometry CD107a degranulation measurements across four consecutive stimulations, we summarise response histories as a 16-state distribution and compare mechanistic hypotheses, including heterogeneity in cytotoxic capacity, dependence on prior responses, and a highly responsive subpopulation. Bayes factors and posterior uncertainty quantification provide a principled way to adjudicate between hypotheses and to suggest informative follow-up experiments for immune surveillance and immunotherapy.

Speaker: Elephes Sung (Imperial College London)

8:10 PM Reconstructing High-Resolution Tau Distributions from Regional tau-PET Data Using Implicit Neural Representations

Introduction & Methods:
Alzheimer's disease (AD) progression involves the accumulation and spread of tau pathology, measurable via tau PET imaging. Conventional analyses using regional standardized uptake value ratios (SUVRs) obscure fine-grained spatial heterogeneity and early tau propagation. We developed an Implicit Neural Representation (INR) model to reconstruct voxel-level tau distributions from regional measures. Using multimodal neuroimaging data from 61 ADNI participants, AV1451 Tau-PET scans were parcellated into 86 regions via the Desikan–Killiany atlas, and MRI-derived atrophy measures were obtained using FreeSurfer. The INR—a 16-layer fully connected network —took spatial coordinates, regional SUVRs, and z-scored atrophy as inputs to predict voxelwise SUVR.
Results:
The model achieved a mean per-subject correlation of R = 0.891 ± 0.111 and a pooled correlation of R = 0.959 (p < 0.01), with unbiased, normally distributed residuals. Excluding MRI atrophy reduced performance to R = 0.831, underscoring its importance. Region-wise accuracy averaged R = 0.936, with highest fidelity in AD-critical regions including the entorhinal cortex (R = 0.952), left thalamus (R = 0.974), and inferior parietal cortex (R = 0.958).
Conclusion:
Our study bridges coarse regional summaries and high-resolution voxel data, offering a scalable, biologically grounded tool for early AD detection, mechanistic modeling, and individualized tau pathology assessment.

Speakers: Anil Kamat (University of California San Francisco), Dr Ashish Raj (University of California San Francisco)

8:10 PM Same Calories, Different Outcomes: the Dynamics of Fasting in Cancer

Intermittent fasting has been proposed as a potential strategy to modulate tumor progression through systemic metabolic regulation\cite{1}. In this work, we develop a mathematical framework that integrates a model of glucose homeostasis with a tumor growth law, enabling the study of how fasting schedules may influence tumor dynamics.
We first introduce a dynamical model of glucose metabolism that includes glucose, insulin, glucagon, and glycogen. The model is specifically designed to capture alternating periods of fasting and feeding through time-dependent glucose inputs. Model parameters are calibrated using data from real patients, ensuring that the simulated glucose dynamics remain physiologically realistic.
Then, we generate a cohort of virtual patients from the calibrated model that reflects inter-individual variability while remaining consistent with clinically observed behavior. Each virtual metabolic profile is then coupled to a tumor growth law. We identify the virtual metabolic patient whose glucose dynamics best reproduce the effective growth rate estimated by fitting the growth law to volumetric tumor data, thereby constructing consistent metabolic–tumor patient pairs.
This integrated approach enables quantitative comparison of tumor evolution under standard feeding conditions and under various intermittent fasting protocols. Overall, the framework provides a basis for investigating how metabolic variability and dietary interventions may help control tumor growth.

Speaker: Andrés Méndiz Fernández (Mathematical Oncology Laboratory (MOLAB), Universidad de Castilla - La Mancha (UCLM))

8:10 PM Sensitivity analysis for biological differential equation models with many parameters

Mathematical models of biology commonly use differential equation formulations. Certain application areas, such as signal transduction modeling or scientific machine learning, involve models that contain many parameters. Efficient training of these models requires sensitivity analysis that scales well as the number of parameters grows. Hence, adjoint sensitivity analysis (ASA) is typically employed, instead of forward sensitivity analysis (FSA) \cite{frohlichScalableParameterEstimation2017}.

In this work, we derive a new sensitivity analysis method that has similar scaling properties to ASA but, unlike ASA, can be solved in the forward direction. This provides some computational efficiency gains in terms of memory and complexity, especially for the stiff systems that are common when modeling biology. Furthermore, higher-order sensitivities are cheaper to compute with the new method. A drawback is that, when the parameter size is small or the state size is large, then the FSA or ASA methods, respectively, can naïvely outperform the new method.

Speaker: Dilan Pathirana (Bonn Center for Mathematical Life Sciences, University of Bonn, Germany. Life and Medical Sciences (LIMES) Institute, University of Bonn, Germany.)

8:10 PM Sex-Specific Temporal Dynamics of Human Sleepiness

Sleepiness is commonly described by the two-process model, in which sleep pressure—a homeostatic drive that accumulates during wakefulness—and the circadian rhythm—an endogenous ~24-hour physiological cycle—interact to regulate alertness. Although this framework explains the primary fluctuations in alertness, substantial inter-individual variability remains unexplained. In this presentation, we apply mathematical modeling to long-term sleepiness data to investigate temporal dynamics beyond the canonical circadian scale and examine potential sex-related differences in these patterns.

Speaker: Hyunji Jeong (Korea Advanced Institute of Science and Technology)

8:10 PM Spatially informed biologically interpretable machine learning approaches for analyzing EEG data

Biological neural networks (BNNs) are machine learning models that enhance the biological interpretability of artificial neural networks by modeling neural dynamics and providing insights underlying neural system behavior. In our previous work, Hodgkin-Huxley neuron models were implemented in BNNs to classify electroencephalogram (EEG) signals \cite{cruz2026bnn}. While biologically interpretable, these models treat each electrode independently and ignore spatial relationships, limiting their ability to capture large-scale brain dynamics.

Here, we extend this framework by developing trainable BNNs using time-aware backpropagation applied to networks of biophysically accurate neurons based on modified Hodgkin-Huxley equations \cite{deistler2024diffsim}, integrated within feedforward and recurrent architectures. Neuron sets represent brain regions, and synaptic weights reflect spatial distances and functional connectivity. These BNNs classify consciousness levels from EEG data, extrapolate deeper brain activity, and exhibit physiologically observed frequencies, while hidden-layer neurons remain biologically interpretable.

Overall, spatially informed BNNs capture deeper structures, generate emergent spatiotemporal patterns, and improve cross-subject generalization, advancing both EEG interpretability and generalizability while bridging neural modeling and modern machine learning.

Speaker: Madelyn Esther Cruz (University of Michigan)

8:10 PM Systems-level Analysis of CAF Signaling Networks Identifies MASTL-driven Angiogenic Regulation

Cancer-associated fibroblasts (CAFs) play a key role in tumor progression by orchestrating complex signaling interactions within the tumor microenvironment. However, the regulatory architecture of CAF-mediated signaling networks remains poorly understood at the systems level. Microtubule-associated serine/threonine kinase-like (MASTL), a mitotic kinase involved in cell cycle regulation, has been implicated in gastric cancer cell proliferation, but its role in stromal signaling is unknown. Here, we investigated whether MASTL functions as a regulatory node in CAF signaling networks. Conditioned media from gastric cancer cells induced MASTL expression in CAFs, suggesting tumor-driven modulation of stromal kinase activity. Functional assays showed that MASTL silencing impaired CAF migration and tumor-promoting properties. To characterize the underlying mechanisms, we performed quantitative secretome profiling using high-resolution LC–MS/MS. Systems-level proteomic analysis identified MASTL-dependent changes in secreted factors. Network-based bioinformatic analyses highlighted VEGFA–VEGFR2 signaling as a central pathway. Consistently, CAF secretomes regulated by MASTL enhanced angiogenic activity in endothelial tube formation assays. These findings suggest that MASTL reshapes the CAF secretory signaling network to regulate tumor angiogenesis.

Speaker: Jae-Young Kim (Chungnam National University)

8:10 PM T-cell Motility in Confined Geometry: a Statistical Analysis and Model Comparison

As immune cells circulate in the body, different factors may influence their movement, such as other immune cells, target cells, and the topology of the space \cite{Jerison2020}. This work investigates how confinement geometry influences T-cell motion and compares results with mathematical models in the literature. The analysis is based on experiments provided by the Swinburne team, focusing on T-cells confined in a square well in the absence of external stimuli. A statistical analysis reveals non-Brownian behaviour, with MSD exponents exceeding 1 at short timescales before dropping below 1 at longer timescales. The Time-Average Mean Square Displacement, Distributional Mean Square Displacement, and Normalised Autocorrelation Function of the velocities serve as benchmarks for evaluating models, including the Self-Avoiding Random Walk, the Beauchemin Model \cite{Textor2013}, and the Generalised Lévy Walk \cite{Harris2012}. The former two fail to reproduce the superdiffusive regime, predicting subdiffusive behaviour throughout. The Generalised Lévy Walk can match both regimes after fine-tuning, and while it lacks a mechanistic justification, it remains a valuable approximation. This work is ongoing, aiming to uncover the underlying dynamics driven by persistence and boundary interactions.

Speaker: Lorenzo Huang (Swinburne University of Technology)

8:10 PM The Nuclear Mechanome: A Stochastic Dynamical Characterization of Leukemic Cell Nuclei

We present a computational framework for the mechanical characterization of leukemic cell nuclei integrating videomicroscopy, image-processing algorithms, and stochastic mechanics. The methodology has been developed within the Leukodomics project, aimed at constructing a digital twin for pediatric acute lymphoblastic leukemia.

Nuclear dynamics are quantified through automated tracking of intranuclear domains. Resulting trajectories are converted into time series of domain positions and analyzed using stochastic process theory. Within a generalized Langevin framework, nuclear fluctuations provide quantitative information on mechanical properties. Tracking data are integrated with confocal fluorescence microscopy, enabling biological annotation with chromatin density and differentiation markers (CD19, CD7, CD34).

Trajectory analysis in temporal and spectral domains yields four descriptor groups: spectral properties (power spectra, entropy, relaxation times); viscoelastic parameters inferred from fluctuation dynamics (effective stiffness, viscosity, diffusion); nonequilibrium activity indicators (Kullback–Leibler divergence, volatility, thermodynamic uncertainty, waiting-time variance); and spatial coherence metrics describing mechanical organization within the nucleus.

Together these descriptors define the nuclear mechanome, enabling single-cell characterization and patient-level signatures, and linking nuclear mechanical heterogeneity with functional biological variability.

Speaker: Carlos del Pozo Rojas

8:10 PM The role of phenotypic plasticity in evolution of coexistence.

Modern coexistence theory (MCT) has been the mainstay of coexistence research in recent years. While competition creates evolutionary changes in traits that affect coexistence, it can also induce rapid plastic changes in individuals. However, a generalised framework that integrates both plasticity and evolution into MCT is lacking. Here, we incorporated competition-induced plasticity into a generalised eco-evolutionary Lotka-Volterra two-species competition model based on quantitative genetic inheritance. We analysed how abiotic environmental breadth modulates the effect of plasticity on the evolution of coexistence. We find that for a broad environment, adaptive plasticity accelerates evolution to coexistence, whereas maladaptive plasticity hinders it. By contrast, for a narrower environment, adaptive plasticity can hinder coexistence when competition width is comparable to abiotic environmental breadth. We find that in narrower environments, the direction of evolutionary change can oppose the direction of plastic trait responses, ultimately shifting the balance between niche overlap and fitness differences and thus affecting coexistence. Our results show that plasticity can reshape the eco-evolutionary trajectories to coexistence and highlight the importance of integrating short-term plastic responses with long-term evolutionary dynamics.

Speaker: Vishnu Venugopal (Bielefeld University)

8:10 PM Threshold Dynamics in a Time-Delayed Logistic Model of Cell Populations

We extend the delayed logistic cell-population model of Baker and
Röst. The generalized equation incorporates distributed delays expressed
via both discrete and integral terms, and explicitly features the death rates of dividing and motile cells as parameters.
We first establish well-posedness, along with the nonnegativity and
boundedness of biologically relevant solutions. We then derive an explicit threshold parameter that determines the stability of the zero equilibrium and the existence of a positive equilibrium. When the zero equilibrium is stable, no positive equilibrium exists and the cell population goes extinct.
When the zero equilibrium is unstable, there exists exactly one positive
equilibrium, which is stable; in this system we prove uniform strong persistence of the population.
Our results quantify how the death rates of dividing and motile cells, as well as the delay representing the duration of the division process, shape the system’s global dynamics.

Speaker: Villő Glavosits (SZTE Bolyai Institute)

8:10 PM Wavelet-Based Machine Learning Prediction of Norovirus Detection Rates in South Korea

Norovirus is a primary agent of acute gastroenteritis in all age groups, with young children under five being particularly vulnerable. Due to the virus’s pronounced seasonal behavior, forecasting its detection rate based on climatic factors is essential. To characterize the periodic relationship between climate variables and norovirus detection rates, wavelet coherence analysis was applied. The phase shift in the one-year cycle was examined to identify temporal changes in seasonal behavior. To further capture long-term nonlinear trends, generalized additive models (GAMs) were used to estimate the underlying trend in the detection rate. Based on the GAM-derived trend, the data were adjusted to reduce long-term variability and emphasize seasonal signals. The model was trained using data from January 2007 to June 2019 and tested using data from June 2019 to December 2020. Weekly detection rates were predicted using four machine learning models, incorporating wavelet-derived features that reflect time-varying seasonal characteristics. The inclusion of wavelet analysis and trend adjustment improved prediction accuracy by approximately 10–15% compared with models using the original climate variables alone.

Speaker: Giphil Cho (Kangwon National University)

Wed, July 15

8:30 AM → 9:30 AM Contributed Talks

8:30 AM → 9:30 AM Contributed Talks

8:30 AM → 9:30 AM Contributed Talks

11:10 AM → 12:30 PM Inferring and designing stochastic biochemical processes at the single-cell level

11:10 AM Stochastic modeling of horizontal gene transfer via M13 bacteriophages in E. coli populations

Horizontal gene transfer mediated by bacteriophages is a critical mechanism for bacterial genome plasticity, among others, responsible for the diffusion of antibiotic resistance. We develop a stochastic Chemical Reaction Network (CRN) model capturing phage-mediated communication between engineered Sender and Receiver E. coli populations, where M13 bacteriophages transport genetic sequences, including antibiotic resistance genes. Our model integrates several scales: cell growth kinetics, phage production, infection dynamics, and population-level interactions under antibiotic selection. Its main features are modeling of infection phases, growth-burden-associated phage production, and the impact of antibiotic selection. The stochastic CRN considers individual cell variability and rare infectious events, which are essential when phage or Receiver concentrations are low. This model allows to make quantitative predictions about resistance transfer efficiency under different conditions such as co-culture proportions and antibiotic concentrations. As an application, we showcase its use in designing bacterial communication systems and understanding the dynamics of genetic transfer in resource-limited environments.

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Speaker: Alexandra Loudieres (Université Paris-Saclay)

11:30 AM Variance-reduced Bayesian Inference for Partially Observed Stochastic Processes

Modern experimental and imaging technologies provide high-resolution time-series measurements of biological systems, revealing dynamic behaviours that are difficult to analyze statistically. The underlying biological processes are typically noisy, partially observed, and high-dimensional, making Bayesian state-space models a natural framework for their analysis. However, exact Bayesian inference is intractable for nonlinear and non-Gaussian systems, and particle filters – widely used approximation schemes – suffer from high Monte Carlo variance in such settings. This limits their applicability to complex biological networks, where inference must remain stable to obtain reliable results. We developped a variance-reduced Bayesian inference method tailored to partially observed stochastic processes. Building on the Rao-Blackwell theorem, our approach decomposes the full system into two nonlinear subsystems: components that are kept explicit in the particle filter and components that are analytically marginalized. While classical Rao–Blackwellized particle filters rely on conditional linear-Gaussian assumptions, our method generalises the concept to fully nonlinear reaction-network dynamics by deriving conditional moment equations for the marginalized components. This yields a marginal particle filter that maintains the flexibility of simulation-based inference while reducing Monte Carlo variance. We demonstrate the approach using case studies of varying complexity.

Speaker: Hanna Wiederanders (MPI-CBG (Dresden))

11:50 AM DNA replication as a hidden driver of single-cell timing variability

Gene expression models often treat the cell cycle as mere background, overlooking the transient gene-dosage shifts introduced by DNA replication. We ask how these dosage changes reshape the time it takes single cells to cross regulatory thresholds—a key currency for decision-making in transcriptional networks. Using a general stochastic framework that captures cell-to-cell variability without relying on system-specific details, we examine how replication-induced changes in effective synthesis rates modulate timing distributions. We find that replication timing can systematically advance or delay threshold crossings and, depending on network context, either sharpen or broaden variability across cells. These effects are most consequential for circuits that gate events requiring precise schedules, such as division checkpoints or developmental transitions. Our analysis highlights qualitative design principles for buffering or leveraging replication-driven noise and suggests inference strategies to disentangle replication from other sources of stochasticity. By placing DNA replication back into the picture, we reveal a general mechanism by which the cell cycle sculpts single-cell temporal coordination.

Speaker: Juan David Marmolejo Lozano (University of Edinburgh)

12:10 PM Unravelling causal interactions of coding and non-coding RNA from genome wide single-cell data

Inferring gene regulatory interactions from transcriptomic data is crucial for understanding gene networks. It is made difficult by technical noise, cell size and other confounding factors which introduce spurious correlations and inference errors. Focusing on regulation via coding and non-coding RNA interactions, we generalise correlation tests in the presence of technical noise to allow accurate inference. Moment estimates from single cell RNA sequencing data are combined with moment equations from interacting telegraph models to form a computationally tractable optimization problem including semidefinite moment constraints, which can be efficiently solved using a cutting plane approach. We demonstrate the approach using total-RNA-sequencing in single cells, which allows us to identify and model interactions between non-coding RNA and their targets. The resulting network across the non-coding genome recovers causal relations that underlie the true gene-gene correlations in the data.

Speaker: William Hilton (Imperial College London)

11:10 AM → 12:30 PM Modelling applications in the pharmaceutical industry (Pharmacometrics Subgroup)

11:10 AM Feature-based prediction of preclinical pharmacokinetic profiles using machine learning and compartmental modeling

For healthcare and drug discovery, particularly during the earlier stages of target identification and hit finding, recent advancements in data availability, computational power, and methods (machine learning (ML) and artificial intelligence (AI)) have shown great promise to further rationalized the drug development pipeline initiating a transition from a “data generation and triaging” to a ”result prediction and verification” pipeline.
We present different feature-based concepts of predicting in vivo PK profiles for chemical and biological identities derived from their chemical structure or amino acid sequences with physics informed neural networks.
The first example evaluates the performance of different state of the art (hybrid) methods for predicting PK profiles based on chemical structures and benchmark their performance on a common data set for pre-clinical species.
Next, a method for predicting non-rodent PK profiles for using allometric AI approach is introduced. The last concept utilizes protein large language models and sequence derived features to predict in vivo clearance and PK profile in pre-clinical species.

Speaker: Felix Jost (Sanofi)

2026_ECMTBAbstractFelixJost.docx

11:30 AM Mathematical modelling as a tool to investigate bell-shaped dose-response relationships in drug development

In traditional pharmacology, dose-response relationships have long been the gold standard for selecting optimal therapeutic doses. Typically, these relationships are monotonic. However, in recent years hormetic, bell-shaped relationships have become more common. This is the case of, for example, bispecific T-cell engager (TCE) drugs, treatments where anti-drug antibodies (ADAs) may act as cross-linkers, or multi-valent molecular targets.
These non-monotonic "hook effects" arise from the unique requirement for complex active structures, such as ternary or higher-order complexes, which are highly sensitive to stoichiometric imbalances. This work demonstrates how mechanistic mathematical modelling can decode the origins of these responses by formulating the kinetics of complex formation through systems of ordinary differential equations.
We explore how different molecular architectures, drive self-inhibition at high concentrations. By simulating the drug-target synapsis, we show that the peak of the bell-shaped curve is a predictable function of the relative concentrations and binding affinities of the molecular species involved. The non-linear nature of these interactions, including non trivial hormetic behaviour, impose a shift towards mechanistic modelling, which can powerfully define the underlying biological drivers rather than describing the observed output, providing an important tool for drug development.

Speaker: Gianluca Selvaggio (Pharmetheus)

Abstract ECMTB.docx

11:50 AM Joint modeling of longitudinal data and survival outcome to improve decision making in oncology drug development

Drug development in oncology faces high failure rates and significant costs due to methodological and operational challenges. Modeling and simulation approaches increasingly support decision-making by integrating biological knowledge and existing data throughout development programs. Nonlinear joint modeling of longitudinal and survival data characterizes the dynamic relationship between biomarker evolution and event occurrence, enabling precise parameter estimation and reduced bias in treatment effect predictions [1]. Increasingly adopted in oncology, it supports trial simulations to explore dosing regimens, identify prognostic factors, or support regulatory decisions [2]. We illustrate the impact of joint PK/PD modeling through four case studies. Joint modeling of serum M-protein (surrogate of tumor burden) and progression-free survival (PFS) supported isatuximab dose selection in relapsed refractory multiple myeloma patients and regulatory approval in combination with dexamethasone in Japan, avoiding a dedicated trial [2]. Remarkably, phase 3 PFS outcomes were accurately predicted using joint models built on early phase 1–2 data alone. This predictive capability was shown across multiple indications: multiple myeloma with isatuximab-pomalidomide-dexamethasone [3], breast cancer with amcenestrant [4], and lung cancer with tusamitamab ravtansine [5]. Beyond efficacy, we developed a novel framework to assess benefit-risk balance, accounting for efficacy-safety interactions and the impact of dose modifications due to adverse events [5]. These case studies demonstrate how joint modeling enhances decision-making in drug development. Future applications include prospective implementation with virtual patient approaches to inform trial designs.

References

[1] Desmée S, Mentré F, Veyrat-Follet C, Guedj J. Nonlinear Mixed-effect Models for Prostate-specific Antigen Kinetics and Link with Survival in the Context of Metastatic Prostate Cancer: A Comparison by Simulation of Two-stage and Joint Approaches. AAPS J. 2015 May;17(3):691-9

[2] Thai HT, Koiwai K, Shitara Y, Kazama H, Fau JB, Semiond D, Veyrat-Follet C. Model-based simulation to support the approval of isatuximab alone or with dexamethasone for the treatment of relapsed/refractory multiple myeloma in Japanese patients. CPT Pharmacometrics Syst Pharmacol 2023;12(12):1846-58 doi 10.1002/psp4.12947.

[3] Pitoy A, Desmée S, Riglet F, Thai HT, Klippel Z, Semiond D, Veyrat-Follet C, Bertrand J. Isatuximab-dexamethasone-pomalidomide combination effects on serum M protein and PFS in myeloma: Development of a joint model using phase I/II data. CPT Pharmacometrics Syst Pharmacol. 2024 Dec;13(12):2087-2101.

[4] Cerou M, Thai HT, Deyme L, Fliscounakis-Huynh S, Comets E, Cohen P, Cartot-Cotton S, Veyrat-Follet C. Joint modeling of tumor dynamics and progression-free survival in advanced breast cancer: Leveraging data from amcenestrant early phase I-II trials. CPT Pharmacometrics Syst Pharmacol. 2024 Jun;13(6):941-953.

[5] Cerou M, Veyrat-Follet C, Fliscounakis-Huynh S, Pouzin C, Fagniez N, Mihaljevic F, Chadjaa M, Comets E, Thai HT. Novel Drug-Disease Modeling Framework for Oncology Benefit-Risk Evaluation: Application to Tusamitamab Ravtansine. CPT Pharmacometrics Syst Pharmacol. 2026 Feb;15(2):e70190

Speaker: Hoai-Thu Thai (Sanofi)

12:10 PM Fit-for-Purpose Modeling in Immuno-Oncology: A Practical Guide to Data and Quantitative Tools Across the Pipeline, featuring a Case Study on novel T Cell Engagers

The development of T cell engagers (TCEs) in immuno-oncology can leverage fit-for-purpose modeling strategy that aligns quantitative tools with the key decisions guiding the development pipeline. In preclinical and first-in-human stages, mechanistic PKPD models translate in vitro and in vivo data into predictions of safe, biologically active starting doses by characterizing trimolecular synapse formation \cite{chen2024}. As programs progress toward a recommended Phase 2 dose, population PK modeling coupled with exposure–response (ER) analyses continue to be widely used to support monotherapy. However, TCE efficacy is primarily driven by trimer formation, so Quantitative Systems Pharmacology (QSP) models that explicitly predict trimer dynamics provide additional mechanistic insight. QSP integrates drug properties, tumor microenvironment, and the immune system to predict interactions, optimize dosing regimens and schedules, and identify determinants of safety and efficacy. Modern QSP platforms—often including 'digital twin' virtual patients—simulate these multiscale dynamics and apply global sensitivity analysis to reveal parameters governing cytokine peaks, attenuation dynamics, bell shaped ER relationships, and efficacy plateaus \cite{Singh2024}. These insights enable CRS risk mitigation, rational step-up dosing, and dose escalation, as illustrated with mosunetuzumab or elranatamab \cite{poels2025}. For late stage (Phase 2b/3), QSP can support dose and regimen optimization, predicts combination and safety outcomes, guides enrichment and trial design, and supports regulatory interactions by translating mechanistic data into decision ready simulations. QSP frameworks also guide combination therapy dose selection by quantifying synergy and therapeutic index boundaries \cite{jafar2023}. Other techniques, such as Physiologically based pharmacokinetic (PBPK) models, further support development by evaluating drug–drug interaction risk. Overall, regulatory agencies increasingly recognize these model-informed approaches as supportive in dose justification and benefit–risk evaluation \cite{musante2024}. This talk will highlight these methods, the decisions they enable, and key agency feedback through case studies of novel T cell engagers.

Speaker: Inmaculada Sorribes (Merck)

SMB Abstract_v2.docx

11:10 AM → 12:30 PM Spatial Ecology: Analysis of population distributions and spatial patterns

11:10 AM Community-Level distribution modelling of endangered pelagic bycatch species: a joint modelling approach

The study of the spatial distribution of marine species has traditionally relied on single-species distribution models (SDMs), which implicitly assume independence among taxa. However, marine species evolve within structured communities whose dynamics are governed by complex biotic interactions. To account for this complexity, we use joint species distribution models (JSDMs) to model the distribution of endangered species bycaught by tropical tuna purse seine fisheries in the Atlantic Ocean. Unlike classical SDMs, JSDMs allow for the simultaneous modelling of multiple binary variables (species presence-absences) by isolating shared environmental effects from residual biotic interactions. By capturing the residual covariance not explained by abiotic variables alone, this methodology allows us to identify the actual interdependencies between species. This approach is particularly interesting in the context of bycatch of pelagic species, which has many rare, but sensitive, species and relatively low predictive power of classic SDMs. The objective of this presentation is to demonstrate how statistical inference on species dependencies improves the accuracy of spatial predictions and provides a robust tool for managing critical biodiversity areas, where traditional approaches fail to capture the ecological reality of marine communities.

Speaker: Clara Lereboug (Institut de Recherche pour le Développement)

11:30 AM Restoring oyster reefs by optimizing metapopulation connectivity

Oyster populations in Chesapeake Bay in the eastern United States have dropped to a few percent of historic levels. Restoration requires building artificial reefs as substrate for oysters to grow on. I will present a metapopulation model for oyster reefs that are coupled by transport of larvae. The model consists of ordinary differential equations for juveniles, adults, dead shell/reef substrate, and sediment at each location. I will first discuss results for up to two reefs. There is a tradeoff between spending more money to start constructed reefs with better initial conditions versus spending more time by restoring different sites in stages over multiple years. Next, I will discuss heuristics for selecting the best locations from a larger set when resources permit restoration of only some of the sites. I will use a realistic connectivity matrix between sites based on water flow and will consider both the total population and the resilience to disturbances. Finally, I will add harvest to the model and consider which reefs should be protected or harvested.

Speaker: Dr Leah Shaw (William & Mary)

11:50 AM Computational topology methods for spatial population pattern quantification

This talk focuses on the use of cubical homology and topological persistence as a framework for pattern quantification and image processing. As illustration, we will discuss a study that applies these methods to noisy spatial population data generated by a coupled-patch model to mimic grey scale satellite images of vegetation. Early work shows promise in detecting early warning signals of collapse as well as automating image processing techniques for noise reduction.

Speaker: Dr Sarah Day (William & Mary)

12:10 PM Prediction of spatial population collapse with coarse grain population distribution pattern data

Populations globally are experiencing undue stress due to climate change, habitat destruction and overharvesting. Predicting impending dynamical change or collapse is challenging due to the complex spatiotemporal dynamics natural populations display and the difficulty in obtaining ecological time series. When we explicitly consider a population’s distribution over space, we can quantify population spatial distribution patterns and how they change during a dynamical transition (such as collapse). Here, we quantify population distribution patterns with computational topology and use this coarse grain information from a very limited number of time steps in a population time series to predict the future state. Using supervised machine learning methods, we find that coarse grain (in space and time) topological information has a high success rate of classifying populations at risk of collapse.

Speaker: Dr Laura Storch (Bates College)

11:10 AM → 12:30 PM Inference, Calibration, and Sensitivity in Agent-Based Models: A Data-Centric View

11:10 AM From Sparse Data to Smart Decisions: Surrogate-Assisted Agent-Based Modeling for Regional Outbreak Response

Effective disease outbreak response requires actionable, region-specific guidance, but most modeling tools rely on detailed surveillance or strong assumptions, such as random mixing. Agent-based models (ABMs) allow us to capture key heterogeneity in contact patterns and intervention mechanisms, but linking these models with data is often computationally intractable, particularly at the larger scales needed for decision-making (e.g., county- or state-level). We present a simulation-based framework that combines ABMs with surrogate modeling to infer key transmission and severity parameters using only routine case and hospitalization data. This enables local health agencies to evaluate candidate interventions while explicitly accounting for uncertainty. Applied to COVID-19 in Michigan counties, our method recovers core parameters (transmissibility, latent period, asymptomatic transmissibility, underreporting, hospitalization risk, and duration) that align with empirical estimates, while demonstrating regional variation linked to age and comorbidity patterns. We find that intervention effectiveness cannot be reliably predicted from simple demographic predictors such as age structure, population density, or workforce participation. While school closures aligned with child population in some settings, other interventions showed weak or counterintuitive relationships with demographics. Traditional ODE models with random mixing assumptions cannot capture how interventions target specific contact networks, making it impossible to assess whether demographic proxies predict intervention success. Our framework addresses this gap by explicitly modeling intervention mechanisms within heterogeneous contact structures. Solely using routine case and hospitalization data, our method enables practical, uncertainty-aware decision support for local health agencies facing COVID-19, influenza, RSV, or future novel pathogens.

Speaker: Carson Dudley (University of Michigan)

11:30 AM Quantifying Uncertainty of ABM Parameters Using Explicitly Formulated Surrogate Models

Agent-based models (ABMs) have become valuable tools for understanding complex systems in biology and medicine. In order to evaluate the robustness and accuracy of the model predictions, uncertainty quantification using global sensitivity analysis should be performed. Unfortunately, most global sensitivity analyses are computational prohibitive for complex ABMs. By leveraging explicitly formulated surrogate models, we develop an efficient and flexible framework for inferring global sensitivity. We evaluate our methodology on two AMBs, one a simple 2D in vitro cell proliferation assay model and a second, more complex ABM of 3D vascular tumor growth. In these models, we simulate cells in their environment as decision making “agents” that have their own individual properties and interactions between agents, both temporally and spatially. In this talk, we show that our method for uncertainty quantification is comparable with other methods in accuracy, such as Morris one-at-a-time method or eFAST, but substantially speeds up the time it takes to complete the analysis from days to minutes. In addition, our method is able to estimate sensitives of ABM parameters that are not explicitly included in the surrogate model.

Speaker: Kerri-Ann Norton (Bard College)

11:50 AM Parameter-wise predictions and sensitivity analysis for random walk models in the life sciences

Sensitivity analysis characterizes input–output relationships for mathematical models and has been widely applied to deterministic models across many applications in the life sciences. In contrast, sensitivity analysis for stochastic models has received less attention, with most previous work focusing on well-mixed, non-spatial problems. For explicit spatiotemporal stochastic models, such as random walk models (RWMs), sensitivity analysis has received far less attention. Here we present a new type of sensitivity analysis, called parameter-wise prediction, for two types of biologically motivated and computationally expensive RWMs. To overcome the limitations of directly analyzing stochastic simulations, we employ continuum-limit partial differential equation (PDE) descriptions as surrogate models, and we link these efficient surrogate descriptions to the RWMs using a range of physically motivated measurement error models. Our approach is likelihood-based, which means that we also consider likelihood-based parameter estimation and identifiability analysis along with parameter sensitivity. Our workflow illustrates how different process models can be combined with different measurement error models to reveal how each parameter impacts the outcome of the expensive stochastic simulation. Open-access software to replicate all results is available on GitHub.

Speaker: Matthew Simpson (Queensland University of Technology)

12:10 PM Probabilistic Estimation of Agent Based Models using Hamiltonian Monte Carlo

Agent-based models (ABMs) are increasingly used to study complex systems in biology, enabled by advances in computing and the growing availability of high-resolution data tracking individual agents. However, fitting ABMs to data remains challenging because their likelihood functions are typically intractable, making standard statistical methods such as maximum likelihood estimation or Markov chain Monte Carlo difficult to apply. Likelihood-free inference approaches, including approximate Bayesian computation and synthetic likelihood \cite{Wood_2010, Price_Drovandi_Lee_Nott_2018}, address this issue by relying on model simulations. Recent work has explored replacing these simulations with learned emulators \cite{Jarvenpaa_Corander_2024, Meeds_Welling_2014}. In this work, we exploit the differentiability of such an emulator within the synthetic likelihood framework, enabling efficient parameter inference using Hamiltonian Monte Carlo with the No-U-Turn Sampler \cite{Hoffman_Gelman_2014}. Using toy models with known likelihoods, we demonstrate the empirical accuracy of our approach. We further show that it improves parameter inference in complex ABMs compared to common likelihood-free inference methods that do not provide a gradient with respect to the parameters, and we investigate the asymptotic accuracy of the proposed emulator.

Speaker: Benjamin Olsson (Uppsala University)

11:10 AM → 12:30 PM Mathematical Modelling of Tuberculosis and Nontuberculous Mycobacterial Infections: From Model Synthesis to Vaccination and Whole-Host Immune Dynamics

11:10 AM Whole-host modeling of immune-pathogen interactions during Tuberculosis infection

Pulmonary tuberculosis (TB) remains a dire concern for countries across the globe, caused by inhaling Mycobacterium tuberculosis (Mtb). Granulomas, tissue-scale nodules that form within lungs of Mtb infected individuals, are hallmarks of human TB and are a central factor that complicates predictions of TB outcomes. Granulomas form in both lungs and lymph nodes (LNs) of pulmonary TB patients, and exhibit heterogeneity within an organ, between organs, and between patients. Experiments implicate both lung and LN granulomas as key drivers of disease outcomes, but the complex interaction of multiple simultaneous infections within an individual makes predicting outcomes challenging. To understand how multiple granulomas within lungs and lymph nodes impact patient outcomes, we have developed two agent-based hybrid models HostSim and LymphSim. HostSim captures formation and maintenance of multiple lung granulomas within a virtual host in the presence of a dynamically-priming immune response including coarse grain blood and LN models. LymphSim is a fine-grained model tracking formation and maintenance of granulomas within lung draining LNs, and the downstream effects to providing adaptive immune response to damage, and hence impairment in that can arise. Using each, we are able to capture heterogeneity of hosts, granulomas and bacterial dynamics observed in experimental studies, and probe the most influential mechanisms governing host outcome using sensitivity analyses.

Speaker: Christian Michael (University of Michigan)

11:30 AM Agent-Based Modeling of Nontuberculous Mycobacteria Infection In Vivo with Multi-Modal Patient Data Integration

Nontuberculous mycobacteria (NTM) lung infection is increasing in prevalence globally
and remains difficult to treat in part due to varied disease presentation and prognosis.
Some patients experience stable symptoms and require observation and bronchial
hygiene treatment; other patients will demonstrate disease progression symptomatically
and radiographically, requiring antibiotic therapy that may cause intolerable side effects.
Predicting patient prognosis to inform therapeutic decisions remains a challenge. To
better understand the biological mechanisms of NTM disease progression and help
identify patient prognostic factors, we developed an agent-based model of a pulmonary
NTM granuloma. These virtual granulomas are initialized to represent existing chronic
infection and are informed by histological studies. Peripheral immune cell data from
NTM patients and lung resection immunohistochemical staining inform model
initialization, parameters and calibration. The model captures multiple trajectories of
granuloma development, recapitulating the heterogeneity in granuloma bacterial burden
and infection progression observed in animal models of mycobacterial infection. The
model demonstrates the feasibility of simulating in vivo NTM granulomas representing
chronic infection. Patient data integration increases model translatability, with the
potential for predicting patient prognosis and simulating patient-specific granulomas.

Speaker: Kali Konstantinopoulos (Purdue University)

11:50 AM Within-Host Mathematical Models of Tuberculosis: Foundations, Progress, and Future Directions

Within host mathematical modelling has become central to understanding the complex, multiscale biology of Mycobacterium tuberculosis infection. This talk will synthesise the major modelling frameworks that have shaped the field, from early ordinary differential equation models to agent based, hybrid, and multiscale approaches linking molecular to systemic processes. We highlight core assumptions, data sources, and the mechanistic insights they offer into host-pathogen interactions, immune dynamics, lesion heterogeneity, and treatment response. We highlight rapidly developing areas including omics-driven personalisation, systems pharmacology integration, virtual clinical trials for regimen optimisation, and modelling of clinically relevant coinfections and comorbidities such as HIV and diabetes. To provide a unified synthesis across this diverse landscape, we present quantitative thematic heatmaps that map modelling approaches to the biological and clinical questions they address. We conclude by identifying key open challenges and outline emerging directions that position within-host modelling as a cornerstone for precision therapy and global tuberculosis control.

Speaker: Roselyn Kaondera-Shava (University of Bath)

12:10 PM Mathematical modeling of impact of BCG vaccination on Mycobacterium tuberculosis dynamics in mice

The BCG vaccine remains the only licensed vaccine against tuberculosis (TB), yet its protective efficacy is highly variable, and the mechanisms behind BCG-induced protection remain poorly understood. Plumlee et al. (PLOS Pathogens 2023) infected over 1,000 mice, half of which were vaccinated with BCG, with an ultra low dose (ULD) of Mycobacterium tuberculosis (Mtb); the authors found that BCG vaccination resulted in fewer infected mice, lower CFU lung burden, and more frequent unilateral lung infection. We have developed several mathematical models of Mtb dynamics and dissemination between murine lungs and fit these models to the CFU data from unvaccinated or BCG-vaccinated mice. Alternative mathematical models incorporating either direct (lung-to-lung) or indirect (lung-intermediate-tissue-lung) dissemination pathways fit the unvaccinated data equally well, suggesting multiple plausible routes of Mtb spread. Yet, irrespective of the dissemination route, the models predicted rapid Mtb replication during early infection, transient control within 1–2 months after infection, and continued bacterial growth in the chronic phase. Fitting models to the data from BCG-vaccinated animals revealed that BCG reduces the rate of Mtb dissemination by 89% while having a more modest effect on the replication rate within the lung, reducing it by 9%. Stochastic simulations incorporating random infection and dissemination between the right lung and left lung explained the observed variability in experimentally measured CFUs well. We used our parameterized mathematical models to calculate the number of mice needed to detect the efficacy of a hypothetical vaccine on the probability of Mtb clearance or dissemination between murine lungs that extends previously provided estimates. Taken together, our novel mathematical modeling-based framework provides a rigorous way for quantifying vaccine efficacy in ULD-infected mice, paving the way for the pre-clinical evaluation of next-generation TB vaccines.

Speaker: Vitaly Ganusov (Texas Biomedical Research Institute)

11:10 AM → 12:30 PM Stochastic and Deterministic Methods in Mathematical Biology: From Theory to Computation

11:10 AM Optimal Bandwith Selection in Biological Field Effect Transistor Measurements

Instruments known as biological field effect transistors (BioFETs) have potential to offer affordable and highly sensitive medical diagnostics that can be administered point of care. Signal is separated from noise in these instruments with stochastic regression, a technique that involves modeling the signal with a linear deterministic drift term and a white noise term that captures stochastic behavior. Both of these terms have coefficients that are estimated from data or simulation with local weighted regression and maximum likelihood estimation. Crucially, these coefficient estimation techniques depend on an averaging function--known as a kernel function--and an averaging window, the size of which is governed by variable known as the bandwidth parameter. In this talk, we determine optimal bandwidth parameters associated with an experimental BioFET measurement and simulation data. Cross validation is performed with respect to different instrument aspect ratios. Results show optimal badwidth parameters are surprisingly consistent across aspect ratios, and suggest a choice of kernel function.

Speaker: Luis Melara (Shippensburg University of Pennsylvania)

11:30 AM Mathematical Tumor Growth Models

Mathematical models of tumor growth are essential for complementing experimental findings and furthering the understanding of cancer development and spread, as well as optimizing therapy. This talk presents a novel age-structured partial differential equation (PDE) model. The underlying process for tumor growth is similar to classical models, where growth is driven by pressure-limited cell division, and Darcy's law, describing cell movement away from regions of high internal pressure. By introducing an age-structure, the model accounts for the life-cycle of tumor cells. This allows for more accurate medical predictions and optimal therapy design. This talk presents results on the existence of weak solutions of the model, convergence to an incompressible limit, and numerical simulations.

Speaker: Maeve Wildes (University of Maryland)

11:50 AM A Numerical Method for a Singular Integrodifferential Equation Model of Biosensor Dynamics

Biological field effect transistors are portable and highly sensitive biosensors that show promise as medical diagnostic instruments. During a typical experiment, chemical reactants from solution diffuse onto a surface to bind with receptors that are confined to the surface. This produces a time series signal that may be used to analyze the reaction of interest. In experimentally relevant parameter regimes, a model for these experiments takes the form of a nonlinear and logarithmically singular integrodifferential equation. A numerical method based on a Nystrom discretization and specialized quadrature will be presented, and it will be demonstrated that this method achieves second-order accuracy. Numerical simulation compares favorably with experiment.

Speaker: Ryan Evans (National Institute of Standards and Technology)

12:10 PM Probabilistic Cellular Automaton Modeling for Monolayer Degredation in Biosensors

A novel chip-scale electrochemical biosensor is being developed to detect biomolecules with high sensitivity. Unlike traditional methods such as qPCR that require specialized equipment and trained personal, these cost-effective and portable chip-scale sensors are designed to administer tests at the point of care. Target molecules of interest are immobilized on the surface, and specific interactions with molecules that diffuse onto the surface from solution produces an electrochemical signal. To prevent non-specific interactions that may contaminate the signal, the sensor surface is coated with a thin passivating self-asssembled monolayer (SAM). The SAM degrades over time, which exposes sensor's bare metal surface and can lead to non-specific interactions. Understanding and predicting SAM degradation is key to producing reliable biosensors. A probabilistic cellular automaton (PCA) model for SAM degradation is given and solved explicitly in one dimension. A continuous-time limit is computed for the case of Poisson distributed probabilities.

Speakers: Anthony Kearsley (National Institute of Standards and Technology), Ryan Evans (National Institute of Standards and Technology), Wes Caldwell (Johns Hopkins University)

11:10 AM → 12:30 PM Novel Data Streams for Disease Modeling: Challenges and Opportunities

11:10 AM A Minimal Model Framework for Robust CAR-T Cell and Oncolytic Virus Combination Therapy

Glioblastoma remains one of the most lethal brain cancers. Combination therapy using CAR-T cells and oncolytic viruses shows promise, yet the mechanisms underlying their synergy remain poorly understood. We develop mathematical models to analyze IL-13Rα2-targeting CAR-T cells and the oncolytic virus C134 using patient-derived glioblastoma data. We propose a minimal model framework for predicting outcomes of combination immunotherapy. By applying timescale separation between rapid viral dynamics and slower cellular processes, we derive quasi-steady-state (QSS) approximations that reduce model complexity while maintaining predictive accuracy. The QSS model contains nine parameters compared with eleven in the full model and achieves comparable fits to the data. Model comparisons using the Akaike Information Criterion indicate that the QSS model is generally favored, particularly for oncolytic virus monotherapy and several combination therapy conditions. These results demonstrate that simplified QSS formulations effectively capture viral dynamics and provide a practical framework for analyzing and optimizing combination immunotherapies.

Speaker: Aisha Tursynkozha (Astana IT University)

11:30 AM Using Naive Bayes to uncover probabilistic maps of SIV tissue spread

Systemic HIV infection is typically established following mucosal exposure, but the earliest events stretching from viral dissemination from those mucosal tissues to body-wide (systemic) infection remain incompletely defined. Using tissue-level SIV RNA data from rhesus macaques (an animal model for HIV) we broadly aim to map paths of infection through tissues as infection is established, to better inform HIV prevention strategies. We will discuss how we transformed our data into a cohort-wide map of viral occupancy and co-occurrence across organs and lymphatic compartments. We converted tissue measurements into presence/absence, and introduced a probabilistic framework using a Naive Bayes classifier to estimate posterior probabilities of SIV tissue spread through time, yielding an interpretable, directed dissemination network. Building on the network, we implement Monte Carlo random walk simulations to explore likely dissemination pathways and quantify mean first-passage step counts to plasma (systemic infection). Probabilistic maps reveal an SIV tissue-hierarchy leading to systemic infection that identifies specific lymphatic tissues, and the spleen, as dominant conduits. Thus we generate hypotheses on modes of establishment of systemic HIV infection. This work also demonstrates how machine learning and network simulation can transform novel biological data into quantitative models of within-host disease spread.

Speakers: Chapin Korosec (University of Guelph), Jessica Conway (Pennsylvania State University)

11:50 AM Modeling wastewater surveillance data for quantifying norovirus transmission dynamics

Norovirus is a leading cause of acute gastroenteritis globally, yet community infection burden remains poorly quantified due to asymptomatic transmission and clinical underreporting. Wastewater-based surveillance provides a community-level signal of infection prevalence, but translating viral RNA concentrations into epidemiological estimates is nontrivial, and requires explicit modeling of the noisy, nonlinear relationship between shedding dynamics and measured wastewater concentrations.

We develop a mechanistic framework that couples a compartmental transmission model to a wastewater observation process driven by symptom-stratified shedding profiles. This structure allows us to infer transmission parameters and reconstruct infection burden directly from wastewater time series, bypassing the underreporting inherent in clinical surveillance. Applied to data from multiple treatment plants in El Paso, Texas, the model estimates up to 13.5% of the population infectious at epidemic peak. Sensitivity analysis identifies the transmission rate and infectious period as the dominant sources of uncertainty in burden estimates.

More broadly, this work illustrates the potential and the challenges of wastewater as a novel data stream. The framework generalizes to other pathogens with high asymptomatic transmission and limited clinical reporting, and points toward open problems in identifiability and data integration for wastewater-based epidemiology.

Speaker: Fuqing Wu (UTHealth Houston School of Public Health)

12:10 PM Inferring Mobility Distributions in Heterogeneous Epidemic Models

Classical compartmental models often overestimate the size of a pandemic due to the assumption of a homogeneous population. At the early stage of an outbreak, individuals with higher mobility are more likely to become infected, resulting in an inflated estimate of the final pandemic size. In this talk, we introduce a heterogeneous compartmental model in which each individual has different mobility levels. We develop a deep-learning framework to infer the mobility distribution from partial observations of epidemic dynamics. We also present theoretical results showing that these partial observations uniquely determine the mobility distribution, which establishes that the corresponding inverse problem is well-posed.

Speaker: Weiqi Chu (University of Massachusetts)

11:10 AM → 12:30 PM Coordination at Tip-Growing Cell Interfaces: Cell Polarity, Membrane Flow, Wall Growth, and Morphogenesis

11:10 AM MS149-1

Speaker: Benedicte Charrier (CNRS Station Biologique Roscoff)

11:30 AM MS149-2

Speaker: Dimitrios Vavylonis (Lehigh University)

11:50 AM MS149-3

Speaker: Nicolas Minc (Institut Jacques Monod)

12:10 PM MS149-4

Speaker: Rholee Xu (Worcester Polytechnic Institute)

11:10 AM → 12:30 PM Mathematical Modeling of Oncolytic Viral Therapy in Solid Tumors

11:10 AM Analysis of a Time-Delayed Reaction–Diffusion Model for Virotherapy and Tumor Control

Oncolytic virotherapy is an emerging cancer treatment that uses viruses to selectively infect and destroy tumor cells while stimulating immune responses. However, most mathematical models consider either spatial diffusion or intracellular viral delay separately, leaving a gap in understanding their combined influence on tumor dynamics and therapeutic outcomes. In this work, our objective is to investigate the combined effects of spatial diffusion and intracellular delay using a time-delayed reaction–diffusion model that describes interactions between tumor cells, infected cells, free virus, and immune effectors. We analyze the kinetic system and derive the basic reproduction number, establishing conditions for viral invasion. Stability analysis shows that delay can induce Hopf bifurcation and oscillatory tumor dynamics. We further study traveling wave solutions to describe spatial infection spread and introduce a tumor control probability framework to assess treatment effectiveness. Numerical simulations show that intracellular delay significantly influences dynamic behavior and that optimized multi-dose injection schedules improve tumor control. These results highlight the combined role of delay and spatial effects in shaping tumor dynamics and provide guidance for optimizing virotherapy strategies.

Speaker: Dr Arwa Baabdulla (United Arab Emirates University)

11:30 AM Resistance and immune response during oncolytic virotherapy

Oncolytic viruses interact dynamically with cancer cells, healthy stromal cells, and immune cells in the tumor microenvironment. Therapeutic success therefore depends on the balance between viral spread, infection resistance, and immune activation. In this talk, I will present insights into these interactions using a spatiotemporal computational modeling framework. Our simulations reveal that therapy failure can arise through
multiple mechanisms. For example, even when infection-resistant cancer cells are initially rare, spatial competition can lead to their rapid expansion and tumor persistence. I also find that fast killing of infected cells can paradoxically reduce efficacy by clearing the virus before it spreads, while infection-resistant stromal cells, like macrophages, can further inhibit infection and protect the tumor. Additionally, incorporating immune responses uncovers a fundamental trade-off. Virus-induced signals can enhance T cell-mediated cytotoxicity, but may simultaneously suppress viral amplification by eliminating infected cells too quickly. This leads to stochastic and sometimes counterintuitive outcomes, where treatment timing and delivery strongly affect success. Finally, I will show that macrophages, despite limiting infection, do not necessarily prevent effective therapy. Instead, rationally-engineered viruses to stimulate T cell responses can induce robust anti-tumor immunity even when infection remains spatially constrained. Together, these results highlight how resistance and immune dynamics jointly shape virotherapy outcomes.

Speaker: Dr Darshak Bhatt (University of Groningen Medical Center, University of Groningen)

11:50 AM Cell evolution in the presence of viruses

Viral infection can substantially alter the selection of mutant cells, particularly in spatially structured settings. Understanding how infection shapes evolutionary dynamics is relevant both for cancer cells targeted by oncolytic viruses and for bacteria subject to bacteriophage infection. While cellular resistance to infection is one important dimension of this problem, I focus here on advantageous and deleterious mutants that remain equally susceptible to infection, such as drug-resistant cancer cell mutants.

I first quantify how selection is modified in spatially structured cell populations subject to virus infection, using mutant fixation probabilities as the key metric. I show that infection substantially weakens selection: advantageous mutants become less advantageous, and deleterious mutants become less deleterious. This effect is driven by spatial patterns that emerge from the infection process itself. I then turn to expanding cell colonies and show that infection can either increase or decrease the number of mutants in the expanding population, depending on assumptions about mutant fitness.

Together, these results illuminate how viral infection reshapes evolutionary dynamics in spatially structured cell populations , with direct implications for understanding how the presence of a virus alters the clonal composition of a tumor and its subsequent response to chemotherapy or targeted therapies.

Speaker: Prof. Dominik Wodarz (University of California, San Diego)

12:10 PM Computational investigation of the interactions between oncolytic viruses and tumour-associated macrophages

The interactions between oncolytic viruses (OVs) and innate immunity are crucial for the success of oncolytic therapies. Here we focus on a heterogeneous and plastic population of innate immune cells, the tumour-associated macrophages, that can be involved in the elimination of OVs, as well as in the replication of OVs and their spread across tumour tissue. Computational approaches are used to investigate the importance of different biological mechanisms in the faster spread of OVs, as helped/hindered by different macrophage phenotypes.

Speaker: Prof. Raluca Eftimie (University of Franche-Comte)

11:10 AM → 12:30 PM Modeling Collective Dynamics in Heterogeneous Cell Populations

11:10 AM Invasion patterns in heterogeneous cell populations

Cell invasion is a striking example of self-organisation in biology, playing a central role in development, regeneration, and disease. Classically, invasion is modelled by the Fisher–KPP equation, which shows that the combination of cell proliferation and diffusion is sufficient to generate an invasive front whose speed is determined by the proliferation rate and cell diffusivity. When crowding constraints are incorporated into proliferation, these processes give rise to travelling wave solutions, namely invasion profiles that propagate at constant speed. In this talk, I will discuss recent work on analogous invasion phenomena in heterogeneous populations composed of two interacting cell types. Such heterogeneity may represent cells at different stages of the cell cycle, cells with distinct phenotypes such as invasive and proliferative subpopulations, chemotactic and consumer cells, or cells with different adhesive properties. I will highlight both the biological insights and the mathematical challenges arising in these systems. On the biological side, the results shed light on how population heterogeneity shapes invasion profile structure and regulates processes such as cell cycle progression or chemotactic migration efficiency. On the mathematical side, I will describe analytical approaches for studying the resulting travelling wave solutions, focusing on asymptotic and variational methods.

Speaker: Carles Falco (Mathematical Institute, University of Oxford)

11:30 AM Understanding the role of space in modulating cellular heterogeneity

The control of gene expression by epigenetic factors, along with gene expression noise, results in a distribution of cell states amongst genetically identical cells. Previous studies have explored the role of gene expression in proliferation and vice versa, which, in turn, shapes cellular heterogeneity within a population. However, in these studies, the population was assumed to be well-mixed. As crowding, migration, local interactions, and other factors are key features of spatial population dynamics, their consideration has important implications for cell growth and migration. Thus, space introduces additional complexity into the feedback between gene regulation and the population's growth rate, modulating cellular heterogeneity within a population with respect to non-spatial contexts. We have developed spatial agent-based models in which cells divide and migrate, along with non-spatial models as a control. The division and migratory rates of cells are governed by their cell states, and an underlying gene regulatory network models the dynamics of cell states. With the developed framework, we compare the roles of regulation and stochasticity in shaping population-level heterogeneity in spatial and non-spatial contexts, and highlight how non-genetic phenotypic selection operates differently in these contexts.

Speaker: Paras Jain (Department of Bioengineering, Indian Institute of Science)

11:50 AM A novel cellular automaton approach for modeling genotypic and phenotypic heterogeneity in cell systems

Cellular automaton models have long been used to study cellular processes, but may be challenging for incorporating heterogeneity, migratory, and high-density effects. In this work, we introduce an extension of the classic lattice-gas cellular automata, a framework which allows to consider changes in cell numbers, cell–cell interactions, migration, and evolution of genotypic and phenotypic heterogeneity. To demonstrate the utility of our approach, we consider a growing population of cells whose genotype—passed on at birth from the mother cell and subject to stochastic mutations—determines their individual proliferation rates. Using spatial simulations, we show that the model exhibits traveling-wave invasion patterns, where the fastest-growing cells accumulate at the leading edge, accelerating population expansion. We predict this behavior using a mathematical analysis based on a mean-field assumption \cite{syga_novel_2026}.

Speaker: Simon Syga (Center for Interdisciplinary Digital Sciences, TUD Dresden University of Technology)

12:10 PM Emergent chase-and-run dynamics in heterogeneous populations

In chase-and-run dynamics, two individuals interact in such a way that one moves towards the other (the chaser), while the other moves away (the runner). This behaviour can be observed in both interacting cells and animal populations. In this talk, I analyse the collective behaviours that emerge at the population level in heterogeneous groups consisting of subpopulations of chasers and runners that interact via non-local sensing mechanisms.

I analyse how different dynamical regimes arise as interaction ranges - the spatial scales over which individuals respond to one another - vary, and how these behaviours are modified by an external bias representing the directional tendencies commonly observed in biological systems. The results identify the conditions that lead to aggregation, spatial segregation and persistent chase-and-run patterns. This analysis provides insight into the underlying mechanisms of collective organisation in cellular and ecological contexts, while paving the way for multi-scale descriptions that integrate behavioural heterogeneity through phenotype-structured population models.

Speaker: Valeria Giunta (Swansea University)

11:10 AM → 12:30 PM Boolean models in Systems Biology

11:10 AM A Boolean Approach to Invasion and Mesenchymal–Epithelial Transition (MET)

Understanding cancer invasion requires linking intracellular regulatory processes with multicellular dynamics. Boolean modelling provides a powerful framework to describe phenotypic transitions such as the mesenchymal–epithelial transition (MET), capturing how signalling networks and environmental cues regulate cell plasticity and state switching.

At a larger scale, intracellular logical models can be integrated with spatial, cell-based simulations to study tumour invasion. By coupling regulatory states with cell–matrix interactions, these models reproduce diverse invasion patterns and offer insight into how individual decision-making processes give rise to emergent collective behaviours.

Speaker: Laurence Calzone (Institute Curie)

11:30 AM Biological Battle Royale: Structural Constraints of Networks Supporting Multi-Fate Cellular Decisions Using Monotone Boolean Models

Cell fate decisions are driven by gene regulatory networks (GRNs). While the mutually inhibitory toggle switch effectively models binary fate decisions, fully connected inhibitory networks with more than two nodes fail to capture multi-fate decisions due to the low prevalence of "single-high states", where only a single master regulator is highly expressed. In this study, we use monotone Boolean models to derive structural constraints necessary for an n-node network to support n phenotypes. We find that the only network that maximizes the prevalence of single-high states is completely disconnected. However, since biological networks typically require connectivity, we further investigate the requirements for equipotency, where a network structure supports all single-high states with equal prevalence. Finally, we characterize the requirements for multistability across all single-high states, finding that it is possible only in networks in which each node either has self-activations or inhibitions with every other node. Our findings provide a theoretical framework for understanding the topological design principles required for master regulator networks to support simultaneous differentiation into multiple distinct cell types.

Speaker: Harshavardhan BV (Indian Institute of Science, Bengaluru)

11:50 AM Long-lived sets: The missing oscillatory phenotypes of Boolean networks

In Boolean networks, biological phenotypes are traditionally mapped to system attractors. However, attractors are often sensitive to the chosen update scheme and the granularity of the influence graph. Applying a more permissive update scheme or adding mediator nodes can easily disrupt plausible attractors, forcing modelers to carefully tune model properties to achieve biologically relevant outcomes.

In this talk, we introduce long-lived sets, a robust generalization of attractors. Long-lived sets are strongly connected sets of states that can be escaped, but never by value percolation (updating a single system variable across all states of the set). Theoretically, long-lived sets are immune to disruptions caused by more permissive update schemes or refinements of the influence graph. Practically, we demonstrate their utility in real-world models: they successfully capture known oscillatory behaviors that standard attractors miss. Furthermore, the number of long-lived sets in a model is often close to the number of attractors, even in models with millions of other "short-lived" strongly connected components. This makes long lived sets not only robust, but highly specific generalization of known attractor-based phenotypes.

Speaker: Samuel Pastva (Masaryk University)

12:10 PM How well do Boolean model capture continuous dynamics of regulatory networks?

Regulatory networks in cell biology specify monotonicity structure of interactions between genes and proteins, but do not specify the interactions between multiple inputs.
We describe several classes of models compatible with a given regulatory network:

$\mathbf{(A)}$ a collection of all monotone Boolean networks (MBF) whose influence graph matches the network;

$\mathbf{(B)}$ a collection of MBFs where influence graph is a subgraph of the network;

$\mathbf{(C)}$ a collection of all ODE models with monotone steep nonlinearities.

We show that these collection of models are strict subsets of each other [\mathbf{(A) \subsetneq (B) \subsetneq (C)}] and describe precise embedding of each smaller class into the larger class.
While the dynamics of protein and mRNA abundance is stochastic, it is usually well approximated by dynamics that is continuous in time and space generated i.e. by models in class $\mathbf{(C)}$.
We illustrate on the set of examples which dynamics is reliably captured by the smaller class(es)of models, and where the set of dynamics of the larger class(es) is significantly richer than that of a smaller class(es).

Our results begin to illuminate the gap between dynamics observed by monotone Boolean models in class $\mathbf{(A)}$ and continuous dynamics of ODE models in class $\mathbf{(C)}$.

Speaker: Tomas Gedeon (Montana State University)

11:10 AM → 12:30 PM Agent-based models, networks and machine-learning methods for epidemiological modelling

11:10 AM MS159-1

Speaker: Jasmina Panovska-Griffiths (Pandemic Sciences Institute, University of Oxford, Oxford, UK)

11:30 AM Starsim: A fast, flexible agent-based disease modeling framework

Background
Agent-based models (ABMs) allow detailed simulation of people and their interactions. However, ABMs often run slowly and are complicated to configure, which has limited their use. Starting with Covasim (for COVID-19), we developed several ABMs designed to make modeling more accessible for people with diverse backgrounds and skill sets. Recently, we codified the principles of these models into an ABM framework called "Starsim" (starsim.org), which aims to facilitate the rapid development of models that can answer real-world policy questions.
Methods
The Starsim modeling framework contains modules that can be used to implement different communicable and non-communicable diseases, plus other health areas. Its features include: co-transmission of diseases (including their natural history, transmission, and effects of co-infection), dynamic transmission networks (including sexual, respiratory, and maternal transmission), vital dynamics (including births and deaths), and interventions (including testing, treatment, and vaccines). It is suitable for answering a wide range of modeling questions, from small outbreaks to multi-decade epidemics. Most simulations can be run in seconds to minutes on a standard laptop. It is free to use, open source (in both Python and R), and extensively documented. A specially trained AI agent is also available to help build Starsim models.
Implications
Since 2020, over 200 people have attended trainings on the Starsim suite of ABMs, including workshops in India, Vietnam, Kenya, Uganda, and the US. The Starsim approach is simple enough that most users can quickly learn it, yet flexible enough to model users' requested policy scenarios. Starsim can be rapidly adapted to new contexts thanks to its modular structure, optimized computations, and pre-loading of commonly used data. Starsim shifts the emphasis from “models as finished products” to the development process itself. Already, collaborators from a dozen institutions have produced more than 30 models using Starsim, covering areas as diverse as HIV, typhoid, tuberculosis, rift valley fever, family planning, and epidemic decision-making. We believe Starsim's community-driven approach to software development has the potential to strengthen capacity and improve access to fit-for-purpose modeling tools, and thus contribute to better model-informed decisions.

Speaker: Robyn Stuart (Gates Foundation)

11:50 AM Comparative evaluation of HIV testing interventions for men who have sex with men in the Netherlands: insights for a low-incidence setting

Background: Despite declining HIV diagnoses among men who have sex with men (MSM) in the Netherlands, a recent plateau and the high proportion of late-stage diagnoses (29% in 2024) indicate ongoing transmission and delayed detection. Infections introduced through immigration are increasingly relevant in this low-incidence setting, motivating a reassessment of testing guidelines, which we evaluate in this study.

Methods: We used an agent-based model of HIV transmission among MSM in the Netherlands, incorporating domestic and imported infections. For 2024–2040, we simulated targeted testing strategies, including testing at immigration, increased testing among resident MSM, and combined approaches.

Results: Testing immigrating MSM at entry averted up to 94 infections over 15 years (95% QI 128–328) with ≥50% uptake. Increasing testing to every 7 months among general resident MSM achieved the largest reduction, with 508 infections averted (95% QI 292–900), followed by targeting MSM with >5 partners within the previous six months (340; 95% QI 132–592). Combining entry testing with 7-monthly testing among resident MSM yielded the greatest impact (534; 95% QI 308–884).

Conclusions: Combining HIV testing at entry for immigrating MSM with 7-monthly testing among resident MSM can substantially reduce infections. The greater impact of population-wide versus risk-targeted testing suggests that current risk-based testing criteria may be too narrow.

Speaker: Ganna Rozhnova (University Medical Center Utrecht)

12:10 PM Improving the use of social contact studies in infectious disease modelling

Up until now, the main use of social contact studies in epidemic modelling has been to create a next generation matrix containing mean number of contacts between different age groups, in order to capture heterogeneity in contacts between age groups. However, empirical evidence show that the majority of variation in contacts is not between age-groups, but within age groups, and also within individuals (between different days). We propose methods for improving the analysis taking also this variation into account.

Speaker: Tom Britton (Stockholm University)

11:10 AM → 12:30 PM Multicellular Reference Models and Applications - The OpenVT Project

11:10 AM Using reference models to compare multicellular simulation frameworks and tools

In this round-table discussion, we will examine how much variation can be accepted when the same spatial model is implemented in different software tools, or when similar biological systems are represented using different modelling formalisms. Using examples such as tissue monolayer growth and a basic angiogenesis model, we will discuss where differences arise, how they should be interpreted, and whether full reproducibility is a realistic goal.
A central topic will be the choice of comparison metrics. We will ask whether simple summary measures are sufficient to detect meaningful discrepancies, or whether they can hide important differences in spatial behaviour. We will also discuss what level of agreement is reasonable in practice, both across different modelling approaches and across tools based on the same formalism.
The goal of this session is to stimulate discussion on practical standards for comparing spatial models and to clarify what reproducibility should mean in the context of spatiotemporal simulation.

Speakers: Inge Wortel (Radboud University), Lorenzo Veschini (Indiana Uniersity), Roman Vetter (ETH Zurich)

11:50 AM Modeling Blastocyst and Organoid Morphogenesis Towards a Virtual Embryo in Morpheus

Multicellular models integrating cell-cell signaling, gene regulation, proliferation and tissue mechanics are needed to unravel the organizational principles of embryo morphogenesis. We(*) here demonstrate, using FAIR and OpenVT principles, how a subcellular element-based blastocyst model can be reproduced in a cellular Potts model (CPM) framework such as Morpheus [1]. The open-source framework Morpheus keeps the model definition strictly separated from the simulation code [2]. It uses the domain-specific language MorpheusML to define multicellular models in a modular manner through a user-friendly GUI [3]. A numerical simulation is then composed by parsing the MorpheusML model definition and automatic scheduling of predefined components in the simulator. These principles enable sharing and maintenance of the blastocyst model through the MorpheusML model repository [4]. Extending the blastocyst model, we analyze how cells dynamically polarize and differentiate in response to signals from their environment and how polarized fluid transport controls amniotic cavity formation in a human embryoid culture experiment.
(*) in collaboration with J. Algorta and L. Edelstein-Keshet (UBC, Canada)
[1] Blastocyst model: https://identifiers.org/morpheus/M9999
[2] Morpheus homepage: https://morpheus.gitlab.io
[3] MorpheusML language: https://doi.org/10.25504/FAIRsharing.78b6a6
[4] Model repository: https://morpheus.gitlab.io/models

Speaker: Lutz Brusch (TU Dresden)

12:10 PM Born or Made? Modeling the Origins of Leader Cells in Collective Cancer Invasion

Collective cancer invasion often displays a distinct spatial hierarchy, with leader cells at the tips of invasive chains and follower cells trailing behind. Experiments using the Spatiotemporal Genomic and Cellular Analysis (SaGA) platform have shown that these subpopulations differ in motile, signaling, and proliferative behavior. But a fundamental question remains unresolved: what makes a leader? Are leader cells a fixed intrinsic subtype, or do leader-like states emerge from local context, biophysical interactions, and phenotypic plasticity? If leaders are removed, can other cells replace them? Here, we develop a computational analogue of the SaGA protocol using a two-dimensional Cellular Potts Model to address these questions. Each tumor cell is initialized with a randomly assigned combination of adhesion strength, migration coefficient, and proliferative probability, drawn from distributions representing four evolutionary scenarios. Leader- and follower-like behaviors are not imposed a priori, but emerge from the collective invasion dynamics and are classified post hoc by spatial position within the evolving tumor. We systematically investigate how the emergence, stability, and replaceability of leader-like cells depend on four biologically motivated scenarios: an unconstrained random baseline, heritable trait transmission with stochastic perturbation, clonally grouped initialization mimicking discrete sublineages, and biophysical trade-offs among adhesion, motility, and proliferation. By asking when leader cells arise, whether they persist, and whether they can be replaced, this model provides a mechanistic framework for distinguishing fixed cellular identity from context-dependent invasive state. It also offers a platform to study how heterogeneity, plasticity, and trade-offs regulate collective invasion and metastatic potential.

Speaker: Sheriff Akeeb (Georgia State University)

11:10 AM → 12:30 PM Optimal Control and Numerical Simulation Methods for Disease Tracking, Diagnosis and Treatment

11:10 AM Modeling of DNA origami electrochemical signaling for optimal biosensor design

Biological field effect transistors (Bio-FETs) have shown great promise in revolutionizing diagnostic testing, enabling the development of inexpensive and portable biosensors with a very low limit of detection that are capable of providing point-of-care diagnostics within minutes. A recent biosensor design using DNA origami nanostructures has shown unique potential, as the nanostructure’s strong negative charge and low relative permittivity is able to greatly affect the electric field within the device to control sensor signaling. This talk will develop a mathematical model and simulation of this electrochemical process, in pursuit of determining optimal nanostructure designs. The model is posed as a modification to the Poisson-Boltzmann equation and a finite difference method approximates its solution. Parameter studies quantifying the effect of numerical and physical variations in the system are used to inform choices on computational parameters. Three different nanostructure designs are studied and their capacity for signaling compared, with optimal bulk salt concentrations suggested.

Speaker: Allison Carson (National Institute of Standards and Technology)

11:30 AM Restoring immune regulation in cancer: a multifaceted optimization problem

The maintenance of healthy immune function requires a complex set of checkpoints to promote a response to genuine threats (such as cancer or infection) while recognizing benign actors to avoid chronic systemic inflammation. This process leads to a delicate balance in which stimulatory and inhibitory receptors compete to dictate a cell’s fate. Cancer cells notoriously ramp up inhibitory signaling, resulting in a lack of immune response. We explore the process of T cell exhaustion, or loss of ability to respond to a threat. Notably, we characterize the progression of T cells through their initial stimulus, activation, and subsequent exhaustion upon the earliest stages of solid tumor infiltration. We quantify, through experimental data and mechanistic modeling, activation and exhaustion scores for T cells upon encountering cancer cells. Introducing macrophages to the system presents an additional layer of complexity due to their highly plastic phenotypes, i.e., their ability to take on both an immunostimulatory and an immunosuppressive role. By characterizing T cell and macrophage activity at high resolution, we identify potential perturbations to leverage in optimizing treatment strategies for restoring a dysregulated anti-tumor immune response to a functional therapeutic state.

Speaker: Anne Talkington (University of Buffalo)

11:50 AM Mathematical Model for Penetration of Zona Pellucida

Mammalian fertilization consists of spermatozoon motion towards an oocyte, followed by penetration of zona pellucida, the outer layer of an oocyte. Experiments reveal that glycan and enzyme kinetics, as well as advection, are important to this process despite their roles not being well understood. Mathematical models bridge the gap between theory and experimentation. I will present an advection-reaction-diffusion model that provides in-silico insight into underlying competing physiological factors. I will show this insight is clearly demonstrated by numerical results. Our model displays desirable properties such as positivity and boundedness while accommodating reaction mechanisms for the underlying chemicals. An important observation realized by my model is that if one assumes the zona pellucida does not diffuse, even in the absence of advection, sperm can penetrate zona pellucida due to reaction and diffusion. This assumption is supported by experimental results. My presentation will conclude with generalizations of our model and some comments about future research directions.

Speaker: Prajakta Bedekar (Birla Institute of Technology And Science)

12:10 PM Probabilistic Modeling of Antibody Kinetics Post Infection and Vaccination

There is a significant gap in the theoretical and experimental understanding of the time- dependent, person-specific viral response to infections and vaccinations. Such events pose considerable modeling challenges, and a mathematical characterization of antibody kinetics is crucial for tackling future questions related to herd immunity and optimal decision-making regarding vaccination policy. We address the important task of tracking the antibody response to multiple infections or vaccinations or combinations of the two immune events, which was previously unresolved. We describe event-to-event transitions for post-infection or post-vaccination antibody kinetics by employing a novel combination of probability distribution models with a time-inhomogeneous Markov chain framework. This approach is ideal to model sequences of infections and vaccinations and predict missed events. We validate our work using SARS-CoV-2 antibody measurements from two datasets with different measurement systems. This work paves the way to future frameworks that can analyze the protective power of natural immunity or vaccination, predict missed immune events at an individual level, and inform booster timing recommendations for both emerging and endemic diseases.

Speaker: Rayanne Luke (George Mason University)

11:10 AM → 12:30 PM Stochastic models and methods in mathematical biology

11:10 AM Branching annihilating random walk models for self-regulating populations

We study a branching-annihilating random walk in which particles evolve on the lattice in discrete generations. Each particle produces a Poissonian number of offspring which independently move to a uniformly chosen site within a fixed distance from their parent's position. Whenever a site is occupied by at least two particles, all the particles at that site are annihilated. This models a population living in demes under a very strong form of local competition. For certain ranges of the parameters of the model, we show that the system dies out almost surely, or on the other hand survives with positive probability. In an even more restricted parameter range, we strengthen the survival results to convergence to a non-trivial invariant measure upon survival, and we show that the population invades space with a linear spreading speed. A central tool in the proof is comparison with oriented percolation on a coarse-grained level, using carefully tuned density profiles which expand in time and are reminiscent of discrete travelling wave solutions.

Speaker: Alice Callegaro (Technische Universität München)

11:30 AM A spectral Koopman framework for stochastic reaction networks

Stochastic reaction networks (SRNs) are a general class of continuous-time Markov jump processes used to model a wide range of systems, including biochemical dynamics in single cells, ecological and epidemiological populations, and queueing or communication networks. Yet analyzing their dynamics remains challenging because these processes are high-dimensional and their transient behavior can vary substantially across different initial molecular or population states. Here we introduce a spectral framework for the stochastic Koopman operator that provides a tractable, low-dimensional representation of SRN dynamics over continuous time, together with computable error estimates. By exploiting the compactness of the Koopman operator, we recover dominant spectral modes directly from simulated or experimental data, enabling efficient prediction of moments, event probabilities, and other summary statistics across all initial states. We further derive continuous-time parameter sensitivities and cross-spectral densities, offering new tools for probing noise structure and frequency-domain behavior. We demonstrate the approach on biologically relevant systems, including synthetic intracellular feedback controllers, stochastic oscillators, and inference of initial-state distributions from high-temporal-resolution flow cytometry. Together, these results establish spectral Koopman analysis as a powerful and general framework for studying stochastic dynamical systems across the biological, ecological, and computational sciences.

Speaker: Ankit Gupta (ETH Zürich)

11:50 AM Stochastic ordering tools for reaction network models

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the abundances of all considered species evolve over time. A possible approach to address this issue is to develop tools to compare the model under study with a similar one whose behavior is better understood. The main contribution of our work is to provide direct and computable conditions that can be used to ensure the existence of an ordered coupling between two stochastic reaction networks and to identify which parameter changes in a given model lead to an increase or decrease in the count of certain species. We also make an algorithm available that implements our theory and we illustrate it with several applications.

Speaker: Giulio Cuniberti (Politecnico di Torino)

12:10 PM Remodelling selection: What is it?

Every population consists of individuals who vary in their traits, and each trait may, or may not, be associated with frailty or fitness. Variation in frailty and fitness traits makes population studies prone to selective depletion bias (SDB). The issue is widespread across fields. When an ageing cohort exhibits declining mortality, is it individuals becoming healthier or selective depletion of the frail? In an epidemic, when growth in cumulative infections decelerates, is it individuals cautiously changing behaviour or selective depletion of the most susceptible? In microbial populations, when mutations increase population vulnerability to stress, it is individuals becoming more vulnerable or mutant populations having higher variance in fitness? In each case, the first explanation invokes individuals changing, while the second recognises that populations change due to selection on pre-existing variation. While the former are intuitive and widely adopted, explanations that rely on selective depletion are more neutral and less commonly considered due to cognitive biases and challenges in estimating all variation that matters.
We propose remodelling selection (ReMS) as a general strategy of study design and analysis to address the SDB problem. We have been using case studies to illustrate how it works but it remains a challenge to formalise ReMS in abstract terms that are broad enough to represent the entire domain of its applicability. Let’s discuss!

Speaker: Gabriela Gomes (University of Strathclyde)

11:10 AM → 12:30 PM Cancer-Immune Ecology

11:10 AM Modelling early immune selection and evasion in tumour evolution

A growing tumour is an evolving system: during tumour development, cancer cells randomly acquire mutations that may provide them with a beneficial phenotype. However, such alterations can also give rise to neoantigens – novel cancer-specific peptides presented on the cell surface that trigger host immune responses. Successfully navigating interactions with the microenvironment and overcoming immune elimination is therefore a crucial step in cancer development. In recent work on colorectal cancer, we analysed the relative timing and evolutionary dynamics of subclones bearing immune-relevant alterations, observing a “Big Bang” pattern in which mutations acquired early in tumour growth shaped subsequent tumour-immune evolution \cite{Lakatos:2025aa}.

Here, we investigate under which biological and sampling regimes such patterns are expected – or not expected –; and how immunogenicity metrics or sequencing strategies capture various modes of tumour-immune co-evolution. Building on our previous stochastic branching process-based model of tumour evolution and neoantigen acquisition \cite{Lakatos:2020aa}, we simulate sequencing data from multi-region biopsies to explore the distribution of neoantigen burden and diversity under different levels of ongoing immune selection and immune escape prevalence. Our simulations span from near-neutral evolution to strong early immune pressure selecting for parallel escape, illustrating how distinct regimes manifest in sequencing data patterns.

Speaker: Eszter Lakatos (Chalmers University of Technology, Sweden)

11:30 AM Deciphering systemic immune cell dynamics to inform immunotherapeutic approaches

Immunotherapeutic approaches that exploit and manipulate cellular immune responses have increased our ability to treat various malignant diseases. However, these approaches still have their limitations and tend to fail in numerous patients, requiring a more mechanistic and quantitative understanding about the complex, intermingled dynamics of cell migration, differentiation and turnover that regulate immune responses. Developing multi-scale population dynamics models and applying them to time-resolved murine and human data on immune dynamics in response to vaccination, as well as immunotherapeutic treatment by CAR-T cell therapies in patients suffering from diffuse large B-cell lymphoma (DLBCL), we determined how individual processes of cell migration, proliferation and differentiation interact to shape cellular immune responses. Our analyses suggest the existence of optimal time windows for therapeutic interventions and are able to recapitulate the dynamics of responders and non-responders to CAR-T cell therapy, suggesting the relation of individual T cell subset kinetics to therapy outcome and toxic side effects. This illustrates the necessity for a mechanistic and quantitative understanding of the individual processes that shape cellular immune responses on a systemic level in order to improve immunotherapeutic strategies.

Speaker: Frederik Graw (Friedrich-Alexander University of Erlangen–Nuremberg, University Hospital Erlangen, Deutsches Zentrum Immuntherapie, Bavarian Cancer Research Centre, Erlangen, Germany)

11:50 AM Mathematical modelling of cytokine dynamics in myeloproliferative neoplasm patients during treatment

The Philadelphia-chromosome-negative myeloproliferative neoplasms (MPNs) are slowly developing haematological malignancies characterised by an overproduction of blood cells. Chronic inflammation is associated with the diseases and suggested to play an important role in disease initiation and progression as well as being a consequence of the diseases.

In the DALIAH trial, treatment-naïve MPN patients were treated with either Hydroxyurea (HU) or low dose interferon-$\alpha$ (IFN-$\alpha$) and followed for up to five years\cite{knudsen_final_2023}. Both HU and IFN-$\alpha$ are commonly used treatments for MPN. On top of their cytoreductive effects, IFN-$\alpha$ is a potent immunostimulatory cytokine, while HU has been shown to decrease the level of pro-inflammatory cytokines and the neutrophil-to-lymphocyte ratio in sickle cell disease patients\cite{zahran_effect_2020}.

With a mechanism-based, nonlinear ordinary differential equation model, we investigate the role of inflammation in MPN disease progression and response to treatment. The model includes stem cell, progenitor cell, and mature cell
compartments of wild-type and mutated hematological cells with a nonlinear
negative feedback from the mature to the stem cell compartments.

By comparing the mechanism-based model to longitudinal measurements of mature blood cell counts, variant allele frequency of the MPN driver mutation \textit{JAK2}V617F, and cytokines of the patients enrolled in the DALIAH trial, we aim to identify a signature of inflammatory mediators with prognostic impact.

Speaker: Johanne Gudmand-Høyer (Roskilde University, Denmark)

12:10 PM A Bayesian ODE model for CAR T-cell kinetics in non-Hodgkin lymphoma

Non-Hodgkin lymphoma (NHL) is a heterogeneous group of hematological malignancies arising from lymphoid cells. In relapsed or refractory cases, chimeric antigen receptor (CAR) T-cell therapy offers a potentially curative treatment by engineering patient-derived T-cells to target tumor-associated antigens. Despite promising outcomes, treatment response remains variable across patients.
Lactate dehydrogenase (LDH) is a serum marker that reflects tumor burden, cell turnover, and tissue damage. It is routinely measured prior to lymphodepletion and during CAR T-cell therapy and may provide insight into the immunological context at treatment onset.
We developed a mechanistic ordinary differential equation (ODE) model that studies the relationship between CAR T-cell kinetics, tumor burden, and treatment response. By integrating individual patients’ longitudinal CAR T-cell and LDH measurements of NHL patients within a Bayesian inference framework, we aim to infer latent tumor burden trajectories, linking tumor-immune interactions to treatment outcome.

Speaker: Yifan Chen (University Hospital Schleswig-Holstein, Kiel University, Germany)

11:10 AM → 12:30 PM Emergence of collective behaviour across biological scales

11:10 AM A cell–cell adhesion model: a multiscale derivation

Cell–cell adhesion is a key organiser of tissue structure, in both healthy and cancerous environments, and plays a crucial role in regulating cancer cell migration. In this talk, we introduce a multiscale modelling framework for the dynamics of a moving self‑adhesive cell population \cite{ZR}. The approach links a detailed microscopic description of deterministic adhesion‑driven motion with a standard mesoscopic representation of a stochastic velocity‑jump process, leading to a kinetic transport equation that features several nonlocal terms. Passing to the macroscopic scale yields continuum equations that couple nonlocal adhesion with myopic diffusion.
The framework lends itself conveniently to representing the underpinning binding dynamics of adhesion molecules such as cadherins. When these microscopic effects are translated to the macroscopic level, they generate a novel nonlinear integral equation coupled to the cell‑density equation. For a rigorous mathematical analysis of models of this type, we refer to \cite{RZ} and the talk “A cell–cell adhesion model: local well‑posedness” in this conference.

Speaker: Anna Zhigun (Queen's University Belfast)

11:30 AM Scaling limits for a population model with growth, division and cross-diffusion

Motivated by the modeling of bacteria microcolony morphogenesis across multiple scales, we explore in this talk models for a spatial population of interacting, growing and dividing particles. Starting from a microscopic stochastic model, we first write the corresponding stochastic differential equation satisfied by the empirical measure, and rigorously derive its mesoscopic (mean-field) limit. We then take an interest in the so-called localization limit, to reach a macroscopic (large-scale) model. The scaling consists in assuming that the range of interaction between individuals is very small compared to the size of the domain. In proving the localization limit using compactness arguments, the difficulties are twofold: first, growth and division render the system non-conservative, preventing the use of energy estimates. Second, the size of the particles, being a continuous trait, leads to new difficulties in obtaining compactness estimates. We first show rigorously the localization limit in the case without growth and fragmentation, under smoothness and symmetry assumptions for the interaction kernel. We then perform a thorough numerical study in order to compare the three modeling scales and study the different limits in situations not covered by the theory yet. These works provide a better understanding of the link between the micro- meso- and macro- scales for interacting particle systems.

Speaker: Diane Peurichard (INRIA Paris)

11:50 AM Spatial phase transition in collective dynamics

I will present the result of a collaboration with Pierre Degond and Sara Merino-Aceituno. We study the emergence of band patterns in the Vicsek model, a minimal agent-based model of alignment dynamics with noise. Agent-based simulations on periodic domains display coexisting ordered (high-density, aligned) bands and disordered (low-density, non-aligned) regions, a phenomenon not explained by classical parameter-driven phase transitions. We review prior kinetic and macroscopic results that identify an spatial phase transition~\cite{degond_phase_2015}~: depending on the local density $\rho$ relative to a critical threshold $\rho_c$, different PDEs govern different spatial regions—Self-Organized Hydrodynamics (SOH, \cite{degond_continuum_2008}) in the ordered regime ($\rho > \rho_c$) and a degenerate diffusive correction (at order $\varepsilon$) in the disordered regime ($\rho < \rho_c$). Building on this framework, we propose a model that couples the ordered and disordered macroscopic equations to simulate the continuum dynamics~\cite{motsch_numerical_2011}, with the goals of reproducing band formation at the macroscopic level, exploring pattern formation, and connecting the linear stability properties of the coupled model with those of SOH.

Speaker: Léo Meyer (University of Vienna)

12:10 PM Multiscale modeling of collective cell invasion in heterogeneous environments

Collective cell invasion in many biological systems emerges from the complex interplay between individual cell behaviour and environmental heterogeneity, mediated by processes acting across multiple spatial and temporal scales. Cells continuously sense and respond to external cues, such as chemical gradients or physical constraints, while undergoing intrinsic dynamics including proliferation, adaptation, and phenotypic variability \cite{conte2023non, conte2021mathematical}. Understanding how these mechanisms integrate across scales is essential to explain the emergence of coordinated population-level dynamics.
In this talk, we propose a novel multiscale modelling framework that connects cell-level responses with macroscopic descriptions of collective invasion. We investigate how external cues influence movement through taxis mechanisms, and how their interplay with internal processes—including cell growth—may shape large-scale behaviour. Particular emphasis is placed on the coupling between scales, showing how the integration of microscopic and macroscopic dynamics can lead to qualitatively distinct collective behaviours.
The proposed approach is flexible and can be adapted to various biological contexts, providing insight into how multiple processes combine to regulate migration and organization in complex systems.

Speaker: Martina Conte (Politecnico di Torino)

11:10 AM → 12:30 PM Stochastic agent- and particle-based models in biology: methods and analytical insights

11:10 AM Pattern Formation and Spike Dynamics in the Presence of Noise

Noise plays a crucial role in the formation and evolution of spatial patterns in various reaction-diffusion systems in mathematical biology and ecology. In this talk, I give two examples where noise significantly influences spatial patterning. The first example describes how patterned states can provide a refuge and prevent extinction under stressed conditions. It also illustrates the importance of not only the absolute level of climate change, but also the speed with which it occurs. The second example studies the effect of noise on dynamics of a single spike pattern for the classical Gierer--Meinhardt model on a finite interval.

Speaker: Chunyi Gai (University of Northern British Columbia)

11:30 AM Genealogical structures under interactive neutral reproduction: Ancestral influence graph and Frankenstein process

Collaborators:
Hannah Dopmeyer (Bielefeld University, Germany),
Fernando Cordero (BOKU University, Vienna, Austria).

Abstract:
We consider the two-type Moran model of population genetics with frequency-dependent neutral reproduction. Relying on the model's graphical representation in terms of a particle system, we establish a (factorial) moment dual. Moment duals are usually related to the genealogy of the population, but in this case, the connection is mysterious. This is because the natural ancestral graph of the model (the so-called ancestral influence graph, AIG) exhibits a complicated hierarchical structure, whereas the moment dual is a simple density-dependent branching process. We solve this mystery by starting from the fact that moment duality is a property in expectation; it need not hold pathwise. This provides the freedom to construct what we call the Frankenstein process by tracing back sample configurations and piecing them together across different realisations of the AIG. This leads to the dual process and resolves the mystery.

Speaker: Ellen Baake (Bielefeld University)

11:50 AM Structure of family trees in finite-population exchangeable models

We give conditions for an exchangeable genealogy model, with an arbitrary sequence of population and litter sizes, to have either a unique infinite path, or a unique lineage whose descendants eventually dominate the population. Conditions relate naturally to the coalescent time scale: the second property holds iff infinite time passes on this scale, while the first property holds if a truncated version of this time scale diverges. We make use of the well-known lookdown representation, also giving a more intuitive derivation of the lookdown via the complementary notions of forward and backward neutrality. We also discuss connections of the first property to the question of identifiability of the lookdown labelling from the unlabelled tree.

Speaker: Eric Foxall (University of British Columbia)

12:10 PM Dimension reduction for the modern Hopfield network

A modern Hopfield network can be viewed as an agent-based model as each neuron (or memory pattern) behaves like an individual agent following local update rules, and their interactions collectively produce the network’s emergent dynamics. In this talk, I will discuss a dimension reduction technique for modern Hopfield networks.

Speaker: Linh Huynh (Dartmouth College)

Thu, July 16

10:40 AM → 12:00 PM Advances in multiple timescale dynamics in neurons and related excitable systems

10:40 AM Timescale separation anxiety in capturing neuronal activity patterns in biophysically detailed models

We consider multi-dimensional, Hodgkin-Huxley type models for single neurons in respiratory and motor components of the brainstem. Such models allow for the analysis of how specific ion currents contribute to the generation and control of a variety of complicated temporal voltage patterns that are observed experimentally. For this analysis to proceed, we nondimensionalize the original models to try to extract the timescales on which model components evolve and group these into distinct classes to which methods of geometric singular perturbation theory (GSPT) can be applied; however, in the models we consider, this classification is not clear-cut. We show how in both cases, GSPT tools such as bifurcation theory and averaging can explain the dynamical mechanisms underlying observed activity, but achieving these results requires us to impose different timescale groupings in different regions of phase space.

Speakers: Anna Thomas (University of Pittsburgh), Jonathan Rubin (University of Pittsburgh), Ryan Phillips (Seattle Children's Hospital), Sushmita John (University of Pittsburgh)

11:00 AM Unfolding neuronal excitability: dynamical paths to depolarization block during spreading depolarization events

Fast mechanisms responsible for action potential generation are modulated by slower processes that can lead to complex sequences of firing regimes. We use a dataset that provides an unusual window into a progression of transitions in neural activity, from baseline excitability to depolarization block and back. The dataset consists of whole-cell patch-clamp recordings of neurons during potassium-induced spreading depolarization events, which are waves of depolarization that spread across the cortex and involve massive changes in ion concentrations. The peculiarity is that these events are partial: they do not reach all cortical layers, creating a gradient in the perturbation to neural activity.

We apply a phenomenological approach to show how this progression arises naturally from minimal dynamical constraints. On the fast timescale, the neuronal excitability class interpreted through the lens of Unfolding Theory provides a generic bifurcation diagram of essential neuronal dynamics. On the slow timescale, simple homeostatic rules and their interaction with external perturbations (such as the potassium waves) steer the neuron through the diagram, giving rise to the experimentally observed progression. The model predicts other transition sequences, which we identified in the experimental and modeling literature. This frames depolarization block as a nuanced dynamical phenomenon, with implications for modeling choices and experimental design.

Speaker: Marisa Saggio (Aix-Marseille University)

11:20 AM Multiscale Organization in a novel Cartwheel Interneuron Model: From averaging to folded node dynamics

A recent eleven-dimensional cartwheel cell (CWC) model \cite{[1]} has provided insight into the evolution of the electrical activity of this interneuron. Specifically, CWCs transit from bursting, via continuous spiking, to complex spiking, as the applied current (IApp) increases \cite{[2]}. Reductions in the maximal conductance of BK (gBK) or L-type Ca2+ (gCaL) channels lead to the loss of continuous spiking, and loss of bursting and complex spiking, respectively. Here, we provide a mathematical explanation of these transitions by analyzing a six-dimensional reduction of the model. The reduced system has three timescales with one fast, three slow, and two super-slow variables. We find that studying the super-slow dynamics, specifically the existence and the stability of the super slow equilibrium point through averaging theory, is informative for understanding the mechanism underlying the transitions between activity patterns as IApp, gBK, and gCaL change. Complementary results are obtained by considering the system as a two-time scale problem where the slow and the super-slow variables are all treated as slow. This approach reveals that the small-amplitude oscillations seen in bursting and complex spiking originate from a folded node structure. The associated geometric features provide an alternative perspective on the regulation of the electrical activity. Overall, by integrating two- and three-timescale analyses, this work provides a coherent framework for understanding CWC dynamics.

Speakers: Jonathan Rubin (University of Pittsburgh), Matteo Martin (University of Padova), Morten Gram Pedersen (University of Padova)

11:40 AM Slow–fast dynamics in a neurotransmitter release model: Delayed response to a time-dependent input signal

We provide a short introduction to the SNARE-SM model proposed in \cite{rodrigues2016time} to describe the release of neurotransmitters in synapses. We highlight the use of slow-fast dynamics to recreate experimental data exhibiting delay between an input stimulus and the corresponding (asynchronous) neurotransmitter release. In particular, we analyse the possible scenarios in a 2D singularly perturbed system of ODEs in standard form, which serves as a building block for the full 6D system. Then, we introduce a generalization \cite{sensi2023slow} of the aforementioned model, which manages to realize more complex transient behaviours. This is achieved by increasing the complexity of the critical manifold of the planar system of singularly perturbed ODEs. We showcase the corresponding entry-exit phenomenon and a variety of canard orbits.

Speakers: Mathieu Desroches (MathNeuro Team, Inria Branch at the University of Montpellier, Université de Montpellier), Mattia Sensi (Università di Trento), Serafim Rodrigues (Basque Center for Applied Mathematics)

10:40 AM → 12:00 PM Applications of reaction networks

10:40 AM CRNT approaches in modelling carbon dioxide removal through direct ocean capture

The mitigation of climate change has stood at the forefront of interest in the interface of mathematics, biology, and chemistry. Recently, direct carbon dioxide removal strategies have been examined which include direct ocean capture, as well as direct air capture. However, the structural and dynamical properties of these expanded carbon cycle models have yet to be explored. We apply methods in chemical reaction network theory (CRNT) to analyze the kinetic properties of these systems. Beyond identifying steady states, we also look at possibilities for multistationarity signaling crucial tipping points in the carbon cycle. We examine the conditions for independence of steady states to starting values and the capability for carbon concentration reduction. Finally, through the methods of flux balance analysis, we present a linear programming technique to show the capability of the carbon cycle to reduce overall free carbon dioxide concentration in both atmosphere and oceans. Our results do not only propose mechanisms to mitigate climate change, but give a consistent approach to analyze other carbon dioxide removal techniques in a general carbon cycle system.

Speaker: Al Jay Lan Alamin (Institute of Mathematics, University of the Philippines Diliman, 1101, Quezon City, Philippines)

11:00 AM Spatiotemporal modeling of signaling pathways: impact of endosomal compartmentalization and application to gonadotropin receptors

Cells communicate by sending extracellular ligands such as hormones. Once recognized by their plasma membrane receptors, these ligands trigger intracellular signaling cascades. G Protein-Coupled Receptors (GPCRs) can activate such cascades both at the plasma membrane and, once internalized, from endosomal compartments. Signal kinetics and spatial organization are key determinants of cellular responses. Receptor trafficking (internalization, recycling, endosomal dynamics) thus plays a crucial role in signaling pathways, yet it remains underexplored in theoretical GPCR models. We developed a mathematical framework incorporating receptor trafficking and signal compartmentalization into generic GPCR models. Using a compartmentalized system of ordinary differential equations, we analyzed how internalization and recycling affect receptor-induced responses. This framework addresses two questions: (i) How does trafficking influence signaling? and (ii) How does signaling feedback affect trafficking? We show that trafficking can enhance or reduce ligand action depending on membrane versus endosomal signaling and that feedback mechanisms can generate multi-stability. Applied to the Follicle-Stimulating Hormone Receptor (FSHR), our model calibrated with kinetic data improves ligand characterization and understanding of FSHR signaling.

Speaker: Chloe Weckel (BIOS, PRC, UMR CNRS, Université de Tours, INRAE, INRAE Centre Val de Loire 37380 Nouzilly, France / MUSCA, Université Paris-Saclay, Inria, Centre Inria de Saclay, 91120 Palaiseau, France)

11:20 AM From Food Webs to Fluxes: A New Decomposition of Ecosystem Networks

Ecosystems are commonly represented as directed graphs describing flows of energy or biomass among species. While these models highlight compartments and flows, neither provides a fundamental dynamical unit. We introduce fluxes as elementary processes that serve as building blocks of ecosystem networks. Inspired by flux balance analysis and metabolic control analysis, a flux represents the smallest process that can theoretically sustain itself, such as a material cycle or a simple food chain embedded within a larger food web. Mathematically, fluxes define a unique network decomposition: any ecological network can be represented as a linear combination of its fluxes. Because this decomposition preserves all network connections, it maintains system-wide properties of the original ecosystem. For example, the total amount of material cycling in the ecosystem equals the sum of cycling occurring within individual fluxes, independent of network size or complexity. More generally, several global ecosystem properties are conserved under this decomposition. We demonstrate the mathematical structure and ecological interpretation of this approach using EcoNet (http://eco.engr.uga.edu), a freely available online platform for ecosystem network analysis.

Speaker: Caner Kazanci (University of Georgia, USA)

11:40 AM A stochastic model of compartmentalized intracellular signalling

We study the long-time behaviour of a stochastic model for compartmentalised receptor signalling motivated by the trafficking of G protein-coupled receptors. The model describes the evolution of several chemical species distributed between the plasma membrane and a random population of endosomes. Chemical reactions follow deterministic dynamics inside each compartment, while stochastic events create endosomes by internalisation and recycle them back to the membrane. This leads to a piecewise deterministic Markov process with a variable number of compartments.

Using techniques inspired by the theory of Markov switching systems, we analyse the stability properties of the process. Under suitable contraction assumptions on the reaction dynamics, we prove the existence and uniqueness of a stationary distribution and establish exponential convergence in Wasserstein distance by a coupling argument. We also investigate exponential convergence in total variation using Harris theorem and identify structural conditions ensuring the existence of accessible Doeblin points.

Speaker: Léo Darrigade (UMR BOA, INRAe Val-de-Loire, 37175, Nouzilly, France)

10:40 AM → 12:00 PM Immunobiology and Infection Subgroup Minisymposium 2026

10:40 AM Spatial Heterogeneity in Tumours: How Tumour-Immune Spatial Relationships Impact Immunotherapy Outcomes in Glioblastoma

Glioblastoma is the most common and deadliest primary brain tumour in adults, with a median survival of 15 months under the current standard of care [1]. Its tumour microenvironment has been shown to be highly heterogeneous [2], meaning the magnitude of cell-cell interactions differ across space due to spatial differences. Agent-based models (ABMs) are well-suited for describing this spatial cell heterogeneity. When initialized with synthetic data obtained from single-cell imaging modalities, like imaging mass cytometry data, ABMs can capture realistic intra-tumoral dynamics [3]. In this talk, we show how spatial relationships between immune and cancer cells shape tumour-immune dynamics and influence predictions of immunotherapy outcomes. To this end, we build a glioblastoma-immune system ABM and include in our new spatial model immunotherapies previously modeled with an ordinary differential equation (ODE) model [4]. Unlike ABMs, ODE models have a very low computational cost. However, they assume cell populations are well-mixed. Our work lays the foundations for combining ABMs and ODE models to leverage both the spatial realism of the former and the computational efficiency of the latter in describing the overall tumour progression.

References
[1] @article{Trager_Geskin_Saenger_2020, title={Oncolytic Viruses for the Treatment of Metastatic Melanoma}, volume={21}, ISSN={1527-2729, 1534-6277}, url={http://link.springer.com/10.1007/s11864-020-0718-2}, DOI={10.1007/s11864-020-0718-2}, number={4}, journal={Current Treatment Options in Oncology}, author={Trager, Megan H. and Geskin, Larisa J. and Saenger, Yvonne M.}, year={2020}, month=apr, pages={26}, language={en} }
[2] @article{Karimi_Yu_Maritan_Perus_Rezanejad_Sorin_Dankner_Fallah_Doré_Zuo_et al._2023, title={Single-cell spatial immune landscapes of primary and metastatic brain tumours}, volume={614}, ISSN={0028-0836, 1476-4687}, url={https://www.nature.com/articles/s41586-022-05680-3}, DOI={10.1038/s41586-022-05680-3}, number={7948}, journal={Nature}, author={Karimi, Elham and Yu, Miranda W. and Maritan, Sarah M. and Perus, Lucas J. M. and Rezanejad, Morteza and Sorin, Mark and Dankner, Matthew and Fallah, Parvaneh and Doré, Samuel and Zuo, Dongmei and Fiset, Benoit and Kloosterman, Daan J. and Ramsay, LeeAnn and Wei, Yuhong and Lam, Stephanie and Alsajjan, Roa and Watson, Ian R. and Roldan Urgoiti, Gloria and Park, Morag and Brandsma, Dieta and Senger, Donna L. and Chan, Jennifer A. and Akkari, Leila and Petrecca, Kevin and Guiot, Marie-Christine and Siegel, Peter M. and Quail, Daniela F. and Walsh, Logan A.}, year={2023}, month=feb, pages={555–563}, language={en} }
[3] @article{Mongeon_Hébert-Doutreloux_Surendran_Karimi_Fiset_Quail_Walsh_Jenner_Craig_2024, title={Spatial computational modelling illuminates the role of the tumour microenvironment for treating glioblastoma with immunotherapies}, volume={10}, ISSN={2056-7189}, url={https://www.nature.com/articles/s41540-024-00419-4}, DOI={10.1038/s41540-024-00419-4}, number={1}, journal={npj Systems Biology and Applications}, author={Mongeon, Blanche and Hébert-Doutreloux, Julien and Surendran, Anudeep and Karimi, Elham and Fiset, Benoit and Quail, Daniela F. and Walsh, Logan A. and Jenner, Adrianne L. and Craig, Morgan}, year={2024}, month=aug, pages={91}, language={en} }
[4] @article{Mongeon_Craig_2025, title={Virtual Clinical Trial Reveals Significant Clinical Potential of Targeting Tumor‐Associated Macrophages and Microglia to Treat Glioblastoma}, volume={14}, ISSN={2163-8306, 2163-8306}, url={https://ascpt.onlinelibrary.wiley.com/doi/10.1002/psp4.70033}, DOI={10.1002/psp4.70033}, number={7}, journal={CPT: Pharmacometrics & Systems Pharmacology}, author={Mongeon, Blanche and Craig, Morgan}, year={2025}, month=july, pages={1156–1167}, language={en} }

Speakers: Blanche Mongeon (University of Montreal), Morgan Craig (CHU Sainte-Justine Research Centre / Université de Montréal)

11:00 AM Modeling SARS-CoV-2 Coinfection Reveals Key Differences in Inflammatory Cytokines

It has been shown that infection with a mild respiratory virus prior to infection with a lethal respiratory infection can prevent mortality and morbidity, with influenza A and SARS-CoV-2 being two such viruses where this has been seen. In this study, we investigate the resulting cytokine storm arising from nonlethal single infection of SARS-CoV-2 and nonlethal coinfection of influenza A and SARS-CoV-2 in mice. Through statistical modeling, we identify regulatory cytokines key to inflammation, viral clearance, and lung damage, as measured by serum albumin. Our analysis indicates single infection with SARS-CoV-2 results in a lower accumulation rate of TNFα compared to coinfection with influenza A, a higher accumulation rate of IFNα, and lower rate of damage, as measured by serum albumin. This highlights key cytokines that, when taken together with serum albumin, can be used to form a holistic mathematical model of the cytokine storm resulting from the innate immune response to viral respiratory infection.

Speaker: Havilah Neujahr (University of Idaho)

11:20 AM Multi-modal data integration and individual cell-based modelling to infer viral spread and innate immune dynamics in human epithelia

Understanding the mechanisms that govern viral spread within human tissues remains a major challenge, especially for identifying and quantifying key factors that influence viral transmission and innate immune responses. Although mathematical models and experimental advances have provided valuable insights, revealing the complex spatio-temporal interactions of infection and immune processes at the tissue level has remained elusive. Here, we present a novel workflow that combines multimodal experimental data and individual cell-based modeling to allow the inference of viral and immune kinetics within tissues. While standard inference methods typically require custom summary statistics and resourceful re-fitting procedures for individual data sets, our workflow relies on simulation-based inference using BayesFlow, a framework for neural posterior estimation that allows for amortized inference of multimodal data. Validating our approach with synthetic data, we showed that integrating spatial information is essential for reliably inferring viral transmission kinetics and innate immune interactions within human airway epithelium, with subsequent application to experimental data on SARS-CoV-2 infection indicating local transmission as the dominant mode of viral spread. Our method can be readily adapted to various respiratory viral infections, helping to investigate co-infection and treatment scenarios, and presents a general framework for analysing viral infections at tissue level.

Speaker: Frederick Graw (Department of Internal Medicine 5, Haematology and Oncology, Friedrich-Alexander-Universität Erlangen-Nürnberg and Universitätsklinikum Erlangen; Deutsches Zentrum Immuntherapie (DZI); Bavarian Cancer Research Centre (BZKF))

11:40 AM Identifying Sex-Specific Immune during Primary Influenza Infection Using Mathematical Modeling

In humans, differences in immune response between males and females influence influenza infection outcomes. During the 2009 H1N1 pandemic, Eshima et al., 2011 found that adult females were ~40% more likely to be hospitalized than their male age-matched counterparts. The innate immune response has been implicated as a factor of these sex differences. Together with collaborators at UW Madison, we have completed experiments on male and female mice infected with CA04-H1N1 influenza. These experiments show that female mice have increased viral production at 36 hours post infection and early, excessive innate immune activation characterized by proinflammatory cytokine profiles, and critical differences in macrophage counts. Histopathology shows lesions are present in the alveolar region of female, but not male, mice, indicating influenza virus penetrates more deeply in female lungs. While experimental data identifies key immune components linked to severity, mathematical modeling enables detection of sex-specific mechanistic differences. We developed a mathematical model of influenza infection to identify mechanisms responsible for observed increases in disease severity in female mice. We have identified two models with significant evidence using Bayesian model selection (AICc), where each model has a different parameter subset with individual male and female values. These parameters are sex-specific and each model points to a unique mechanism that could be targeted for regulating severe influenza disease.

Speaker: Dr Jason E. Shoemaker (1. Department of Chemical and Petroleum Engineering, University of Pittsburgh; 6. McGowan Institute for Regenerative Medicine, University of Pittsburgh; 7. Department of Computational and Systems Biology, University of Pittsburgh; 8. Department of Bioengineering, University of Pittsburgh)

10:40 AM → 12:00 PM Population Dynamics in Disturbed Landscapes

10:40 AM Goshawk-Squirrel Predator-Prey Dynamics in Patchy Forests Subject to Fire and Forestry Disturbances

Our work focuses on understanding predator-prey dynamics in a complex
landscape that is constantly changing due to forest growth and disturbances
such as wildfire or logging. Climate change is increasing the frequency and
severity of wildfires, causing additional stress to the forest ecosystem on top of
existing anthropogenic activity. We seek to understand how these landscape
disturbances affect the persistence of resident predator-prey populations. In
particular, how changes to disturbance frequency and magnitude alter ecosystem
stability. As a practical example of this interconnected system, we focus on the
goshawk-squirrel predator-prey system in Canadian coniferous forests.
Most predator-prey models that consider patchy landscapes, keep patch
properties constant over time. We include time-varying patch properties, ac-
counting for the disturbance-regrowth cycle. An additional complicating factor
we take into account is the territoriality of squirrels. We present a mathematical
model for this system and show how species persistence is affected by a chang-
ing disturbance regime. Our results show that changes in disturbance frequency,
along with patch sizes affects species densities and their persistence.
Ultimately, we hope that the results and the model will inform conversa-
tion efforts for the goshawk and for predator-prey systems that rely on mature
forests.

Speaker: Christian Wiewelhove (University of British Columbia - Okanagan)

11:00 AM Starvation-driven cell patterning: integrating lab experiments and mathematical modelling

We present a reaction–diffusion model describing the interactions among cells, nutrients, and growth factors, aimed at capturing the emergence of starvation-driven cell pattern formation, a phenomenon recently observed in laboratory experiments under nutrient-limited growth conditions. Experiments and modelling were developed in parallel, enabling progressively more targeted experimental design while enhancing the biological realism of the model. This interdisciplinary feedback loop led to the formulation of new hypotheses and enabled the estimation of several key parameters. Numerical simulations show that the model reproduces pattern formation in both one- and two-dimensional spatial domains. To provide theoretical support for these findings, we performed a Turing instability analysis to investigate the potential for diffusion-driven instability. The analysis indicates that the observed patterns are not driven by chemotaxis; rather, they arise naturally under starvation conditions and display structural similarities to the Klausmeier model for vegetation pattern formation in semi-arid environments, suggesting the robustness of the underlying mechanism across biological scales.

Speaker: Cinzia Soresina (University of Trento)

11:20 AM Patterned biodiversity responses to disturbance severity in competition-governed metacommunities

Whether static, e.g. habitat destruction, or dynamic, e.g. environmental fluctuations, disturbance of a landscape has typically been expected to degrade its resident ecosystems. However, recent modelling studies \cite{Zhang2023, Zhang2025} have predicted that community biodiversity can oscillate, both rising and falling, as disturbance severity increases. Similar patterns have been found by re-examination of empirical data collected in disturbed ecosystems. While the overall trend is for biodiversity to decline with disturbance severity, these responses could mislead ecosystem managers as to the impact of ongoing climate change and the effectiveness of conservation interventions.

In this talk, I will outline the general mechanism that gives rise to these responses; specifically, the effect of a tradeoff in growth rate and competitive ability. I will then explore why identical results are obtained for apparently different types of disturbance.

Speaker: Daniel Bearup (University of Leicester)

11:40 AM Response scenarios of the total population size in fluctuating environments

Habitat fragmentation, driven by human activities, poses a major threat to biodiversity by isolating populations and disrupting ecological processes. Metapopulation models are essential for understanding these dynamics, but they often assume temporally homogeneous environments. This assumption overlooks the reality that abiotic and biotic factors, such as temperature or resource availability, fluctuate over time, altering growth and competition. In this talk, we will show that such temporal heterogeneity can alter the impact of dispersal on total population size, leading to new response patterns not observed in constant environments using a discrete-time two-patch model.

Speaker: Daniel Franco (Universidad Nacional de Educación a Distancia, Spain)

10:40 AM → 12:00 PM Viscoelastic and multifunctional modelling and applications in biology (on the occasion of the 60th birthday of Victor A. Kovtunenko)

10:40 AM What Has Biology Done for Mathematics: Nondegenerate vs Degenerate

In my talk I consider a new class of degenerate "parabolic" type ODE-PDE couplings arising in the modelling of life sciences. The long-time dynamics of solutions is studied in terms of their attractors. Some open problems will also be discussed.

Speaker: Messoud Efendyev (Munich Helmholtz Center)

11:20 AM A Cell–Cell Adhesion Model: Local Well Posedness

We present a result on local well posedness for a highly nonlocal nonlinear diffusion–adhesion system [RZ]. Macroscopic systems of this type were previously obtained through upscaling [ZR] and can account for the effect of microscopic receptor binding dynamics in cell–cell adhesion. The system couples an integro PDE featuring degenerate diffusion of porous medium type and nonlocal adhesion with a novel nonlinear integral equation. The approach is based on decoupling the system and using Banach’s fixed point theorem to solve each of the two equations individually and subsequently the full coupled system. A key challenge lies in identifying a suitable functional setting. One of the main results is the local well posedness of the integral equation with a Radon measure as parameter. The analysis of this equation employs the Kantorovich–Rubinstein norm, marking what appears to be the first use of this norm in the study of a nonlinear integral equation. For details of a multiscale derivation of models of this kind, we refer to [ZR] and to the talk “A cell–cell adhesion model: a multiscale derivation” in this conference.

Speaker: Anna Zhigun (Queen's University Belfast)

11:40 AM Well-Posedness of a Diffuse Interface Model for Tumor Growth

We propose a diffuse interface model to describe a tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a mechanical equilibrium equation with phase-dependent elasticity coefficients. The resulting PDE system couples two Cahn-Hilliard type equations for the tumor phase and the healthy phase with a PDE linking the evolution of the interstitial fluid to the pressure of the system, a reaction-diffusion type equation for the nutrient proportion, and a quasistatic momentum balance. We prove here that the corresponding initial-boundary value problem has a solution in appropriate function spaces.

Speaker: Pavel Krejčí (Czech Academy of Sciences)

10:40 AM → 12:00 PM Mechanistic insights from in-vivo and in-vitro data: modelling tissue physiology and pathology away from equilibrium

10:40 AM Collective cell dynamics driven by active boundaries and cell turnover: a multi-scale approach.

During morphogenesis, hundreds of cells undergo large-scale movements, and the biological or mechanical regulatory factors involved are still poorly understood, despite intensive research. To better characterize the emergence of these movements, we propose a microscopic Vicsek-type model, combining the alignment of polarities and contact forces, and have studied the dynamics in confined environments. A first study has raised the key role of active boundaries in triggering rotational motion. Cells are then confined within an annular region bounded by self-generated elastic cables and comparisons between numerical simulations of the model and experiments show quantitative agreement. In a second study, we have investigated apoptosis, the spontaneous death of cells, which plays an ambiguous role in these dynamics: we have thus added reorientation of polarities near apoptotic cells in the model. In this case, numerical simulations allow us to highlight the influence of apoptosis in congested situations. Through a statistical description of the dynamics, we then propose the derivation of fluid-type models (Self-Organized Hydrodynamics) under different parameter regimes, enabling a better understanding of the process.

These works are the result of strong collaborations with Simon Lo Vecchio, Daniel Riveline, Roxana Sublet and Marcela Szopos and recent developments are also in close cooperation with all the members of the ANR Mapeflu project (ANR-22-CE45-0028).

Speaker: Laurent Navoret (Université de Strasbourg)

11:20 AM Pattern formation in a phenotype-structured Shigesada-Kawasaki-Teramoto model

Shigesada, Kawasaki, and Teramoto showed that introducing cross-diffusion into the spatial Lotka–Volterra competition model can destabilise homogeneous equilibria and generate spatial patterns. In this talk, I will consider populations with phenotype heterogeneity and introduce a general framework in which individuals’ movements and interactions are phenotype-dependent. Motivated by cellular plasticity, I study a regime of rapid phenotype switching and derive conditions for cross-diƯusion- and phenotype-driven instabilities. I conclude with numerical simulations illustrating the role of the phenotype distribution and its impact on competitive outcomes. This is a joint work with Tommaso Lorenzi and Gaetana Gambino.

Speaker: Davide Cusseddu (https://orcid.org/0000-0002-6882-9486)

11:40 AM A Starling resistor model for choroidal venous flow

The choroid is a densely vascularised layer of tissue of the eye, lying between the retina and the sclera (outer layer of the eye), which carries the majority of ocular blood flow. Vortex veins
drain blood out of the eye (to the orbit), crossing the sclera from the choroidal circulation.
Animal experiments have shown that pressure in these veins is tightly linked to intraocular pressure (IOP) \cite{1}. Partial collapse of the vortex veins in the sclera has been hypothesised to be responsible for venous pressure control in the choroid \cite{2,3}.
In this work, we formulate a Starling resistor model of a vortex vein, investigating whether it can explain the observed pressure behaviour. We model the vein as a collapsible tube, with a segment within the choroid subjected to IOP, and a segment crossing the sclera in which the
external pressure linearly decreases from IOP to the orbital tissue pressure. In order to fully reproduce the experimental results \cite{2}, we extend the model to account for more than one vortex vein.
We show that, under physiological conditions, the experimentally observed behaviour of the choroidal venous outflow can be reproduced by the model, if the vortex vein is collapsed in the scleral segment. In this case, increasing IOP results in an increase of choroidal venous
pressure of almost the same amount.
In summary, the model suggests a mechanical explanation for passive control of choroidal venous pressure by vortex vein collapse within the sclera.

Co-authors:
- Peter Stewart, School of Mathematics & Statistics, University of Glasgow, Glasgow, UK
- Alexander J. E. Foss, Department of Ophthalmology, Nottingham University Hospitals
NHS Trust, Nottingham, UK
- Jennifer Tweedy, Mathematical Sciences, University of Bath, Bath, UK
- Rodolfo Repetto, Department of Civil, Chemical and Environmental Engineering,
University of Genoa, Genoa, Italy.

Speaker: Federica Vanone (Gran Sasso Science Institute)

10:40 AM → 12:00 PM Cell Migration Across Scales – exploring different mathematical frameworks

10:40 AM MS145-1

Speaker: Chiara Giverso (Politecnico di Torino)

11:00 AM Multiscale modelling of cancer invasion and metastasis: the effects of tumour heterogeneity

Cancer invasion and metastasis are multiscale processes driven by complex interactions between cancer cells and the tumour microenvironment. A key mechanism underlying cancer heterogeneity is the Epithelial-to-Mesenchymal Transition (EMT), through which proliferative epithelial-like cancer cells (ECCs), forming the bulk of solid tumours, progressively acquire migratory and invasive mesenchymal-like traits. Mesenchymal-like cancer cells (MCCs) can actively invade surrounding tissue and disseminate to distant organs via the vasculature. At secondary sites they may undergo the reverse Mesenchymal-to-Epithelial Transition (MET), enabling metastatic growth. Importantly, EMT is a continuous process that generates intermediate hybrid phenotypes with progressively increasing invasive potential. In this talk, we will explore a variety of models that incorporate phenotypic transitions for cancer invasion across mathematical and biological scales. Firstly, I will introduce a novel 3D hybrid multiscale model which couples individual-based representations of migrating cancer cells with continuum descriptions of tumour growth. The model illustrates how EMT-driven phenotypic changes shape macroscopic invasion patterns within a multi-organ framework. Furthermore, I will present a phenotype-dependent individual based model and its corresponding macroscopic model, which incorporates continuous transitions along the epithelial–mesenchymal spectrum, providing a tractable framework to study the emergence and maintenance of phenotypic heterogeneity in cancer.

Speaker: Dimitrios Katsaounis (RWTH Aachen University)

11:20 AM Bayesian parameter inference of stochastic two-population cell movement models with spatial statistics

Linking models to experimental data is a common challenge in mathematical biology. Several techniques have been developed to parameterize theoretical frameworks, including maximum likelihood estimation and Approximate Bayesian Computation. Previous work established that combining these approaches with spatial data analysis, specifically with statistics known as pairwise correlation functions (PCFs) that quantify the relative degree of clustering or exclusion among cells across multiple length scales, can recover parameters in models of cell movement in homogeneous populations. Yet it remains unclear whether PCFs are equally useful at parameterizing models in cases with multiple cell types. I will describe a simplistic mathematical framework created to address this gap, which is based on in vitro experiments of immune cell infiltration into tumor-dense space. The model tracks individual cell positions using an overdamped version of Newton’s law, with forces arising from short-range repulsion and long-range attraction between cells. I create multiple synthetic datasets in which tumor and immune cells interact with varying length scales and strengths of attraction, and apply Approximate Bayesian Computation-Sequential Monte Carlo to determine how well the posterior parameter distribution recovers the “ground truth”. I demonstrate that the attractive forces between cells are practically identifiable, even when their underlying parameters may not be.

Speaker: Duncan Martinson (The Francis Crick Institute)

11:40 AM A Physiologically Based Pharmacokinetic (PBPK) Model of Whole-Body CAR T-Cell Trafficking in Humans

Chimeric antigen receptor (CAR) T-cell therapy has shown remarkable clinical success in the treatment of B-cell malignancies. Numerous mathematical models have been developed to describe the interactions between CAR T cells and malignant B cells at the tumor site \cite{LT21, S25}; however, these approaches often neglect the systemic trafficking of CAR T cells across physiological compartments, which plays a crucial role in linking intravenously administered doses to quantitative measurements at the tumor site \cite{Z96}. In this work, we develop a physiologically based pharmacokinetic (PBPK) framework for CAR T-cell trafficking in humans, comprising both a full whole-body model and a sensitivity-analysis-based minimal PBPK model. The full model describes organ-level transport processes, intra-tissue kinetics, and interactions with malignant B cells within lymph nodes \cite{S25}, and is used for parameter calibration and validation against clinical data from more than 100 patients. The minimal model is used to perform equilibria and stability analyses, providing insight into biologically uncertain mechanisms such as organ uptake. Our results highlight the importance of migration dynamics for a quantitative understanding of CAR T-cell therapy and support the use of mechanistic whole-body models for dose optimization and personalized treatment planning through simulation-guided approaches.

Speaker: Elio Campanile (University of Trento)

10:40 AM → 12:00 PM Whole-cell modelling: progress and perspectives

10:40 AM Producing quantitative protein function data at scale to enable mechanistic simulation - and protein design

To this day, there is still no existing quantitative model that can simulate the reaction rates and concentration changes in the comprehensive biochemical reaction network of a cell. Such a simulation model would be useful for understanding the nature of living cells.

A primary barrier is the lack of accurate parameters. Key biochemical parameters are notoriously difficult to measure, with published values for the same reaction often varying by orders of magnitude. This uncertainty severely limits the predictive power of mechanistic models. Furthermore, while advances in machine learning have enabled protein structure prediction, predicting quantitative functional properties (e.g., catalytic constants) remains a major hurdle, largely due to the scarcity of high-quality in vivo data for model training.

Here, we present a framework that overcomes this limitation. Using convex optimization, we integrate mechanistic constraints with high-throughput measurements, and demonstrate that this approach yields large-scale estimates of protein functional parameters that are consistent with in vivo phenotypes and diverse experimental data. These parameters enable accurate mechanistic simulation of cellular metabolism and provide a rich, quantitative dataset of biomolecule function, creating a valuable resource for training next-generation predictive models for protein design.

Speaker: Cyrus Knudsen (Stanford University)

11:00 AM Thermodynamically Consistent Mechanochemical Modelling of Actin Dynamics

Actin assembly drives force generation and membrane remodelling (protrusion, budding, tethering). Many actin kinetic models omit explicit energy accounting with force production \cite{Vavylonis2005,Ditlev2009}, limiting reliable coupling to multiscale models of whole-cell remodelling. Prior efforts linking actin kinetics to continuum mechanics often approximate energy flows and omit explicit nucleotide states \cite{Mogilner1996,Gawthrop2025}. Here, we present a modular, thermodynamically consistent actin model combining nucleation, polymerisation, depolymerisation, ATP/ADP states, and force production. Built using a bond graph approach (thermodynamically consistent ODEs) \cite{Gawthrop2025,Gawthrop2014,Rajagopal2022}, the technique preserves energy accounting and provides modular ports for mechanical coupling. The model is currently being used to explore sensitivity and parameter identifiability, with a particular focus on how ATP/ADP state changes influence conservation of thermodynamic consistency, reproduce canonical behaviours (growth regimes, force-velocity relations, nucleotide turnover), and how Gibbs free energies tune relationships. More broadly, this thermodynamically consistent scaffold lays a foundation for predictive multiscale studies of energy consumption during cell migration and protrusion generation.

Speaker: Volkan Ozcoban (University of Melbourne)

11:20 AM The landscape reconsidered: non-equilibrium constraints on cell fate

Cells don’t roll downhill. Waddington’s epigenetic landscape has shaped our thinking about cell fate for decades, inspiring rich mathematical frameworks such as quasi-potential methods, catastrophe theory and energy landscapes. These frameworks share a hidden assumption: that cellular dynamics are gradient systems, derived from a scalar potential.
Whole-cell models (WCMs) allow us to test this assumption directly. We prove that chemical reaction networks with mass-action kinetics are gradient systems if and only if they satisfy detailed balance, the hallmark of thermodynamic equilibrium. But living cells are not at equilibrium. ATP hydrolysis, ion gradients, and irreversible regulatory cascades generically violate detailed balance as a result. This extends to genome-scale metabolic models, showing that flux balance analysis captures non-equilibrium steady states that lie outside the gradient framework. The landscape picture is therefore fundamentally incompatible with the biochemistry that WCMs describe.

Rather than simply rejecting landscape ideas, this perspective clarifies when gradient approximations remain useful. It points instead toward a new class of non-equilibrium descriptions, where cell fate is shaped not by descent along a potential, but by fluxes, cycles, and dynamics far from equilibrium.

Speaker: Lucy Ham (The University of Melbourne)

11:40 AM Membrane Transport and Metabolic Patterns: Mathematical Building Blocks and Data‑Driven Insights

Understanding nutrient transport is essential for mathematically modelling bacterial functions because transport processes govern the rates at which cells acquire substrates that fuel all downstream metabolic activity. Nutrient uptake directly shapes intracellular metabolite levels and thereby constrains metabolic pathway fluxes.

Some data driven mathematical approaches to model membrane nutrient transport and metabolic flow are explored. These model building blocks need to be scoped for different levels of biophysical specificity to enable future hybrid modelling and incorporation into whole cell models.

Techniques to identify inconsistencies between models, observations, and the data itself are discussed, and illustrate how mathematical modelling can guide experimental interpretation.

Speaker: Adelle Coster (University of New South Wales Sydney)

10:40 AM → 12:00 PM Data-driven modeling in biology and medicine

10:40 AM Interconnected Axes of Phenotypic Plasticity Drive Coordinated Cellular Behaviour and Worse Clinical Outcomes in Breast Cancer

Phenotypic plasticity plays a key role in cancer progression and metastasis, enabling cancer cells to adapt and evolve, but precisely how distinct axes governing phenotypic plasticity interact to shape tumour progression and patient outcomes remains unclear. We investigated five major interconnected axes of plasticity in ER-positive (ER+) breast cancer: Metabolic Reprogramming, Epithelial-to-Mesenchymal Plasticity (EMP), Luminal–Basal (Lineage) Switching, Stemness, and Drug-resistance using network dynamics simulations, integrative bulk and single-cell transcriptomic analyses and patient survival analyses. We show that these axes are not independent but drive one another, forming two mutually inhibiting ‘teams’ of nodes enabling specified cellular behaviour. One team (favouring high glycolysis, stem-like, basal-like, mesenchymal/hybrid and tamoxifen-resistant phenotype) was found to be associated with aggressive progression and worse survival. On the other hand, the opposing team (favouring high oxidative phosphorylation, non-stem-like, luminal-like, epithelial and tamoxifen-sensitive phenotype) correlated with better outcomes. Importantly, altering one axis of plasticity often drove coordinated responses along other axes and vice versa. Our findings establish phenotypic plasticity in cancer as a coordinated, multi-axis dynamical process, suggesting novel strategies to disrupt systems-level reprogramming enabling metastasis and therapeutic resistance.

Speaker: Mohit Kumar Jolly (Department of Bioengineering, Indian Institute of Science, Bengaluru, India)

11:20 AM Multi-omics Investigation Reveals Molecular Determinants of Cancer Cell Evolution on Soft Extracellular Matrix

Cancer cell adaptation to their physical tumor microenvironment is a key driver of malignancy. Recent experimental evolution experiments show that the soft extracellular matrix (ECM) can impose a selection pressure on genetically variable tumor populations. Over months of sustained culture, the selection pressure leads to enrichment of specific genetic variants with high fitness, but the mechanisms underlying the high fitness of these soft-selected clones are not fully understood. Here, we used a combination of RNA-seq, ATAC-seq, and RRBS-seq to compare soft-selected populations with non-selected ancestral populations cultured on soft ECM. We demonstrate that ancestral populations grown on soft ECM for short durations are characterized by a low fitness cell state marked by cell cycle arrest whereas sustained culture selects for a robust proliferative phenotype. Mechanistically, selected cells exhibit a silenced ancestral stress response through epigenetic modifications, with reduced chromatin accessibility and de-novo DNA methylation. This repressive landscape supports a high-fitness state defined by elevated MYBL2 and FAK levels. An in-silico mechanism-based model shows that these molecular differences, together with high YAP1 nuclear localization in soft-selected cells, are key features of genetic clones capable of FAK upregulation. These findings uncover a coordinated genetic and epigenetic mechanism driving cancer cell evolution in mechanically soft substrates.

Speaker: Sarthak Sahoo (Department of Bioengineering, Indian Institute of Science, Bengaluru, India)

11:40 AM Model Selection and Treatment Prediction in ODE Models for ER+ Breast Cancer

In this talk, I will introduce four systems of ODEs to identify the most plausible model and the key reactions governing the dynamics of the tumor microenvironment (TME) in estrogen receptor–positive (ER+) breast cancer. All models quantitatively fit the experimental data for radiation therapy (RT) and endocrine therapy fulvestrant (Fulv) in TC11 ER+ cells, as well as RT and immune checkpoint inhibitor (anti-PD-1/anti-PD-L1) treatments in 4T1-HA and MCF-7 breast tumor cells.
The Akaike information criterion analysis suggests that interactions among tumor cells, CD8$^+$ T cells, and estrogen are the primary drivers of the dynamics in the TC11 and MCF-7 cell lines, whereas interactions involving dendritic cells (DCs) and M2 macrophages are required to capture the dynamics in the 4T1-HA cell line. Global sensitivity analysis and identifiability analysis are then conducted to evaluate the uniqueness of parameter values in model calibration and to suggest additional data points that may improve model reliability. Furthermore, numerical simulations and model comparisons indicate the optimal treatment protocols for different cell lines and provide guidance for additional experimental designs to identify the most plausible model.

Speaker: Kang-Ling Liao (Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada)

10:40 AM → 12:00 PM Stochastic models and methods in mathematical biology

10:40 AM Mean field limit of non exchangeable interacting diffusions on co-evolutionary networks

Traditional models of interacting particle systems often assume a fixed network of connections, which simplifies analysis but fails to capture the dynamics of many real-world phenomena. Consequently, co-evolutionary network models, where the network structure and particle states evolve in mutual influence, are increasingly recognised as essential in diverse fields. For instance, in neuroscience, where learning is encoded through the strengthening and weakening of synaptic connections
(synaptic plasticity). Similarly, in social sciences, the co-evolution
of opinions and social ties is a key driver of social dynamics.

This presentation discusses the rigorous derivation of the mean-field
limit for systems of interacting diffusions on co-evolutionary networks. While previous research has primarily addressed continuum limits or systems with linear weight dynamics, our work overcomes these restrictions. The main challenge arises from the coupling between the network weight dynamics and the agent states, which results in non-Markovian dynamics where the system’s future depends on its entire history. Consequently, the mean-field limit is not described by a partial differential equation, but by a non-Markovian stochastic
integrodifferential equation.

Speaker: Julian Cabrera-Nyst (University of Granada)

11:00 AM The effects of individual versus community-influenced isolation on SIS epidemic persistence on finite random graphs

The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy neighbors at rate $\lambda$ and recovers at rate $1$. We study the contact process in the presence of additional intervention measures by introducing a third possible state for vertices, which we call isolated. Vertices may enter the isolated state either because of individual decisions or due to community-influenced decisions, which leads to two distinct models that we call the isolation model and the vigilance model, respectively. In the isolation model, infected vertices self-isolate at rate $\alpha$. In the vigilance model, each healthy vertex causes each of its infected neighbors to isolate at rate $\alpha$. Unlike the usual contact process, these models lack the key features of attractiveness and existence of a dual, which makes analyzing them more challenging. We study the persistence times of the infection on large, finite, degree-heterogeneous random graphs. We show that the infection in the isolation model persists for at least stretched exponential time in the size of the graph for all values of $\alpha$ and $\lambda$. By contrast, in the vigilance model, for every fixed $\alpha$ the persistence time of the infection exhibits a phase transition in $\lambda$: for small $\lambda$ the infection persists for at most a linear time in the size of the graph, while for large $\lambda$ the infection persists exponentially long. This contrast demonstrates that individual versus community-influenced isolation can substantially affect the persistence of an epidemic.

Speaker: Matthew Wascher (Case Western Reserve University)

11:20 AM Self-intersection local times for Volterra Gaussian processes: Applications to polymer models

Self-intersection local times of a random process are random variables describing how much time the process spends in small neighbourhoods of points where the trajectory intersects itself a multiple number of times. Le Gall’s classical result on the asymptotic expansion of the planar Wiener sausage (1990) shows that self-intersection local times are geometric characteristics of random processes describing its topological complexity. It is widely used for the construction of continuous polymer models helping to define polymer measures penalising trajectories with many self-intersections highlighting the excluded volume effect of real polymers.

In this talk, self-intersection local times are discussed for Volterra Gaussian processes. Volterra Gaussain process is defined as a stochastic integral of a deterministic Volterra kernel with respect to a Wiener process. The existence of self-intersection local times for Volterra Gaussian processes is discussed in terms of conditions on Volterra kernels generating processes. Moreover, the aymptotics of conditional moments for self-intersection local times of some classes of Volterra Gaussian processes is described given the end-to-end distance tends to infinity.

Speaker: Olga Izyumtseva (University of Nottingham)

11:40 AM Information and Energy in Stochastic Reaction Networks

Biological information processing is constrained by energetic costs, making it natural to treat information flow and dissipation jointly. We develop a unified framework for continuous-time chemical reaction networks (CRNs) that couples trajectory-level mutual and directed information between disjoint species sets with process-based stochastic thermodynamics for open, multi-reservoir systems. The formulation covers causal conditioning and indistinguishable reactions at the subnetwork level arising from multiple reservoir coupling or projection. We also give a conversion from species–reaction graphs to local-independence graphs on reactions and link local independence to causally conditioned directed information.

Speaker: Heinz Koeppl (TU Darmstadt)

10:40 AM → 12:00 PM Identifying the origin and consequences of non-genetic cell-to-cell variability

10:40 AM Identifiability of phenotypic adaptation from low-cell-count experiments and a stochastic model

In this talk, we develop a stochastic individual-based model of phenotypic adaptation through a continuously structured phenotype space. Probabilistically, our model corresponds to common partial differential equation models of phenotypic heterogeneity, allowing us to formulate a likelihood that captures the intrinsic noise ubiquitous to low-cell-count proliferation assays. We apply our framework to study the identifiability of key model parameters relating to the adaptation velocity and cell-to-cell heterogeneity. Significantly, we find that cell-to-cell heterogeneity is practically non-identifiable from both cell count and proliferation marker data, implying that population-level behaviours may be well characterised by homogeneous ordinary differential equation models.

Speaker: Alexander Browning (University of Melbourne)

11:00 AM From noisy cell size control to population growth: When variability can be beneficial

Single-cell experiments revealed substantial variability in generation times, growth rates, birth and division sizes between genetically identical cells. Understanding how these fluctuations determine the fitness of the population, i.e. its long-term growth rate, is necessary in any quantitative theory of evolution. In this talk, I will present a biologically relevant agent-based model of population dynamics which accounts for single-cell stochasticity. I will derive expressions for the population growth rate and mean birth size in the population in terms of single-cell fluctuations. Allowing division sizes to fluctuate reveals how the mechanism of cell size control (timer, sizer, adder, ...) influences population growth. Surprisingly, we find that fluctuations in single-cell growth rates can be beneficial for population growth when slow-growing cells tend to divide at smaller sizes than fast-growing cells. Our framework is not limited to exponentially growing cells like Escherichia coli, and we derive similar expressions for cells with linear and bilinear growth laws, such as Mycobacterium tuberculosis and fission yeast Schizosaccharomyces pombe, respectively.

Speaker: Arthur Genthon (Max Planck Institute for the Physics of Complex Systems)

11:20 AM A geometric surface PDE model for cell–nucleus translocation through confinement

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in navigating narrow pores or highly constrained spaces. In this talk, I will present a novel geometric surface partial differential equation (GS-PDE) framework in which the cell plasma membrane and the nuclear envelope are modeled as evolving energetic closed surfaces governed by force-balance equations. To validate the model, we replicate a biophysical experiment using a microfluidic device that imposes compressive stresses on cells driven through narrow microchannels under a controlled pressure gradient. I will discuss the results of our parametric sensitivity analysis, which highlights the dominant influence of specific parameters, such as surface tension and confinement geometry, as key determinants of translocation efficiency. Finally, I will show how this framework, while tailored to a specific experimental setup for validation, provides a robust, flexible, and generalizable tool for investigating the broader interplay between cell mechanics and confinement, laying the groundwork for integrating more complex biochemical processes like active migration.

Speaker: Francesca Ballatore (Université Côte d’Azur, Laboratoire J. A. Dieudonné)

11:40 AM Trait-structured chemotaxis: Exploring ligand-receptor dynamics and travelling wave properties in a Keller-Segel model

A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derived and analysed. Unlike traditional Keller-Segel models, this framework introduces an explicit representation of ligand-receptor bindings on the cell membrane, where the percentage of occupied receptors constitutes the trait that influences cellular phenotype. The model posits that the cell's phenotypic state directly modulates its capacity for chemotaxis and proliferation, governed by a trade-off due to a finite energy budget: cells highly proficient in chemotaxis exhibit lower proliferation rates, while more proliferative cells show diminished chemotactic abilities. The model is derived from the principles of a biased random walk, resulting in a system of two non-local partial differential equations, describing the densities of both cells and ligands. Using a Hopf-Cole transformation, we derive an equation that characterises the distribution of cellular traits within travelling wave solutions for the total cell density, allowing us to uncover the monotonicity properties of these waves. Numerical investigations are conducted to examine the model’s behaviour across various biological scenarios, providing insights into the complex interplay between chemotaxis, proliferation, and phenotypic diversity in migrating cell populations.

Speaker: Viktoria Freingruber (TU Delft)

10:40 AM → 12:00 PM SMB MathOnco Subgroup Mini-Symposium: Emerging Themes in Mathematical Oncology

10:40 AM A quantitative and phenotype-resolved model for melanoma cell populations

Melanoma is an aggressive skin cancer driven by a phenotypically heterogeneous cell population. While a full mechanistic understanding is currently lacking, the leading micropthalmia-associated transcription factor (MITF) rheostat theory asserts that the downstream activity of MITF regulates transitions between differentiated, proliferative and invasive states. The population dynamics implied by the MITF rheostat and the conditions for which these dynamics are consistent with published data are currently unknown. To address this, we have developed a phenotype-structured model for melanoma cell populations in vivo. In this talk, I first introduce a subcellular SDE system that illustrates how stochastic fluctuations in MITF RNA and protein concentrations propagate to a downstream phenotype variable. By exploiting a timescale separation, we reduce the coupled SDEs to an effective phenotype flux that informs the full structured population model. Numerical solutions indicate that the model population transitions from a balanced exponential growth phase with mainly differentiated and proliferative cells to either a steady state or limit cycle. Both long-term behaviours exhibit a substantial proportion of invasive cells. Parameter value calibration via Bayesian inference indicates that the "window" of proliferative phenotypes must be small for consistency with data. Together, these results clarify the role of MITF in shaping the phenotype heterogeneity of melanoma cell populations.

Speaker: Keith Chambers (University of Oxford)

11:00 AM Stochastic Optimization of the Evolutionary Race between Pathogens and Clinicians

In this talk, I will discuss data-driven stochastic optimization strategies for the evolutionary race between a pathogenic cell population and a clinician. In this system, the clinician seeks to eliminate the adversarial cell population through optimally changing their environment and fitness, while conversely, the cells make optimal decisions to adapt and survive. I will present a stochastic differential equation (SDE) model of pathogens whose birth and death rates are influenced by drug dynamics. A clinician, in turn, controls the drug dynamics through a machine-learning-based optimization framework based on the probability distributions of pathogen population sizes. In addition to its applications in translational medicine, our work generalizes to businesses and institutions to optimize their adaptability and resilience to environmental stress. This is joint work with Tony Cicerone.

Speaker: Linh Huynh (Dartmouth College)

11:20 AM Oncolytic Virotherapy: Mathematical Analysis and Optimization

This talk focuses on the mathematical modeling of oncolytic virotherapy (OVT), based on joint work with T. Hillen. We begin with a qualitative analysis of an extended model that captures the interactions between tumor cells, viruses, and the immune system. Building on this foundation, we investigate strategies to improve treatment efficacy, showing through analysis and simulations that combination therapies and optimized protocols can significantly outperform monotherapy approaches. A central theme of this work is the emergence and role of travelling wave solutions, which describe the spatial spread of infection and its interaction with both the tumor and the immune response. We present numerical evidence of complex wave dynamics and establish their existence rigorously using analytical techniques.

Speaker: Negar Mohammadnejad (University of Alberta)

11:40 AM Agent-Based Modeling of Tumor-Immune Interactions and Therapeutics in the Tumor Microenvironment

The tumor microenvironment is a complex system involving cross-talk between tumor cells, stromal cells, and therapeutics in the microenvironment. One major avenue of my research has been the interactions between cancer cells, immunotherapy, and immune cells. In order to examine this, we developed an agent-based model that examines the interplay between cancer cells and their surrounding host environment, including blood vessels, hypoxia, therapeutics, and immune cells. This talk will look at the various computational models that examine tumor therapeutics and the tumor microenvironment. This will include monotherapies such as anti-angiogenesis therapies, salinomycin, T-cell therapy, and macrophage polarity as well as combination therapies. This type of modeling allows us to predict under which conditions immunotherapy would be most successful under different assumptions.

Speaker: Kerri-Ann Norton (Bard College)

10:40 AM → 12:00 PM From dose to response: advances in modelling treatment efficacy and toxicity in tumor forecasts

10:40 AM Efficacy-toxicity and toxicity-toxicity trade-offs in head and neck cancer treated with radiotherapy

Radiotherapy (RT) is an effective localized therapy used to treat ~75% of head and neck cancer (HNC) patients. However, delivery to surrounding normal tissues induce toxicities that exacerbate patient symptoms. Motivated by a published dataset of longitudinal patient reported outcomes (PROs) in HNC patients treated with RT, we developed a mathematical model to capture both on-target tumor response and off-target toxicities. The classical linear-quadratic model was employed to describe tumor response to RT. To model off-target toxicities, we introduce a novel concept of radiation exposure analogous to drug exposure. We then employed a Markov chain model with radiation exposure as a time-varying covariate to describe PRO dynamics. While efficacy-toxicity trade-offs were sensitive to RT dose and use concurrent chemotherapy, toxicity-toxicity trade-offs were more sensitive to RT plan (sparing vs. non-sparing). We also derived minimum efficacious dose (MED) and maximum tolerable dose (MTD) for various tumor response and toxicity endpoints. Overall, this model offers adaptable, data-informed treatment decisions by integrating both tumor control and quality of life considerations. Future iterations of the model could aid clinicians in RT dose-finding and selecting a RT plan that will optimize tumor control and patients’ goals of care.

Speaker: Daniel Glazar (Moffitt Cancer Center, US)

11:00 AM Beyond Dose, What Really Drives Radiation-Induced Brain Necrosis?

Brain necrosis after brain and head & neck radiotherapy presents a fundamental inference problem since by the time a lesion is visible on MRI, it has already expanded, remodeled, and erased the evidence of where and why it began. Behind this expansion lies a spatially dynamic process governed by brain architecture and patient-specific biology, which are not captured in clinical dose thresholds. Dosimetric indices showed no consistent voxel-level correlation with necrosis in our cohort, leading us to hypothesize that the dose-outcome relationship is masked by patient heterogeneity. Decomposing this heterogeneity through an expert-augmented Bayesian network revealed that brain anatomy, particularly proximity to ventricles and white matter, governs necrosis risk more strongly than dose alone. Building on this, a 3D cellular automaton incorporating MRI-derived vascular density maps reproduced the anisotropic spatial progression of lesions with AUC 0.87-0.95. Inverting the model's rules allowed backward-in-time simulation to localize lesion initiation sites invisible to standard imaging. A multi-channel Vision Transformer model was developed to integrate 3D dose distributions with crucial nondosimetric factors to predict necrosis risk. Disentangling the biological, anatomical, and dosimetric drivers of brain necrosis aims to redefine biological effective radiation dose to personalize treatment planning.

Speaker: Ibrahim Chamseddine (Harvard Medical School, US)

11:20 AM Precision Medicine in Real-World Patients: Model-Informed Precision Dosing of High dose Busulfan in Hematopoietic Stem Cell Transplantation conditioning regimen

Haematopoietic cell transplantation (HCT) is a potentially curative treatment for leukaemia. Pre-transplant conditioning plays a central role in the successful outcome of allogeneic HCT and requires the administration of myeloablative drugs at a high dose. Busulfan is the backbone of such conditioning regimens in both adults and children. Busulfan is an alkylating agent with a narrow therapeutic window and unpredictable inter-individual and intra-individual variability on pharmacokinetics (PK). HD busulfan is administered via several injections (three to 16) to achieve a cumulative plasma exposure (area under the curve, AUC) associated with severe aplasia without triggering life-threatening toxicities, such as multi-organ failure or veno-occlusive disease. With regard to the PK variability of Busulfan, adaptive dosing should help reduce the risk of toxic death while ensuring adequate exposure to achieve clinical efficacy. This can be achieved using either a mechanistic, bottom-up approach or top-down, phenomenological modelling. By developing dedicated population pharmacokinetics (pop-PK) approaches in our institute, it was possible to set up a sampling plan to collect blood samples for therapeutic drug monitoring based upon a first standard administration. This allows us to identify individual PK parameters, derive exposure and calculate a customised dose of Busulfan for the remaining administrations, thereby maintaining the patient within the desired target. We will present how this strategy can be successfully implemented at the bedside for both adults and children, and demonstrate how it translates into correcting plasma exposure to the target and improved clinical outcome eventually.

Speaker: Joseph Ciccolini (INSERM, France)

11:40 AM Incorporating Toxicity Constraints in Adaptive Cancer Therapy

Adaptive cancer therapy is a new paradigm of treatment for non-curative disease that aims to prolong emergence of resistance, and thus treatment failure. Here we use a mathematical model to explore how incorporating treatment toxicity into the protocol of adaptive therapy can be beneficial by both extending time to treatment failure and improving the quality of life for the patient \cite{gevertz2026delaying}. Our mathematical framework implements treatment-pausing adaptive therapy with a tumour comprised of sensitive and resistant cancer cells. We show that the degree of competition between these populations critically modulates the impact of toxicity feedback, and treatment breaks. We explore circumstances where these breaks provide benefit both at our baseline parameterization and across heterogeneous virtual populations.

Speaker: Kathleen Wilkie (Toronto Metropolitan University)

10:40 AM → 12:00 PM Game theory in ecology and evolution

10:40 AM Evolutionary game theory and the emergence of noisy learning

This talk has two complementary aims. The first part provides a self-contained and accessible introduction to (evolutionary) game theory, focusing on some key tools used to describe the dynamics of strategies in adaptive populations. In the second part, I explore a counterintuitive question: why might evolutionary processes favour seemingly suboptimal learning rules? To this end, I present a model showing how occasional selection of low-payoff strategies can, under certain conditions, enhance long-term success.

Speaker: Christian Hilbe (Interdisciplinary Transformation University)

11:20 AM The role of structure and mobility in the evolution of cooperation

Human and non-human animals form structured social systems in which individuals interact preferentially within groups shaped by environmental structure, movement, and social preferences. To study how structure and mobility affect collective behaviour and the evolution of cooperation, we consider a model in which individuals move across nodes of a spatial network representing interaction sites (e.g., resource patches or social hubs). Those at the same node engage in a multiplayer game capturing conflict between individual and collective interests arising from resource production and shared use, and their behaviour evolves through selection. This work identifies community structure and conditional movement as two distinct yet complementary mechanisms, in which network structure and evolution interplay differently to sustain cooperation. First, under limited independent movement, populations form separate communities, leading to a nested evolutionary process. Although defection holds an advantage within communities, cooperation spreads effectively between them. Consequently, small communities sustain cooperation, independent of network topology. Second, under conditional (Markov) movement, individuals move based on satisfaction with current group composition. Cooperation co-evolves with high mobility, as cooperators find each other while avoiding defectors. In contrast to the first mechanism, less network degree heterogeneity and low movement costs are key drivers.
References:
Pires DL, Broom M (2024) The rules of multiplayer cooperation in networks of communities. PLoS Comput Biol 20(8): e1012388. https://doi.org/10.1371/journal.pcbi.1012388
Pires DL, Erovenko IV, Broom M (2023) Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations. PLoS ONE 18(8): e0289366. https://doi.org/10.1371/journal.pone.0289366

Speaker: Diogo Pires (University of Copenhagen)

11:40 AM Direct reciprocity under constraints: information and evolutionary dynamics

Direct reciprocity is a central mechanism for the evolution of cooperation, yet most theoretical results rely on simplifying assumptions about information, interaction structure, and evolutionary dynamics. In this talk, I revisit direct reciprocity by analysing how relaxing these assumptions affects evolutionary outcomes. Building on recent work, I study settings in which agents have access to limited payoff information and where alternative evolutionary processes govern strategy updates. Under such constraints, the set of viable strategies changes, and classical reciprocity mechanisms can lose their effectiveness. In particular, I show that evolutionary outcomes depend sensitively on how agents update their behaviour, highlighting the role of modelling assumptions in shaping cooperation.

Speaker: Nikoleta Glynatsi (RIKEN Center for Computational Science)

10:40 AM → 12:00 PM Heterogeneity in epidemic modelling

10:40 AM Estimating epidemic risk in spatially and behaviorally structured populations

Assessing epidemic risk, both the probability that pathogen introductions lead to major outbreaks and the trajectory of ongoing circulation, often relies on population-level indicators derived from compartmental models. These frameworks typically assume homogeneous mixing within epidemiological compartments, yet real populations are structured by space, behavior, and heterogeneous exposure. Such heterogeneities complicate both the description of epidemic dynamics and the implementation of public health interventions. How should these different sources of heterogeneity be handled for mathematical models to inform public health policymaking? In this talk I discuss when heterogeneity must be explicitly represented, when it can be simplified, and when it may mislead intervention design. Different forms of heterogeneity play different roles. Variation in individual exposure risk can shape transmission patterns but does not necessarily justify targeted interventions: broad non-selective distribution of preventive measures may outperform strategies aimed at high-risk groups, as shown for HIV prevention. Even when heterogeneity is present, it may sometimes be handled through aggregation, for instance by combining spatial data with surveillance information to improve epidemic monitoring for respiratory pathogens. Together these examples highlight which forms of heterogeneity matter for estimating epidemic risk and how they can be incorporated into models used for policy.

Speaker: Eugenio Valdano (INSERM)

11:20 AM Sideward contact tracing in an epidemic model with mixing groups

We consider a stochastic epidemic model with sideward contact tracing. Infection is assumed to occur through mixing events, that is, gatherings of two or more individuals \cite{ball2022epidemic}. When an infective is diagnosed, each person infected at the same event is traced with a given probability. Instead of tracing who infected a diagnosed person or whom they later infected, sideward tracing identifies people who were infected at the same event. This makes it especially relevant in settings such as large gatherings and potential superspreading events.
Assuming a small number of initial infectives in a large population, the early phase of the epidemic can be approximated by a branching process with sibling dependencies. To address these dependencies, we group together individuals infected at the same event and treat them as macro-individuals, leading to a corresponding macro-branching process. This allows us to derive an effective reproduction number that acts as an epidemic threshold, with critical value 1.
The results show that the sideward tracing becomes more effective when more infections occur within the same event. At the same time, if gatherings are very large, sideward tracing alone may not be sufficient to bring the effective reproduction number below 1.

Speaker: Dongni Zhang (Linköping University)

11:40 AM How Within-Host Heterogeneity Shapes Population-Level Transmission: Insights From a Multiscale Model

Host heterogeneity is a key driver of epidemic dynamics, yet most epidemic models assume homogeneous hosts and represent transmission and recovery using constant rates. In many infections, however, variation in within-host pathogen dynamics generates substantial differences in infectiousness, disease progression, and infection outcomes across individuals. Understanding when such heterogeneity must be represented explicitly remains an important challenge in epidemic modeling.
We investigate this question using West Nile virus (WNV), a mosquito-borne pathogen maintained in transmission cycles between mosquitoes and a diverse community of avian hosts that exhibit strong heterogeneity in viral load dynamics and infectiousness. We develop a stochastic individual-based multiscale model that explicitly represents within-host viral dynamics for multiple bird species and mechanistically links viral load to mosquito infection probability. This framework captures biologically grounded heterogeneity in infectiousness, latent and infectious periods, and disease-induced mortality.
By comparing the resulting epidemic dynamics with those predicted by an equivalent single-scale model parameterized using mean epidemiological traits, we assess when average transmission parameters suffice and when explicitly representing within-host heterogeneity is necessary to capture epidemic behavior.

Speaker: Fernando Saldaña (INRAE Nantes)

10:40 AM → 12:00 PM Social dynamics and behavioural interactions in infectious disease modeling

10:40 AM Non-monotonic attack rates arising from risk-aware and imitation-driven behaviours during epidemics

Human behaviour can profoundly alter disease dynamics and the impact of public health interventions. Recognising this socio-epidemiological interplay, recent modelling efforts have increasingly incorporated behavioural responses triggered by perceived risk, disease outcomes, policy recommendations, or conformity pressure. We present a mathematical model that integrates two types of behavioural responses---reversible and irreversible--- to investigate the effect of risk-based and imitation-driven mechanisms on the proportion of population infected (i.e., the attack rate). Reversible behaviours---such as adopting non-pharmaceutical measures---are represented using threshold-like functional responses that capture sharp increases in protective behaviour once disease prevalence exceeds a critical level. Irreversible behaviours---such as vaccination---are modelled through a dynamic imitation process influenced by population-level adoption. Extending previous approaches, we demonstrate that behavioural feedbacks can generate non-monotonic relationships between the attack rate and disease transmissibility for a broad range of parameters representing behavioural effectiveness or adoption strength. We observed that, for sufficiently high imitation rates, distinct intrinsic transmission rates can yield the same attack rate, even though the corresponding epidemic durations and peak prevalence levels may differ substantially.

Speaker: Prof. Gergely Röst (Department of Applied and Numerical Mathematics, University of Szeged, Hungary)

11:00 AM COVID-19 contact tracing provides insight into the fine-scale social interactions structure of England

Understanding social interactions and the structure that arises from them is central to developing realistic epidemic models of many human pathogens. Surveys are often limited in size and limited in the information they can collect. Contact tracing, where contacts of cases are themselves traced and information collected, represents an idea way to collect social mixing information, but is generally restricted to small outbreaks with limited generalisability. The ubiquity of infection and the unprecedented scale and detail of information collected through contact tracing during the COVID-19 pandemic provides a unique opportunity to quantitatively describe in-person social interactions. Here, we investigate patterns of social interactions over space and demography as recorded in the extensive contract tracing data, which includes almost half of the residents of England. We find evidence that interactions were associated with the age, ethnicity and geographical proximity of individuals, but that the importance of these attributes and the pattern of mixing changed during the pandemic. These dynamics were conserved for many parts of the pandemic, however, we observed significant departures during specific time points, indicating a compensatory effect following a release from lockdown. We also explore the utility of mixing patterns information collected a priori in predicting and explaining social interaction dynamics.

Speaker: Prof. Jonathan M Read (Lancaster Medical School, Lancaster University, Lancaster, LA1 4YG, United Kingdom)

11:20 AM The influence of human interactions on waterborne diseases: a reaction-diffusion model

Waterborne diseases continue to pose a major global public health concern, particularly in areas lacking adequate water infrastructure. During outbreaks, changes in human behavior often play a crucial—sometimes dominant—role in shaping disease transmission. We introduce a reaction–diffusion model that accounts for varying patterns of human mobility and behavioral responses within a spatially heterogeneous environment to better understand the disease dynamics and control strategies. The model incorporates both direct and indirect transmission pathways, and assumes a cubic growth for bacterial intrinsic dynamics to highlight more interesting and complicated dynamics. The existence and uniqueness of biologically meaningful equilibria is investigated, along with their stability analysis. The effects of diffusion on the stability of the equilibria are also considered. Numerical simulations are used to explore how environmental heterogeneity, mobility, and behavioral adaptation influence the final epidemic size and, consequently, the spread of the disease.

Speaker: Dr Maria Francesca Carfora (Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, 80131 Napoli, Italy)

11:40 AM A network model from sociodemographic heterogeneity to individual infection risk

Social interactions and disease transmission are tightly intertwined, with behavioural responses and risk perception evolving during an epidemic. Capturing these feedbacks remains a major challenge in epidemic modeling. In social networks, the “ego” denotes the focal individual, while “alters” are individuals directly connected to the ego. We propose a type-configuration algorithm based on node attributes, including demographic and contact information, to assess individual infection risk in a network. Individual infection risk is defined as a function of epidemiological parameters – relative susceptibility, infectiousness, contact frequency, and baseline disease transmission rate, with values depending on social factors such as education level, residence area, gender, and age. Model inputs are derived from sociodemographic data from a representative Hungarian population sample and contact surveys. Our framework captures the heterogeneous impact of sociodemographic variables on individual risk during epidemics. This data-driven approach reveals how social characteristics and contact patterns shape the local vulnerability landscape, providing insights on both individual- and population-level risk. Ultimately, individuals can use this framework as a personalized risk predictor by providing sociodemographic and contact information, allowing the algorithm to assign a type-configuration and compute an interpretable estimate of infection risk under a given epidemiological scenario.

Speaker: Dr Congjie Shi (Laboratory for Industrial and Applied Mathematics, York University, Toronto, ON, Canada; Bolyai Institute, University of Szeged, 6720 Szeged, Hungary)

10:40 AM → 12:00 PM Data Science × Mathematical Modeling for Transforming Quantitative Life and Medical Sciences

10:40 AM How choices in quantifying data affect parameter identifiability in agent-based models of pattern formation

Pattern formation arising from the collective behaviour of autonomous agents occurs across many areas of biology, including skin patterns. Agent-based models provide a natural framework for describing such systems. However, the high-dimensional nature of the data and model stochasticity pose significant challenges for parameter inference and identifiability analysis. To help address this challenge, researchers often rely on lower-dimensional summaries of model output, such as cell number or stripe width. However, it remains unclear which quantitative summaries are most informative for inference. In this work, we compare topological signatures derived from Vietoris–Rips and sweeping-plane filtrations with classical statistical summaries, such as pair correlation functions. We evaluate the effectiveness of these different quantitative approaches within a Bayesian pipeline for parameter inference, and show how the choice of method for summarizing pattern data impacts parameter identifiability.

Speaker: Yue Liu (Purdue University)

11:00 AM Cancer systems immunology reveals the tumor-immune dynamics that determine responses to novel combination therapies in metastatic tumor microenvironments

Tumors grow and metastasize through intricate interactions among the diverse signals and cell types composing the tumor microenvironment (TME). Cancer systems immunology combines mathematical modeling with analysis of high-dimensional multi-modal data and machine learning to gain insight into the complex ecosystems created by the immune system in and around a tumor. Immunotherapies such as checkpoint inhibition can provide durable responses in a subset of metastatic breast cancer patients, yet the mechanisms governing intrinsic resistance and response remain poorly understood. Here, via cancer systems immunology methods we integrate single-cell genomics and spatial transcriptomics with mathematical modeling to dissect metastatic breast cancer TMEs. We developed methods to identify the cell circuits mediating responses with treatment in specific TMEs. In the mouse lung TME, using cell circuits we discovered that treatment with entinostat (a histone deacetylase inhibitor) modulates chemokine and adhesive signaling pathways. We revealed that the benefits of this treatment with checkpoint inhibitors are mediated by activating B cells and decreasing immunosuppressive myeloid cell---T cell interactions. We validated these predictions using mathematical modeling and analysis of clinical samples from a phase 1b trial. We further developed mathematical models of the tumor-immune dynamics of tumors at different sites of metastasis and fit them to RECIST clinical response data via Bayesian parameter inference. In doing so, we derived mechanistic explanations for differential patient outcomes and generated testable predictions for therapeutic interventions. Together, this work offers a generalizable framework for decomposing complex TMEs, inferring multiscale interaction networks, and modeling their dynamics to guide therapeutic strategy.

Speaker: Adam Maclean (University of Southern California)

11:20 AM Theory and Algorithms for Constructing AI-Based Dynamic Virtual Cells

Artificial Intelligence Virtual Cell (AIVC) is increasingly emerging as a frontier in the interdisciplinary integration of biology and artificial intelligence. Its core vision is to construct digital twins capable of simulating and predicting the dynamic evolution of cellular states, thereby providing computational support for experimental design and mechanistic analysis. We have explored a unified modeling framework that integrates generative artificial intelligence methods and dynamical systems theory. By combining mathematical theories such as Optimal Transport, Schrödinger Bridge, and differential geometry with generative AI techniques like Flow Matching and diffusion models, this framework effectively infers continuous dynamic processes of complex state transitions—such as cell proliferation, apoptosis, differentiation, migration, and interactions—from static, heterogeneous single-cell omics temporal snapshots. Compared to black-box methods, this approach not only exhibits strong generative and generalization capabilities but also offers improved mechanistic interpretability. It enables the generation of cell state data across temporal scales and spatial structures, providing a promising direction for constructing dynamic virtual cell models with interpretability, predictive power, and the ability to integrate biological priors.

Speaker: Peijie Zhou (Peking University)

11:40 AM Deep State Space Modeling for Real-World Biomedical Time-Series Analysis

Real-world biomedical time-series data, including clinical records and measurements of complex biological phenomena, contain valuable insights into disease progression and underlying mechanisms. However, such data are often noisy, irregularly sampled, and partially observed, posing significant challenges for analysis. Extracting latent temporal structures from these observations is therefore crucial for advancing our understanding of dynamic biological systems. In this talk, we introduce a framework based on deep state space models (DSSMs) with variational inference to capture complex temporal dependencies in such data. The proposed approach infers latent trajectories corresponding to unobserved disease states or physiological processes, enabling interpretable analysis of system dynamics. As a real-world example, we demonstrate the application of DSSMs to electronic health record data, highlighting their ability to uncover meaningful patient representations. Furthermore, we present recent advances in constrained state space modeling, where prior knowledge—such as stability and physiological consistency—is incorporated into latent dynamics through structured constraints. These techniques improve identifiability, robustness to noise, and consistency with known biological principles. Overall, this framework provides a powerful and principled approach for analyzing real-world biomedical time-series data.

Speaker: Ryosuke Kojima (RIKEN/Kyoto University)

10:40 AM → 12:00 PM Stochastic agent- and particle-based models in biology: methods and analytical insights

10:40 AM Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities

Abstract
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage. We first study the frequency of the disadvantageous type, once the population approaches the carrying capacity. Adapting techniques from [Kat91], we show that this process converges to a Gillespie-Wright-Fisher diffusion process. We then study the dynamics backward in time: we fix a time horizon at which the population is at carrying capacity and we study the ancestral relations of a sample of individuals. We prove that, provided that the advantageous and disadvantageous branching measures are stochastically ordered, this ancestral line process converges to the moment dual of the limiting diffusion. This talk is based on [DPK25].

References
[DPK25] M. Dai Pra and J. Kern. Multi-type logistic branching processes with selection: frequency process and genealogy for large carrying capacities. 2025.
[Kat91] G. Katzenberger. Solutions of a stochastic differential equation forced onto a manifold by a large drift. The Annals of Probability, 19(4):1587 – 1628, 1991.

Speaker: Marta Dai Pra (Humboldt University Berlin)

11:00 AM Multitype Lambda-coalescents: Characterisation and duality

Lambda-coalescents, or multiple merger coalescents, have been extensively studied since their introduction in 1999, and were interpreted as genealogies of populations with skewed offspring distribution. More recently, multitype versions of such coalescents have garnered attention. However, it turned out that generalising the characterisation of multiple merger coalescents in terms of a finite measure on [0,1] isn't quite as straightforward a task as one might guess. In particular, the notion of asynchronity of mergers, or transitions, needs to be carefully treated when characterising multitype multiple merger coalescents.

In this talk, we discuss how multitype multiple merger coalescents are related to continuous state branching processes via duality, and we provide a characterisation as a class of partially exchangeable Markov coalescent processes.

This is joint work with Adrián González Casanova (Arizona State University), Imanol Nunez Morales (CIMAT, Guanajuato) and José Luis Pérez (CIMAT, Guanajuato).

Speaker: Noemi Kurt (Goethe University Frankfurt)

11:20 AM Multi-Type Birth-Death Processes with Mean-Field Interactions for B-cell Phylodynamics

Abstract
Antibody binding affinity maturation is a crucial process of the adaptive immune system. Motivated to model this process, we formulate a system of multi-type birth-death processes that can interact through their empirical distribution. We show that the empirical distribution process of the system of birth-death processes converges to a deterministic probability measure-valued flow as the system size tends to infinity. In this limit, a focal process evolves as a multi-type birth-death process with rates governed by the probability measure-valued flow, which is, in turn, the flow of the one-dimensional marginal distribution of the focal process. Individual processes become independent in the limit, which suggests inference to be feasible for this model.

Names and affiliations of coauthors
William S. DeWitt (University of Washington)
Steven N. Evans (University of California, Berkeley)
Ella Hiesmayr (CNRS and ENS Lyon)

Bibliographic reference
DeWitt, William S., et al. “Mean-Field Interacting Multi-Type Birth–Death Processes with a View to Applications in Phylodynamics.” Theoretical Population Biology, vol. 159, Oct. 2024, pp. 1–12., https://doi.org/10.1016/j.tpb.2024.07.002.

Speaker: Sebastian Hummel (BOKU University Vienna)

11:40 AM Recurrent disease outbreaks and their frequency

We derive the frequency and distribution of outbreaks in an SIR model with noise. This involves techniques from matched asymptotics combined with stochastic ODEs and random maps.

Speaker: Theodore Kolokolnikov (Dalhousie University)

10:40 AM → 12:00 PM Differential modelling and numerics for human diseases

10:40 AM Global sensitivity-driven simplification and calibration of Cancer-on-Chip nonlocal integro-differential model

Cancer-on-Chip experiments reproduce complex biological environments to study the immune response to cancer and test the effect of therapies. Following a digital-twin approach, mathematical models reproducing Cancer-on-Chips dynamics have the potential to be able to produce in-silico different scenarios and to be largely economically convenient. However, a critical aspect in the employment of mathematical model outcomes in biomedical research is the necessity of a careful calibration of the model parameters, to ensure reliable outcomes.
In this context, we focus on a nonlocal integro-differential model for Cancer-on-Chip experiments where chemotherapy-treated tumour cells release chemical signals activating the immune response. Model reliability is assessed through a Global Sensitivity Snalysis to capture parameter influence and nonlinear effects.
The impact of 13 parameters is evaluated over a region of the parameter space using 11 outputs describing immune cell spatial distribution and temporal dynamics. To address computational costs, a two-step approach is adopted: the Morris method first ranks parameter importance, identifying six key parameters affecting all outputs; the extended Fourier Amplitude Sensitivity Test (eFAST) then quantifies their contributions.
Results highlight the feasibility of the parameter space and identify parameters related to the chemical field and cell–substrate adhesion as dominant. These findings suggest model simplifications—such as neglecting cell–cell alignment in the absence of experimental evidence—and emphasize the need for additional data to reduce uncertainty in the most influential parameters and improve predictive accuracy.

Speaker: Annachiara Colombi (Politecnico di Torino)

11:00 AM An adaptive high-order polytopal method for modeling neuronal electrophysiology

Traveling wave phenomena are central in many biological processes, including electrical activity in neural and cardiac tissues. Their simulation is challenging due to sharp, fast-moving wavefronts that demand high spatial and temporal resolution, resulting in high computational costs.
Brain electrophysiology at the tissue level is a key example: the transmembrane potential exhibits steep wavefronts propagating along preferential axonal directions. Modeling these dynamics involves multiple scales and complex, anisotropic domains. We employ a high-order discontinuous Galerkin method on polygonal meshes (PolyDG) that remains computationally demanding. To address this, we propose a p-adaptive algorithm that exploits the localized nature of traveling waves: strong variations are confined to small regions, while the rest of the domain is nearly stationary. We design a posteriori error indicators to detect wavefronts and locally adjust the polynomial degree. Numerical results show that the method accurately captures wave dynamics and effectively simulates epileptic events in heterogeneous brain tissues, reducing degrees of freedom and computational cost while preserving high-order accuracy.

Speaker: Caterina B. Leimer Saglio (Politecnico di Milano)

11:20 AM A Thermodynamically Consistent Multiphysics Model of Irreversible Electroporation for Cutaneous Melanoma: Coupling GENERIC Thermo-Poromechanics with Tissue Electroporation

Irreversible electroporation (IRE) is a promising non-thermal ablation technique for cutaneous melanoma, where high-voltage, short-duration electric pulses induce permanent membrane permeabilisation and cell death. We present a coupled multiphysics framework integrating a thermo-poromechanical model of skin with a nonlinear electroporation model. The tissue response is described within the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework, providing a thermodynamically consistent formulation. The skin is modelled as a uid-saturated porous medium governed by energy and entropy functionals through Hamiltonian and Onsager operators satisfying a noninteraction condition ensuring energy conservation and entropy production. The electroporation component uses a model where tissue conductivity increases nonlinearly with the local electric eld via a sigmoid law. The
coupling arises naturally: Joule heating enters the poromechanical thermal balance, while the heterogeneous temperature eld inuences conductivity and the electric eld distribution, yielding spatially varying temperature proles critical for delineating the ablation zone. In this preliminary study, we consider an idealised geometry with a skin slab and planar needle electrodes, solved via the nite element method. Results show that neglecting the poromechanical response leads to errors in the predicted ablation volume. Future work will incorporate realistic morphologies from photonics-based imaging.

Speaker: Davide Baroli

11:40 AM A Data-Informed Agent-Based Model of Tuberculosis Granuloma-Like Structures

Tuberculosis (TB) remains a major global health challenge, with nearly 10 million new cases annually and increasing drug resistance.

As part of the ERA4TB initiative, which aims to advance new treatment regimens, multiple research institutes collaborated to develop and characterise in vitro granuloma-like structures (GLSs), aggregates of human PBMCs that exhibit key features of tuberculosis granulomas \cite{Puissegur2004}.

While physiologically more relevant than standard cell line models, GLS experiments remain costly, and studying granuloma biology in vivo is challenging. Host-directed therapies, which target the host immune response rather than the pathogen directly, remain relatively underexplored and represent an area where GLS could provide valuable information.

Computational modelling can complement GLS experiments by reducing cost and providing mechanistic insight\cite{Michael2024}. We developed an agent-based model (ABM) of GLS dynamics using PhysiCell, a scalable and extensible platform for simulating multicellular systems \cite{Ghaffarizadeh2018}.

The model was calibrated using a multi-laboratory dataset comprising CFU time series obtained from drug-free and drug-treated conditions, together with quantitative measures of GLS size and number, the latter extracted from microscopy images, both via expert annotation and automated machine learning analysis.

Given the inherent biological variability, this parameter estimation was performed using Approximate Bayesian Computation (ABC), yielding a posterior distribution for a subset of parameters~\cite{Tavar1997}.

Speaker: Davide Moretti (CNR - IAC)

12:30 PM → 2:30 PM BMB Office Hours of Bulletin Editor-in-Chief and Editorial Board Members

Speaker: Matthew Simpson (Queensland University of Technology)

3:10 PM → 4:30 PM Advances in multiple timescale dynamics in neurons and related excitable systems

3:10 PM Multimodal Synchronization of Pancreatic Islets

The activity of insulin-secreting beta-cells within pancreatic islets of Langerhans is oscillatory, with a period of approximately 5 min. There are hundreds of islets in the mouse pancreas and hundreds of thousands in the human pancreas, and they are physically isolated from one another. Yet somehow that exhibit a great deal of synchrony. In addition, there is often an ultradian rhythm in blood insulin levels, with a period close to one hour. How does the islet synchrony occur? What is the mechanism for the ultradian rhythm? We will present a unified explanation for both the synchronozation of the fast oscillations and the generation of the slow ultradian rhythm. This explanation is explored using computer simulations and a reduced mathematical model, and tested using a hybrid approach utilizing islets studied in a microfluidic device.

Speakers: James Thornham (Florida State University), Michael Roper (Florida State University), Richard Bertram (Florida State University)

3:30 PM Cardiomyocyte Models: Bifurcations and Fast-Slow Decomposition

Early afterdepolarizations (EADs) are abnormal behaviors that can lead to heart failure and even cardiac death. In this presentation, we review
recent results and we mathematically investigate the occurrence and development of these phenomena in two realistic ventricular myocyte models: the rabbit model of Sato (2009) and the human model of O’Hara (2011). These models are of high dimension, 27 and 41 respectively, so a mix of techniques must be used in their study. We connect the results with a reduced low-dimensional model, the Luo-Rudy cardiomyocyte model (1991). The combined use of analytical and numerical techniques allows us to propose a global conjecture of a mathematical mechanism of EAD creation in low- and high-dimensional models. By examining the bifurcation structure of the model, we elucidate the dynamical elements associated with these patterns and their transitions. Using a fast-slow analysis, we explore the emergence and evolution of EAD in the low-dimensional model and develop new methodologies for fast-slow decomposition for the realistic high-dimensional O’Hara model. This decomposition has allowed us to propose some new theoretical techniques for the control of prearrhythmia situations.

Speakers: Hiroyuki Kitajima (Kagawa University), M. Angeles Martinez (Universidad de Zaragoza), Roberto Barrio (University of Zaragoza), Sergio Serrano (University of Zaragoza), Toru Yazawa (Kagawa University)

3:50 PM Mechanisms for strong symmetry-breaking in coupled fast-slow oscillators

Two identical oscillators with mutual inhibition provide a conceptual framework for modeling a latching mechanism in cell cycle regulation. In this talk, we study two such coupled oscillator models and investigate mechanisms of symmetry-breaking. In both models, inhibitory coupling induces stable alternating large-amplitude oscillations corresponding to the normal cell cycle. However, the systems also exhibit strong symmetry-breaking states in which the two oscillators display qualitatively different rhythms. In one case, this corresponds to endocycles, in which only one of the two oscillators undergoes large-amplitude oscillations. Using bifurcation analysis and geometric singular perturbation theory, we identify and characterize two distinct strong symmetry-breaking mechanisms: one arising through a homoclinic bifurcation and the other through a novel type of symmetric folded singularity.

Speaker: Yangyang Wang (Brandeis University)

4:10 PM How slow rhythmic inputs induce spike-adding in neuronal model

Bursting is a common firing pattern in neurons, characterized by alternating active (spiking) and silent phases. While the transition from tonic spiking to bursting has been widely studied, the mechanisms underlying spike-adding within a burst remain less understood. We investigate spike-adding in a three-dimensional neuronal model with three distinct timescales. Using the FitzHugh–Nagumo system with slow periodic forcing of the voltage equation as a prototypical example, we show that decreasing the forcing frequency and increasing its amplitude induce transitions from single-spike responses to complex bursting with spike-adding. We relate these transitions to folded node and folded saddle singularities in the underlying fast–slow structure. Finally, we demonstrate that similar spike-adding mechanisms arise in the more physiologically realistic Morris–Lecar model.

​This work is joint with Pake Melland (Oregon Institute of Technology) and Rodica Curtu (Michigan Technological University) \cite{Melland_ Curtu _ Aminzare _2025}.

Speakers: Pake Melland (Oregon Institute of Technology), Rodica Curtu (Michigan Technological University), Zahra Aminzare (University of Iowa)

3:10 PM → 4:30 PM Applications of reaction networks

3:10 PM Mathematical modeling to infer signaling bias: kinetics and spatial compartmentalization

An active area of research in pharmacology and drug discovery applies to biased signaling: the ability of a ligand to selectively activate some signal transduction pathways as compared to the native ligand acting at the same receptor. At the practical level, experimentalists seek to quantify ligand bias in order to classify ligands according to their selectivity. One popular method uses the so-called operational model to fit dose-response curves.

In this presentation, I will review the main limitations of this methodology, recently pointed out by our group and others. Our objective is then to design a method that fully take into account the kinetic nature of signaling pathways and as well as their possible cross-talks. Kinetic experiments, that measure the activity of several downstream effectors of a receptor after ligand binding with respect to time, are now widely available. I will explain how one can exploit such data and dynamical reaction network modeling with suitable statistical framework to provide a complete “bias map” of a ligand, compared to the native ligand, that successfully answer to our objective.

Going further, we can extend this methodology to take into account recently discovered compartmentalised signaling, which can eventually lead to spatial or location signaling bias. We have thus build a dynamical model that incorporate endocytosis/recycling event and spatial specificity, helping to quantify kinetic experiments under various receptor trafficking perturbations. This new methodology is formulated as either partial differential equations (PDE) or piecewise deterministic Markov processes (PDMP), which calls for interesting new developments in applied mathematics.

Speaker: Romain Yvinec (UMR PRC, INRAe Val-de-Loire, 37380, Nouzilly, France / Musca, Inria, Université Paris-Saclay, Inria Saclay-Ile-de-France, Palaiseau, 91120, France)

3:50 PM A reaction network approach to modeling carbon dioxide removal systems

As the global community seeks viable solutions to achieve climate stabilization, understanding the dynamics of the Earth’s carbon cycle is essential. This talk introduces the Reaction Network Carbon Dioxide Removal (RNCDR) framework, an application of Chemical Reaction Network Theory (CRNT) to global biogeochemical modeling. We construct an integrated system-level model comprised of a pre-industrial carbon subnetwork, anthropogenic emissions, and specific modules for carbon capture and storage. We specifically analyze two critical NETs: Bioenergy with Carbon Capture and Storage (BECCS) and Direct Air Capture (DAC). Our results suggest that despite their differing physical implementations, these two distinct methods share remarkably similar network properties. We demonstrate how both systems can exhibit steady-state multiplicity and absolute concentration robustness in key species. These findings provide a theoretical foundation for understanding the dynamics of large-scale carbon removal interventions.

Speaker: Noel Fortun (Department of Mathematics and Statistics, De La Salle University, Taft Avenue, Manila 0922, Philippines)

4:10 PM Mapping the co-expression landscape: network sparsification and null models

Network reconstruction from high-dimensional omics data remains an open challenge. While one can calculate gene-gene co-expression statistics for every pair of genes, these complete weighted graphs must then be sparsified to obtain an interpretable network. Common sparsification approaches (such as thresholding) can lead to an excessively fragmented network, masking the relationship between genes and neglecting the "strength of weak ties," wherein a critical but weak relationship may serve as a vital link between two subnetworks. Here we present Network Skeleton Extraction (NSE), a co-expression network generation method using spectral sparsification to sparsify co-expression statistics into minimal co-expression graphs. Spectral sparsification has the advantage of maintaining connections among genes in a manner that preserves the coarse-grained structure and dynamical properties of the input graph. This yields networks that are highly sparse while still being predictive of gene expression. We also present a probabilistic model to generate a null distribution of networks with similar spectral properties, against which inferred networks can be compared. We illustrate the method by applying it to Xenopus transcriptome data across six developmental stages (from pluripotency to lineage commitment), identifying networks whose structure changes over the course of development to give rise to cell-type specific networks.

Speaker: Rosemary Braun (Northwestern University, Evanston, IL 60208, USA / Santa Fe Institute, Santa Fe, NM 87501, USA)

3:10 PM → 4:30 PM Immunobiology and Infection Subgroup Minisymposium 2026

3:10 PM Regularized estimation in high-dimensional mechanistic models: Application to vaccine development

Objectives: Mechanistic models describe biological processes over time, but they often rely on few observed compartments and sparse longitudinal data. They may therefore be too simple to capture complex processes, such as post-vaccination immune dynamics, or may suffer from identifiability issues, especially in nonlinear mixed-effects models based on differential equations. At the same time, longitudinal high-throughput data, including transcriptomics and proteomics, are increasingly available and may help inform unobserved biological processes. Integrating such high-dimensional data into mechanistic models with latent compartments remains difficult.

Methods: We hypothesize that observed omics biomarkers can inform the dynamics of unobserved immune compartments. We propose a regularized estimation method for mechanistic models with latent compartments measured indirectly through high-dimensional longitudinal biomarkers. Relevant biomarkers are selected by regularizing the parameters linking them to latent compartments while estimating population mechanistic parameters. The algorithm alternates between a regularization step, based on penalized log-likelihood derivatives, and a mechanistic inference step using SAEM in Monolix.

Results: We evaluated the method in simulations and applied it to immune responses after Pfizer/BioNTech COVID-19 vaccination in 15 infection-naïve individuals (Rinchai et al.). Daily blood samples were collected for 9 days after each dose, with 8,172 gene expression measurements grouped into 34 pathways, and serology at baseline, day 7, and day 14. Inflammation, neutrophils, interferon, and type I interferon were most strongly associated with short-term immune response dynamics.

Conclusion: Transcriptomic data improved identifiability of latent compartments. Limitations include the assumed linear biomarker-compartment relationship and high computational cost. The method is implemented in the REMixed R package on CRAN.

References:
@article{tibshirani1996regression,
title={Regression shrinkage and selection via the lasso},
author={Tibshirani, Robert},
journal={Journal of the Royal Statistical Society Series B: Statistical Methodology},
volume={58},
number={1},
pages={267--288},
year={1996},
publisher={Oxford University Press}
}

@article{kuhn2005maximum,
title={Maximum likelihood estimation in nonlinear mixed effects models},
author={Kuhn, Estelle and Lavielle, Marc},
journal={Computational statistics \& data analysis},
volume={49},
number={4},
pages={1020--1038},
year={2005},
publisher={Elsevier}
}
@article{rinchai2022high,
title={High--temporal resolution profiling reveals distinct immune trajectories following the first and second doses of COVID-19 mRNA vaccines},
author={Rinchai, Darawan and Deola, Sara and Zoppoli, Gabriele and Kabeer, Basirudeen Syed Ahamed and Taleb, Sara and Pavlovski, Igor and Maacha, Selma and Gentilcore, Giusy and Toufiq, Mohammed and Mathew, Lisa and others},
journal={Science advances},
volume={8},
number={45},
pages={eabp9961},
year={2022},
publisher={American Association for the Advancement of Science}
}

Speaker: Lisa Crépin (Université de Bordeaux, Bordeaux Population Health Inserm; Inria Bordeaux SISTM, Vaccine Research Institute)

3:30 PM Modeling how memory CD8 T cells may effect post-treatment control of HIV infection

Antiretroviral therapy (ART) for HIV-1 infection is not curative. Treatment interruption typically results in viral rebound and progressive disease, necessitating lifelong ART. However, a small fraction of people living with HIV achieve long-term post-treatment control (PTC) of the virus, offering hope that strategies may be devised that obviate the need for lifelong treatment. While mechanisms underlying PTC remain to be understood, recent studies have identified early treatment initiation as a key factor and suggested a role for CD8 T cells. Here, we developed a within-host mathematical model to elucidate the associated mechanisms. We hypothesized, based on immunological studies, that upon infection, virus-specific CD8 T cells accumulate ‘antigenic experience’ through continual exposure to the antigen, which compromises their survival. Early ART initiation limits this experience, preserving memory CD8 T cells and enabling better response to rebounding virus post-ART. We fit the model to longitudinal data from a recent macaque study using a nonlinear mixed effects approach. The model exhibited bistability. One stable steady state had low viral load and high memory cell levels, and the other vice versa, recapitulating PTC and progressive disease, respectively. Early treatment initiation made the control state more accessible. The model predicted treatment initiation times and the associated memory CD8 T cell pool sizes for maximizing PTC, informing interventions.

Speaker: Narendra Dixit (Indian Institute of Science)

3:50 PM Quantitative modeling of proliferation and differentiation in cell populations

Cell populations consist of heterogeneous cells and are maintained through cell production via complex differentiation processes. To quantitatively understand these intricate dynamics, we employed mathematical modeling across two distinct biological domains: the hematopoietic system and oncogenic proliferation. Regarding the differentiation dynamics of hematopoietic stem cells (HSCs), we performed a mathematical analysis of experimental tracking data from blood cell production following transplantation. This allowed us to quantify which production pathways play a dominant role in long-term hematopoietic maintenance, thereby identifying the importance of pathways within a hierarchical differentiation system. In parallel, we modeled the cancer proliferation process driven by extrachromosomal DNA (ecDNA) harboring driver mutations. Our model elucidates how the unequal segregation mechanism of ecDNA during cell division generates profound genetic heterogeneity within the population, and how this heterogeneity contributes to overall growth rates and environmental adaptability. Through these two studies, we discuss the broader outlook for the quantitative understanding of cell population dynamics. By formulating these processes mathematically, we aim to provide a comprehensive theoretical foundation for manipulating cell fates in regenerative medicine and forecasting therapeutic resistance in oncology.

Speaker: Shoya Iwanami (Interdisciplinary Biology Laboratory, Graduate School of Science, Nagoya University, Japan)

4:10 PM Identifying determinants of long-term viral suppression following broadly neutralizing antibody treatment against HIV-1

Due to their long circulating half-life, high neutralization potency, and large breadth of coverage, broadly neutralizing antibodies are increasingly studied for the treatment of HIV-1 infection. Recent phase I clinical studies of antibody treatment have demonstrated robust and durable antiviral effects in viremic participants and in participants undergoing analytical treatment interruption. Consequently, these antibodies are an attractive novel treatment candidate for long-term, antiretroviral therapy-free, viral control. However, these early-stage trials are small, time consuming, and expensive. I'll show how mechanistic mathematical modelling can identify clinically actionable determinants of treatment response and uncover the evolutionary dynamics driving viral rebound. Further, I’ll show how combining mechanistic modelling and virtual population approaches can predict the duration of viral suppression in both monotherapy and combination clinical trial results. The resulting virtual population platform provides mechanistic insight that identifies clinically relevant biomarkers that are predictive of bnAb response and individualize bnAb combination therapy against HIV-1 infection. Further, this computational approach can quantify the increased antiviral effect of recently developed bnAb variants.

Speaker: Tyler Cassidy (University of Leeds)

3:10 PM → 4:30 PM Viscoelastic and multifunctional modelling and applications in biology (on the occasion of the 60th birthday of Victor A. Kovtunenko)

3:10 PM Recent Results on Sweeping Processes with Asymmetric Continuity Properties

Sweeping processes are a class of evolution problems with unilateral constraints which were originally introduced by J.J. Moreau, motivated by problems in elastoplasticity and nonsmooth mechanics. Later they have then found applications in several diverse disciplines: economic theory, electrical circuits, crowd motion modeling, biology.

In his work, Moreau considered moving convex constraints having suitable continuity properties with respect to the asymmetric Hausdorff distance, also called \emph{excess}, which is very natural for evolution problems. His results were later generalized by several authors to non-convex prox-regular constraints, but in the simpler framework of the symmetric Hausdorff distance.

In this talk I will present some recent results where for the first time sweeping processes are driven by non-convex prox-regular constraints having suitable continuity properties with respect to the asymmetric Hausdorff distance. Some of these results were obtained in collaboration with Federico Stra (Politecnico di Torino, Italy).

Speaker: Vincenzo Recupero (Politecnico di Torino)

3:30 PM Variational Modeling of AFM Indentation of Living Cells with a Pericellular Coat

Qualitative and quantitative variations in mechanobiological markers, such as extracellular matrix stiffness, cell adhesion, and cellular Young’s modulus, are strongly correlated with physiological state and frequently associated with pathological conditions. Atomic force microscopy (AFM) enables mechanical testing at the single-cell level, but interpreting indentation data is challenging due to contact nonlinearity and complex cell surface structure.
We develop a heuristic variational framework for unilateral indentation in AFM probing of living cells. Interpreting the augmented Lagrangian formulation of quasi-variational inequalities as a Winkler-type compliant coating, we propose a variational model for the indentation of an elastic substrate covered by a nonlinearly deforming, brush-like layer that represents the pericellular coat. Its compressive response follows the Alexander–de Gennes model, capturing strong nonlinearity. Building on Itou, Kovtunenko, and Rajagopal’s general solution for viscoelastic substrates with non-increasing contact area, we derive explicit displacement–force relations for monomial (axisymmetric) and self-similar (non-axisymmetric, e.g., Berkovich pyramidal) indenters.
The proposed formulation provides a mathematically consistent route to separating bulk cellular mechanics from pericellular coat effects, thereby improving the interpretation of AFM measurements in mechanobiology.

Speaker: Prof. Ivan Argatov (Malmö University)

3:50 PM On the Mathematical Analysis of Generalized Fractional Viscoelastic Models

Viscoelastic materials appear in a wide range of fields: engineering, biology, geophysics, etc., such as synthetic polymers, biological tissues and concrete. In this talk we discuss a mathematical model of nonlinear fractional viscoelastic materials within the context of infinitesimal strain theory under quasi-static situation. Constitutive relations of such a generalized fractional viscoelastic models (shortly GFV models) are given by Volterra hereditary integrals with creep functions described by Prony series replaced with a Mittag-Leffler function. For a boundary value problem of the GFV model, we show the existence of a solution. Moreover, we also perform a numerical simulation for one-dimensional creep test under isotropic expansion, analyzing the effects of the fractional derivative order and non-linearity on material behavior in each of three stages: loading, maintaining, and release stages of the creep test.

Speaker: Hiromichi Itou (Chuo University)

4:10 PM Towards Robust Quantitative Photoacoustic Tomography

In photoacoustic tomography, biological tissue is illuminated with a short laser pulse of near infrared light. The absorbed energy creates a local pressure increase that propagates through the tissue, governed by the acoustic wave equation and can be measured on the boundary. From this measured time-series the initial pressure in the tissue is reconstructed, providing valuable information on local structures. Subsequently, it is possible to recover the quantitative optical parameters of absorption and scattering. Correct recovery of the optical parameters would provide valuable functional and biological information.
Solving both the acoustic and optical inverse problem comes with challenges. From limited-view geometries to modelling errors and uncertainties. The above challenges can be effectively mitigated by training a learned reconstruction method, but three crucial ingredients are necessary: a learned method with good generalisability for out-of-distribution data, a computationally fast model to allow for feasible training and inference times, and finally reference data for the training procedure.
Here, we use a learned model-based iterative reconstruction. A novel fast FFT based approach to solve the acoustic problem in circular geometries. And finally, training and evaluation using a digital twin providing a link between experimental and simulated data. Reconstructions are presented for experimental data and the digital twin.

Speaker: Andreas Hauptmann (University of Oulu)

3:10 PM → 4:30 PM Mechanistic insights from in-vivo and in-vitro data: modelling tissue physiology and pathology away from equilibrium

3:10 PM Active shape evolution in tissue mechanics

Since D'Arcy Thompson, the interplay between mechanics and shape in living organisms has been a central question in mathematical biology. In tissue mechanics, shape variation has been studied through growth, development, and wound healing with various modeling approaches and objectives (\cite{10.1088/1367-2630/adcd93,10.1039/d3sm01419c}).

We develop a variational approach to active deformable materials where shape evolution is characterized by its dissipative behavior in response to internal activity. Inspired by Generalized Standard Materials’ extension to tissue mechanics (\cite{10.1140/epje/i2015-15033-4, 10.1038/s41578-018-0066-z}), the tissue is described by an Eulerian velocity field determined at each instant by minimizing a functional combining energy dissipation and active energy input. The tissue boundary evolves as a free boundary carried by this velocity — making shape a dynamical consequence of the material's internal processes rather than a prescribed input.

We will discuss the mechanistic insights of this modeling approach for tissue mechanics, its mathematical properties, and its biological interpretation in physiology and pathology.

This is joint work with L. Alasio (INRIA & LJLL) & M. Szopos (UPCité & MAP5).

Speaker: Naoufel Cresson (INRIA, LJLL)

3:30 PM Modelling the emergence of connective tissue architecture

Mathematical models present numerous advantages when studying biological issues, mainly because they enable us to explore hypotheses that cannot be tested in vitro and even less in vivo, such as evolutionary scenarii, possible alternative mechanisms or arbitrary setting of physiological parameters.

In this talk, we will use a 3D agents-based model to explore the question of how biological tissues acquire their 3D functional architecture. The spatial organization of any living tissue has a deep impact on this tissue's functionality. We focus on the case of white adipose tissue (WAT), which can represent up to 50\% of the body weight and is now recognized to be an important endocrine organ involved in all physiological functions. Mature WAT consists of lobular clusters of adipocyte cells surrounded by an organized collagen fiber network. However, tridimensional observations show that the cells clusters are not as well separated as what 2D imaging could lead us to believe, but are instead organized into connected macro-structures \cite{Dichamp2019}. Hence, a fully tridimensional investigation of how WAT acquires its functional structure is needed.

Our hypothesis is that the emergence of WAT structuration could be explained by simple mechanical interactions between adipocyte cells and collagen fibers \cite{Peurichard2017}. To test it, we developed an agent-based model featuring cells represented as spheres appearing and growing in a dynamical 3D network of cross-linked spherocylinders (modelling the collagen fibers) \cite{Chassonnery2024}. Using state-of-the-art 3D data visualization and segmentation tools, we will show that this model is able to produce cell structures morphologically similar to those observed in experimental images \cite{ChassonneryInPrep}. Through fine parametrical analysis, we will identify the key parameters of the model and study their influence on the simulation outcome. We will show that this simple model can give insights on how complex 3D cell and fiber structures could spontaneously emerge as a result of simple mechanical interactions between cells and fibers, highlighting the key role of mechanics in tissue structuration.

List of co-authors: Pauline Chassonnery, Jenny Paupert, Anne Lorsignol, Childérick Séverac, Marielle Ousset, Pierre Degond, Louis Casteilla, Diane Peurichard.

Speaker: Pauline Chassonnery (BRGM Orléans, Bureau de recherches géologiques et minières)

3:50 PM A new size-dependant individual based model for epithelial tissue

Epithelial tissues are densely packed, confluent systems whose organization and mechanics are commonly described mathematically using vertex models. While these approaches successfully capture membrane dynamics and cell–cell junction remodeling, they inherently lack the ability to explicitly account for intercellular attraction and/or repulsion forces. As a result, key aspects of tissue organization driven by such interactions remain insufficiently explored. In this work, we introduce a novel individual-based model in which cells are represented as radius-dependent spheres. This framework explicitly incorporates both attractive and repulsive interactions between cells, enabling a more direct description of mechanical cell coupling within the tissue. A central feature of our model is the ability of cell size to dynamically evolve, allowing the system to adapt to the balance of forces and reach mechanically consistent configurations. We analyze the stationary states of this system and characterize the resulting tissue organization across parameters regimes. Finally, we validate our approach by comparing model predictions with experimental data from retinal pigment epithelium.

Speaker: Sophie Hecht (Sorbonne Universite)

4:10 PM PDE models for the growth of heterogeneous cell populations: travelling fronts, sharp interfaces, and concentration phenomena

In this talk, PDE models for the growth of heterogeneous cell populations will be considered. Both models with discrete phenotype states, which consist of coupled systems of nonlinear PDEs, and models wherein the phenotype enters as a continuous structuring variable, which are formulated as non-local PDEs, will be examined. Focusing on scenarios where cells with different phenotypes are spatially segregated across invading fronts, travelling wave solutions that exhibit sharp interfaces, for the first class of models, and concentration phenomena, for the second class of models, will be studied. The insights into the mechanisms that underpin collective cell migration generated by these mathematical results will be briefly discussed.

Speaker: Tommaso Lorenzi (Politecnico di Torino)

3:10 PM → 4:30 PM Cell Migration Across Scales – exploring different mathematical frameworks

3:10 PM MS145-5

Speaker: Gabriella Bretti (CNR - IAC)

3:30 PM Heterogeneous elastic wires: a toy model for biological membranes

Motivated by variational models for heterogeneous biological membranes such as those described by the Canham-Helfrich functional, we study closed planar elastic curves whose bending stiffness depends on an additional scalar density. The resulting energy can be seen as the one-dimensional analogue of 2D membrane models.

Previous work on the static problem include \cite{bjss2023}, where the energy minimization under fixed length and total mass constraints is performed, followed by a bifurcation analysis around the trivial circular state is carried out. In \cite{dALR2024}, the authors study a related time-dependent problem, i.e. the associated $L^2$-gradient flow. Local well-posedness, global existence, and full convergence of the flow to a stationary solution are established, using a version of the Łojasiewicz–Simon gradient inequality.

This talk focuses on the qualitative properties of the $L^2$-gradient flow solutions, like the (non)preservation of convexity, embeddedness, positivity of the density, and rotational or axial symmetry of the initial datum. In particular, we identify conditions on the model parameters and the bending stiffness under which the asymptotic limit can be explicitly characterized as a homogeneous elastica, i.e., an elastica with constant density. Some numerical experiments will also be shown.

Speaker: Gaspard Jankowiak (University of Graz)

3:50 PM Towards optimal scaffolds for cell migration

Cell-extracellular matrix interaction and the mechanical properties of the cell nucleus have been demonstrated to play a fundamental role in cell movement across fibrous networks, micro-channels, basal membranes, and confining environment in general. So, their study is important on one hand in oncology to understand the spread of cancer metastases and on the other hand in tissue engineering to build artificial scaffolds that are able to promote cell re-population. It is known that key ingredients are the geometrical properties of the environment, the stiffness of the cell nucleus and the ability of cell to exxert traction forces. This talk will review previous results, merging the outcome of some continuum mechanics models with individual cell-based models that allow to identify an invasion criterium and optimal characteristics for cell migration. Such criteria will be used to identify the geometric characteristics that some triply periodic porous structures need to have to optimize cell migration.

Speaker: Luigi Preziosi (Politecnico di Torino)

4:10 PM The biomechanics of the single cell-ECM interaction during migration

Cell migration is involved in many developmental process such as embryogenesis, morphogenesis, angiogenesis or cancer invasion and critically depends on the mechanical properties of the extra-cellular matrix (ECM). Indeed, in the mesenchymal migration mode, cells tend to follow ECM stiffness gradient. This durotaxis (\cite{Durotaxis}) is explained by the ability of the cell to probe its environment thanks to mechano-sensors (\cite{MechanoSensing}) (filopodia). Moreover, the migration process relies on the ability of the cell to self propel through a combination of events comprising cell anchoring to the ECM through maturation of focal adhesions and contractions of the actin cytoskeleton to generate a traction force strong enough to translocate the cell nucleus. The cell-ECM interactions during cell migration is thus a bidirectionnal process : the cell traction force on the matrix generate ECM deformation that in return can be perceived by neighbouring cells through mechano-sensors. This leads to the question of the existence and importance of inter-cellular communication through matrix deformation to favour cell-cell encouter in processes such as tumoral angiogenesis. In this talk a single cell motility model (\cite{SingleCellModel}) mechanically coupled to a continuous deformable substrate will be presented. The model is designed to incorporate minimal a priori assumptions. In that sense, no mechanism of cell polarization nor stiffness dependent traction force is implemented. The main objective is to evaluate if those behaviours can emerge solely from cell-ECM mechanical interactions and probing. Particular attention will be given on the range and magnitude of cell induced ECM deformations that the model can reproduce. Reciprocally the influence of imposed ECM deformations on the migratory patterns will be considered and compared to those obtained on a rigid substrate. In conclusion the effective impact of the mechanical cues on the cell encounter will be assessed.

Speaker: Nicolas Louviaux (Université Grenoble Alpes)

3:10 PM → 4:30 PM Whole-cell modelling: progress and perspectives

3:10 PM What would a smart yeast do? Mapping biosynthetic resource allocation to explain prevalence of the Crabtree effect in yeasts

Genome-scale metabolic models (GEMs) are computable knowledge bases containing information of all biochemical reactions in an organism of interest. Typically, Flux Balance Analysis (FBA) is used to predict intracellular flux distributions corresponding to limiting substrate-efficient metabolic phenotypes. For fast-growing microbes (Escherichia coli, yeasts), alternative efficiency calculi (e.g., proteome efficiency) might govern their physiology in different growth regimes – inaccessible to classical FBA. Extensions of GEMs, called proteome-constrained GEMs (pcGEMs), on the contrary, capture complex metabolic phenotypes based on optimal biosynthetic resource allocation to the enzymatic machinery operating the metabolic network. We have constructed pcGEMs for yeasts Saccharomyces cerevisiae and Schizosaccharomyces pombe to identify constraints ruling the respiration-fermentation switch in aerobic growth, also known as Crabtree effect. Both yeasts started fermenting glucose into ethanol after hitting the mitochondrial protein capacity constraint. Contrary to Crabtree+ yeasts, this constraint was never hit in a pcGEM of a Crabtree- yeast Pichia kluyveri. Contrasting quantitative proteomics data with pcGEM predictions hinted to P. kluyveri possessing more catalytically efficient electron transport chain proteins, sustaining a respiratory phenotype even at fast growth.

Speaker: Pranas Grigaitis (Karlsruhe Institute of Technology)

3:30 PM How Do T Cells Migrate Through Collagen? Inferring Subcellular Forces from Fiber‑Resolved Extracellular Matrix Deformations

Cell migration through extracellular matrix (ECM) is fundamental to many biological processes, including development, immune responses, and cancer metastasis. However, this migration is governed by mechanical interactions that occur at the subcellular scale of individual collagen fibres, and conventional traction‑force methods treat the ECM as a continuum. To move beyond this, we introduce a framework that accounts for the complex global architecture of the fibrillar network to infer the subcellular‑scale forces imparted by a cell as it migrates through collagen in 3D.

Our approach combines high‑resolution imaging with deep‑learning models for collagen‑fibre skeletonization, cell segmentation, and displacement tracking. Using a mechanical model of the fibre skeleton that incorporates extensional tension, torsional stiffness at junctions, and drag forces, we solve a physics‑based inverse problem to infer the fibre tensions, torques, and forces applied by the cell. This discrete network formulation naturally captures non‑local, long‑range mechanical interactions that existing continuum approximations cannot recover.

This framework reveals how migrating cells coordinate forces across multiple fibres to navigate complex 3D environments. More broadly, it provides new mechanistic insight into cell movement and force transmission across diverse biological contexts.

Speaker: Jeremy Worsfold (University of New South Wales Sydney)

3:50 PM Agent-based Modelling of Molecular Dynamics in the Gram-negative Outer Membrane

The outer membrane of Gram-negative bacteria is a crucial defensive structure, conferring - among other properties - substantial protection against antibiotics. Decades of high-resolution molecular dynamics modelling has provided powerful insights into the structures of the chemical species that reside in the Gram-negative outer membrane and their chemical and physical interactions. However, the extraordinary complexity of these models limits their use to microseconds of simulation time. In this talk, we introduce a coarse-grained, agent-based modelling approach which can provide insights into membrane dynamics on the seconds-to-minutes time scale of cell growth. The model reveals that spatial constraints play a key role in the growth dynamics of the Gram-negative outer membrane, demonstrates the emergence of characteristic spatial structures, and challenges the current biological dogma of how the Gram-negative outer membrane grows.

Speakers: Thomas Williams (University of Melbourne), James Osborne (University of Melbourne), KJ Goh (Monash University), Trevor Lithgow (Monash University), Jennifer Flegg (University of Melbourne)

4:10 PM Model-based integration of large-scale datasets

Mechanistic mathematical models are powerful tools in modern life sciences. Similar to experimental techniques, mechanistic models enable the investigation of biological processes and hypothesis testing. Furthermore, they allow the integrative analysis of multiple datasets as well as the prediction of latent variables and future experimental outcomes.

In this talk, I will outline how mechanistic modeling can support the analysis and integration of large-scale datasets. First, I will present tailored computational methods for training large-scale mechanistic models of cellular pathways using multi-omic data. This includes recent advances in combining mechanistic modeling with machine learning approaches to enable scalable inference and the handling of qualitative measurements. Second, I will introduce methods for handling heterogeneous data types and and population-level variability. In particular, I will discuss approaches for the analysis of cell-to-cell variability using amortized inference techniques, which enable efficient inference in complex stochastic and multi-cellular models.

Speaker: Jan Hasenauer (Bonn Center for Mathematical Life Sciences, University of Bonn)

3:10 PM → 4:30 PM Dynamics of Vector Populations and Pathogen Transmission

3:10 PM Could malaria mosquitoes be controlled by periodic releases of transgenic mosquitocidal Metarhizium pingshaense fungus? A mathematical modeling approach.

Insect pathogenic fungi present a promising alternative to chemical insecticides for controlling insecticide-resistant mosquitoes. One proposed method involves releasing male Anopheles mosquitoes contaminated with transgenic Metarhizium pingshaense (Met-Hybrid) to lethally infect females during mating. This study presents a novel deterministic mathematical model to evaluate the impact of this control approach in malaria-endemic areas. The model incorporates two fungus transmission pathways: mating-based transmission and indirect transmission through contact with fungus- colonized mosquito cadavers. We found that the fungus cannot establish in the mosquito population without transmission from infected cadavers (in this scenario, the reproduction number of the model is zero). However, if transmission from colonized cadavers is possible, the fungus can persist in the local mosquito population when the reproduction number exceeds one. Simulations of periodic releases of infected male mosquitoes, parameterized using Met-Hybrid-exposed mosquito data from Burkina Faso, show that an 86% reduction in the local female mosquito population can be achieved by releasing 10 Met-Hybrid- exposed male mosquitoes per wild mosquito every three days over six months. This matches the efficiency of some genetic mosquito control approaches. However, a 90% reduction in the wild mosquito population requires, for instance, daily releases of the fungal-treated mosquitoes in a 6:1 ratio for about 5 months, which proves less efficient than some genetic approaches. This study concludes that fungal programs with periodic releases of infected males may complement other methods or serve as an alternative to genetic-based mosquito control methods, where regulatory, ethical, or public acceptance concerns restrict genetically-modified mosquito releases.

Speaker: Salman Safdar (University Of Maryland, College Park)

3:30 PM Modeling the Geospatial Dynamics of Lyme Disease in Maryland Under Current and Projected Climate Change Scenarios

Lyme disease is the most prevalent vector-borne illness in the United States, with incidence rising across Maryland over recent decades. Transmission of Borrelia burgdorferi by Ixodes scapularis ticks is highly sensitive to climatic conditions, making it essential to understand how ongoing and projected warming will shape future disease dynamics. In this presentation, I will introduce a climate-driven epidemiological model developed to investigate the spatiotemporal dynamics of Lyme disease across Maryland. I will describe how the framework integrates fine-scale ecological and epidemiological data with temperature-dependent processes governing tick development, host interactions, and pathogen transmission. I will then present simulation results under current and future warming scenarios, specifically RCP 4.5 and 8.5, highlighting how projected warming influences tick population dynamics, seasonal activity shifts, and the geographic distribution of transmission risk. I will identify regions of heightened vulnerability under each warming scenario and discuss the implications of these spatial shifts for public health planning. Finally, I will evaluate the potential of targeted interventions, including environmental management and rodent-focused tick suppression, to mitigate transmission risk, and I will present coverage thresholds at which such strategies can meaningfully reduce disease persistence. Together, these findings highlight the need for climate-adaptive approaches to vector-borne disease prevention. The modeling framework presented offers a transferable tool for informing evidence-based public health strategies in regions facing similar climate-driven challenges.

Speaker: Salihu Musa (Department of Mathematics, University of Maryland, College Park, MD, 20742, USA)

3:50 PM Investigating the Impact of Novel Transmission-Blocking Anti-malarial Drugs: A Mathematical Modeling Approach

Most available drugs kill malaria as it gets established in the liver or after it has infected red blood cells, but cannot tackle it once the parasite is released from the cells as gametocytes, which is when it is transmissible to other people via mosquito bites. Recently, promising clinical advances have been made in developing novel antimalarial drugs that block parasite transmission, cure the disease, and have prophylactic effects, called transmission-blocking drugs (TBDs) [2, 3, 4]. Our main aim is to explore the potential effects of such TBDs on malaria transmission in the effort to control and eliminate the disease using mathematical models to ascertain how the presence of TBDs can mitigate the transmission of malaria parasites on both asymptomatic and symptomatic carriers in a defined hotspot of malaria. Our special focus was on the effects of the treatment coverage and the efficacy of TBDs along with the protective effect and waning effect of TBDs. For this, we propose and analyze a mathematical model for malaria transmission dynamics that extends the SEIRS-SEI type model to include a class of humans undergoing treatment with TBDs and a class of those protected because of successful treatment. The mathematical and epidemiological implications of TBDs are assessed using different approaches.  
Furthermore, we fit the model to malaria data using the library "lmfit”  in Python and use the validated model to explore the model's predictions under various scenarios. Results from our analysis show that the effect of treatment coverage rate on reducing reproduction number depends on other key parameters such as the efficacy of the drug. The projections of the validated model show the benefits of using TBDs in malaria control in preventing new cases and reducing mortality [1]. We find that treating $35\%$ of the population of Sub-Saharan Africa  with a $95\%$ efficacious TBD  from $2021$ will result in approximately $82\%$ reduction on the number of malaria deaths by $2035$.

Speaker: Woldegebriel Assefa Woldegerima (York University, Canada)

4:10 PM Mathematics of Wolbachia-based biocontrol of mosquito-borne diseases

The release of Wolbachia-infected mosquitoes into the population of wild mosquitoes is one of the promising biological control methods for combating the population abundance of mosquitoes that cause deadly diseases, such as dengue. In this lecture, I will present a two-sex mathematical model for the population ecology of dengue mosquitoes and disease, and use the model to assess the potential impact of the periodic release of Wolbachia-infected mosquitoes (into the wild mosquito population in the community) on the population ecology of the dengue mosquitoes and disease.

Speaker: Abba Gumel (University of Maryland)

3:10 PM → 4:30 PM Mathematical and Experimental Approaches to Retinal Degeneration and Visual Restoration

3:10 PM Retinal processing of natural scenes

While a great deal is known about how neurons of the early visual system respond to simple stimuli, our understanding of how they process natural stimuli is still limited. Machine learning models have been invaluable to predict how these neurons respond to natural stimuli. However, the increasing complexity of these models make them difficult to interpret, and their ability to generalize to new stimuli is limited.
I will describe recent works from my lab where we address these issues at the level of the retina. We developed a new perturbative approach to probe the selectivity of individual neurons during natural scenes, and to understand the features they extract. We use this method to characterize and model how short-term adaptation impact how the retina processes natural scenes. Our results show that adaptive mechanisms are not just here to normalize the response to the average luminance and contrast: during natural scene stimulation it also reshapes the selectivity of specific types of ganglion cells. Finally, we show that the ability of artificial neural networks to generalize can be dramatically enhanced in specific ganglion cell types by incorporating in the model a new geometry constraint derived from a natural hunting behavior.
Together our results suggest that scaling up model size may not be enough: including knowledge about the biological basis of visual processing in artificial neural network models might be necessary to understand sensory processing.

Speaker: Olivier Marre (Institut de la vision)

3:50 PM A Mathematical Framework for Photoreceptor Dynamics in Health and Disease: Modeling Metabolic Mechanisms and Spatial Dependence

Retinitis Pigmentosa (RP) is a group of genetically heterogeneous retinal diseases characterized by the progressive loss of rod and cone photoreceptors, leading to irreversible blindness. While genetic mutations in RP primarily affect rods, secondary cone degeneration inevitably follows.
This phenomenon is linked to the loss of rod-derived cone viability factor (RdCVF), a rod-secreted protein that stimulates aerobic glycolysis in cones to support the metabolic demands of outer segment (OS) renewal. To understand these complex mechanisms, we use mathematical models to investigate the dynamics governing photoreceptor dynamics. We first developed a system of nonlinear ordinary differential equations to model RP progression. Through stability, global sensitivity, and bifurcation analyses, we identified key parameters driving the transition from health to blindness. Our results interpret model equilibria as distinct degenerative states and reveal that stable limit cycles emerge at critical junctions, suggesting specific windows for therapeutic intervention. We find that the balance between OS shedding and renewal is vital for cone preservation. Next, we developed a spatially-dependent model to include photoreceptor density distributions and nutrient diffusion. The model was validated against experimental data, accurately predicting OS length and regrowth. These findings establish a foundation for exploring various retinal pathologies and spatial treatment strategies.

Speaker: Danielle Brager (District of Columbia Public Schools)

4:10 PM A Dual-Intervention Optimal Control Framework for Photoreceptor Degeneration Using RdCVF and RdCVFL

Rod and cone photoreceptors are among the most metabolically active cells in the human body, relying on tightly regulated redox homeostasis to maintain function. In retinal degeneration resulting from chronic blue light exposure or inherited degenerative conditions such as retinitis pigmentosa (RP), the progressive loss of photoreceptors disrupts this balance, leading to an accumulation of reactive oxygen species (ROS) that accelerates further cell death. Two proteins produced by rod photoreceptors have emerged as promising therapeutic targets. The rod-derived cone viability factor (RdCVF) promotes cone survival by enhancing glucose uptake and supporting aerobic glycolysis. Its long isoform (RdCVFL) protects both rods and cones by regulating the redox environment. While the therapeutic potential of each protein has been investigated independently, their combined effect has not yet been examined in a unified mathematical framework. RdCVF and RdCVFL act on distinct but coupled biological processes, targeting metabolic support and oxidative stress regulation, respectively. A dual-intervention strategy may therefore offer substantially greater neuroprotection than either treatment alone. In this work, we develop and analyze an optimal control model incorporating both RdCVF and RdCVFL as co-administered treatments. This provides a mathematical basis for evaluating the synergistic potential of this dual-intervention approach in slowing or halting photoreceptor degeneration arising from chronic blue light exposure, RP, and related retinal diseases.

Speaker: Erika Camacho (The University of Texas at San Antonio)

3:10 PM → 4:30 PM Data-driven modeling in biology and medicine

3:10 PM Parameter identifiability for the Data-Driven Modeling

Integrating high-dimensional biological data into mechanistic models requires practical identifiability for reliable inference. We develop a computational framework that reveals scaling laws for identifiability via asymptotic analysis, combining Fisher information with perturbed Hessians to quantify identifiability and uncertainty in non-identifiable subspaces. Validated on several benchmark data-driven models, the framework uncovers key mechanisms and provides principled scaling laws for data-driven mechanistic modeling and digital twins.

Speaker: Wenrui Hao (Department of Mathematics, Pennsylvania State University, University Park, PA, USA)

3:30 PM How Intermediate Filaments Move: Experiments and Models

Intermediate filaments are key components of the cytoskeleton, playing essential roles in cell mechanics, signaling and migration. Their spatiotemporal organization, which supports these functions, results from the interplay between assembly and disassembly processes, as well as retrograde actin flow and motor protein–driven transport. Investigating the different mechanisms involved in the intracellular transport of intermediate filaments requires a combination of experimental setups and complementary biological and mathematical models. In this talk, several examples illustrating these approaches will be presented.

Speaker: Stephanie Portet (Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada)

3:50 PM How Random Forces Help Rather Than Hinder Dynein Cargo Transport

Recent experimental work has shown that dynein transports cargo faster in vivo than in vitro, although counter intuitive, the results are consistent with other experimental data \cite{Torosawa:2025:AFC}. Typically, it is assumed that the cytoplasm, a more viscous and complex environment, should slow down transport compared to in vitro experiments. It is postulated that the catch bond nature of dynein allows this counter intuitive result. In this talk I will discuss a stochastic tug-of-war model of dynein transport that sheds light on this phenomena.

Speaker: John Dallon (Department of Mathematics, Brigham Young University, Provo UT, USA)

4:10 PM Senolytic Drugs Reduce Cancer Resistance to PD-1 Blockade

Resistance to immune checkpoint inhibitors (ICI), including anti-PD-1 and anti-PD-L1 therapies, remains a major limitation in cancer treatment, with most patients relapsing despite initial responses. Previous studies have shown that inhibition of TNF-alpha or TGF-beta overcome resistance to anti-PD-1. Here, we develop a mathematical model to investigate a mechanism of ICI resistance driven by age-associated senescence of CD8+ T cells. In the model, senescent T cells secrete VEGF, thereby promoting tumor growth through enhanced vascular support. To counteract this effect, we incorporate the senolytic drug navitoclax (ABT-263), which selectively eliminates senescent T cells, and assess the efficacy of combined senolytic-ICI therapy in extending tumor remission. Model predictions are validated against independent experimental data from murine studies involving navitoclax and anti-PD-L1 treatment. Using the validated framework, we conduct in silico clinical trials simulating multi-cycle anti-PD-1 treatment in young and old patient cohorts with different timings of senolytic administration. The results demonstrate that the optimal timing of navitoclax depends on immune age: maximal remission extension is achieved when senolytic therapy is initiated in the second treatment cycle in older patients, whereas earlier administration is most effective in younger patients. These findings highlight immune senescence as a key determinant of response to cancer immunotherapy and suggest that age-adapted scheduling of senolytic drugs may improve the durability of ICI-based treatments.

Speaker: Nourridine Siewe (School of Mathematics and Statistics, Rochester Institute of Technology, Rochester, NY, USA)

3:10 PM → 4:30 PM Algorithmic Approaches to Biochemical Network Reduction

3:10 PM Rigorous and Automated Non-dimensionalisation, Preprocessing, and Reduction of Biochemical Reaction Networks

Mathematical models provide a powerful framework for analysing the dynamics of biochemical reaction networks (BCRNs); however, effective modelling of complex biological systems requires balancing complexity and accuracy. As such, the rigorous and principled reduction of BCRNs via systematic, model-independent methods, while ensuring that key dynamics are preserved, is of vital importance.

In this talk, we discuss how to automate the fast yet rigorous non-dimensionalisation, preprocessing, and reduction of BCRNs, without being limited to low-dimensional models, as many current approaches are. Using the parametrisation method, the constructive counterpart to Tikhonov–Fenichel theory, together with techniques from algebraic geometry and linear algebra, we automate the end-to-end, principled reduction of a wide class of BCRNs without dimensional constraints. Importantly, the true power of the parametrisation method lies in its ability to deal with systems exhibiting multiple timescales, where standard geometric singular perturbation theory approaches can fail. We demonstrate the approach by rigorously reducing numerous well-known and real-world BCRNs, many of which we reduce for the first time, establishing its utility and showing that even low-order reduced models can achieve high fidelity and accuracy.

Speaker: Georgio Hawi (University of Sydney)

3:30 PM Tikhonov-Fenichel Reductions: A Systematic Approach to Timescale Separation and its Application to Modelling Population Dynamics

Modelling biological systems imposes the challenge to balance realism and complexity. Precise mechanistic models are often difficult to analyse and thus yield little insight, whereas simpler conceptual models tend to lack justification, as they rely on implicit descriptions of the underlying mechanisms. Model reduction via timescale separation can mitigate this trade-off by allowing to derive models of the latter type from the former while essential properties remain unchanged.

Tikhonov-Fenichel reduction theory developed by Goeke and Walcher \cite{goeke2014} allows us to find all timescale separations of rates (i.e.\ slow-fast separations of processes) for polynomial ODE systems algorithmically and to compute the corresponding reductions \cite{goeke2015}. Therefore this is a systematic, coordinate-free approach to geometric singular perturbation theory, which can be readily applied using the \texttt{Julia} package \texttt{TikhonovFenichelReductions.jl} \cite{apelt2026a}.

Following \cite{apelt2025}, the starting point of this talk is a detailed ``super model'' describing the population dynamics of mutualistic partners. From this we consider embedded conceptual models derived via Tikhonov-Fenichel reduction theory. The focus lies on the relationship between the mathematical formalism and the underlying biology resulting in good interpretability of the reductions. This for instance enables us to answer the question under which circumstances mutualism may break down.

Speaker: Johannes Apelt (Universität Greifswald)

3:50 PM Lumping of Reaction Networks: Generic and Critical Parameters

Lumping methods reduce biochemical reaction networks by aggregating species concentrations via algebraic conditions that hold globally. We study linear lumping for parameter-dependent mass action systems, asking how lumpability depends on rate constants. Our first result shows that for generic parameters---those ranging over a non-empty open subset of parameter space---exact linear lumping yields only ``obvious'' reductions: elimination of non-reactant species or projections along stoichiometric first integrals \cite{LiRabitz1989}. This characterization extends to product-form kinetics, including Michaelis--Menten and Hill-type rate laws, and structurally explains why parameter-independent approaches such as CLUE \cite{OvchinnikovPerezVeronaPogudinTribastone2021} often fail to find nontrivial reductions.

Beyond generic parameters, we develop an algorithmic approach to identify critical parameter sets---algebraic subvarieties where non-trivial lumpings become available. Determining critical parameters reduces to solving finitely many polynomial systems, and extends naturally to constrained lumping. For proper lumpings of quadratic systems, covering all networks with at most bimolecular reactions, we provide a complete characterization via block-structured Jacobian conditions. Applications to a self-replicator model \cite{GijimaPeacockLopez2020} and a two-pathway enzyme mechanism show that critical parameters reveal hidden conservation laws, with approximate lumpings available near these values \cite{LeguizamonRobayoEtAl2024}.

Speaker: Santiago Schnell (Department of Mathematics, Dartmouth College, Hanover, NH, USA)

4:10 PM Total QSSA: Pharmacokinetic Applications and the Validity of Its Stochastic Extension

For over a century, the Michaelis–Menten (MM) equation has provided the foundation for modeling enzyme kinetics in biochemistry and pharmacology. Despite its remarkable success, MM relies on assumptions that may break down in physiologically relevant regimes. In this talk, we revisit these limitations and introduce the total quasi-steady-state approximation (tQSSA) as a principled generalization of MM. We show that this framework enables more accurate quantitative predictions in pharmacokinetic applications, including enzyme-mediated drug–drug interaction modeling relevant to regulatory practice. We further discuss how this deterministic reduction extends to stochastic simulations. By clarifying the validity conditions of its stochastic extension, we identify when tQSSA reliably captures intrinsic biochemical noise and propose alternative stochastic reaction functions when it does not.

Speaker: Yun Min Song (Institute for Basic Science)

3:10 PM → 4:30 PM SMB MathOnco Subgroup Mini-Symposium: Emerging Themes in Mathematical Oncology

3:10 PM A Multiscale Mathematical Framework for Modeling Ductal Deformation in Early Pancreatic Neoplasia

Pancreatic cancer precursor lesions (PanINs and IPMNs) generate pronounced ductal deformations, arising from reciprocal interactions between epithelial mechanics, basement membrane integrity, and stromal remodeling. Yet the dynamic feedback loops governing this structural evolution remain poorly characterized. We present a multiscale mathematical modeling framework that couples ductal epithelial cells, the basement membrane, and cancer associated fibroblasts (CAFs). The model integrates mechanistic rules for cell-matrix adhesion, epithelial mechanical responses, and CAF driven matrix remodeling to characterize how specific parameter combinations generate the ductal morphologies observed in precursor lesions. Simulations reveal how variations in epithelial stiffness, basement membrane degradation kinetics, and CAF remodeling rates produce canonical deformation modes consistent with histological sections from resected human pancreas tissues. Current work extends the framework to enable predictive exploration of lesion progression, identifying parameter regimes that shift lesions toward increased morphological irregularity and potential invasiveness. This modeling approach provides a mathematically rigorous platform for quantifying multicellular interactions and uncovering mechanistic drivers of early pancreatic neoplastic evolution.

Speaker: Daniel Bergman (University of Maryland Baltimore)

3:30 PM Mechanistic learning for spatio-temporal brain tumor response predictions

Magnetic resonance imaging (MRI) is central to diagnosis, longitudinal monitoring, and response assessment in brain tumors, motivating predictive models that operate not only on volumetric trajectories but directly in the imaging domain. While mechanistic models capture individualized tumor dynamics and treatment effects, they compress the spatial and anatomical information contained in radiographic data; conversely, generative AI solutions such as guided denoising diffusion models, enable anatomically coherent prediction of future MR images and tumor growth probability maps, but require temporal structure that is often difficult to learn from limited follow-up data. Hybrid mechanistic-learning approaches are therefore particularly suitable in this application, where longitudinal imaging is sparse and irregularly sampled, especially in rare pediatric tumors. By coupling biologically plausible ordinary differential equation models of tumor growth with guided denoising diffusion models, these frameworks combine interpretable estimates of future tumor burden with patient-specific image synthesis and spatially resolved progression maps. This integration supports biologically informed, anatomically meaningful prediction of spatio-temporal tumor evolution and provides a foundation for improved response assessment, treatment monitoring, and radiotherapy planning.

Speaker: Sarah Brueningk (University of Bern)

3:50 PM Mechanistic computational modeling of clonal dynamics in the aging hematopoietic system

Blood cell formation is maintained throughout the lifespan of an organism by a small population of hematopoietic (blood-forming) stem cells (HSCs). HSCs sustain their population through self-renewal while simultaneously giving rise to more differentiated offspring, referred to as progenitors and precursors, that mature into the various blood cell types. Over time, HSCs accumulate mutations that can confer growth advantages and trigger clonal expansion. This leads to a condition known as clonal hematopoiesis of indeterminate potential (CHIP). The incidence of clonal hematopoiesis increases with age, however, the underlying mechanisms are not fully understood. As CHIP can eventually transform into severe blood cancers, it is crucial to understand and quantitatively predict its dynamics. Evidence suggests that the interplay between mutation accumulation and age-related systemic changes, such as chronic inflammation, altered growth factor levels, and changes in the bone marrow micro-environment, contributes to CHIP evolution. We propose mechanistic mathematical models that account for stem and progenitor cell self-renewal and differentiation, nonlinear feedback regulation, chronic inflammation, and changes in the stem cell niche to understand how these processes influence clonal dynamics. The models are informed by data on steady-state blood cell formation and clonal expansion after stem cell transplantation.

Speaker: Thomas Stiehl (RWTH Aachen University)

4:10 PM Digital Twins in (Radiation) Oncology

To personalize cancer radiation therapy, we must give the right dose and dose fractionation, at the right time, dynamically adapted, to best harness the radiobiological effects of radiation as well as synergy with the patient’s immune system. I present the latest developments in the mathematical and computational modelling in radiation oncology to develop digital twins – constructs that mimic the structure and behavior of the patient and the tumor to make predictions and inform decisions that realize value. I present different simple approaches to build predictive pipelines and how to integrate those into clinical decision making towards the concept of real-time adaptive personalized radiation treatments. I will discuss past, present, and future clinical trials of such model-guided treatments.

Speaker: Heiko Enderling (MD Anderson Cancer Center)

3:10 PM → 4:30 PM From dose to response: advances in modelling treatment efficacy and toxicity in tumor forecasts

3:10 PM From mechanism to meaning: causal interpretation of PKPD models in oncology

Mechanistic pharmacokinetic/pharmacodynamic (PK/PD) modeling provides a quantitative framework for characterizing how drug dose and exposure relate to efficacy and toxicity over time \cite{bender2015pkpd_oncology, mould2015exposure_response}. In oncology, such models are increasingly used to inform dose selection, treatment evaluation and the interpretation of therapeutic response. However, the clinical meaning of model-derived quantities is often left implicit. In practice, estimated dose–exposure–response relationships may correspond to different causal questions depending on how post-initiation events such as dose reductions, treatment discontinuation, rescue medication, switching, and death are handled. The ICH E9(R1) estimand framework offers a principled structure for linking pharmacometric and tumor-forecasting models to clinically interpretable treatment effects \cite{ich2019e9r1}. In addition, epidemiologic concepts such as confounding, selection bias, immortal time bias, and effect modification illustrate how post-baseline summaries can yield misleading inferences when the underlying causal question is not explicitly defined \cite{hernan2020whatif}. The aim is not to replace mechanistic modeling with epidemiologic methods, but to show how causal thinking can sharpen model interpretation, improve alignment with regulatory and clinical decision questions and strengthen the relevance of model-based evidence in oncology.

Speaker: Maddalena Centanni (Uppsala University, Sweden)

3:30 PM Agent-based modeling of intratumor heterogeneity coordination

Deciphering intratumor spatial configuration of cell communities is fundamental for mechanistically understanding how heterogeneity in tumor phenotypes impacts the effectiveness of treatments. Such dynamic interplay in the tumor microenvironment determines a continuum of transition stages, having different levels of compliance to therapy \cite{prunella2025pharmacometric}. Scheduling and sequencing of two or more treatments starting from routinely available H&E-stained Whole Slide Images could hence be improved by considering also longitudinal interactions between cancerous and immune cells. Agent-based modeling is a computational modeling framework that deploys dynamic cell-to-cell inter-actions within a drug-modulated selective environment, and can provide a time-resolved quantitative approach for more informed and adaptive treatment \cite{kather2017silico} selection. The temporal dimension of the model allows not only simulating under fixed behavioral rules, but also includes the cumulative effects of drug exposure over time \cite{surendran2023agent}. This enables the representation of plastic interactions between cells and therapeutic agents, whereby cellular behavior can dynamically change as a function of prior treatment history. Such a framework allows the simulation of clinically relevant phenomena frequently observed in oncology, including the emergence and selection of therapy-resistant clones.

Speaker: Michela Prunella (Politecnico di Bari, Italy)

3:50 PM Mechanistic and Machine Learning Models for Dose Scheduling and Treatment Response Prediction

The integration of mechanistic models with machine learning is becoming increasingly important for predicting treatment response and optimizing dose schedules in cancer therapy. Mechanistic models based on differential equations capture biological processes such as tumor growth and drug dynamics, while machine learning provides flexible tools for learning unknown components from data. However, two major challenges arise in this integration: identifiability of model components and the computational cost of repeated inverse problems. In this talk, I present recent work addressing both challenges. First, we develop a framework that establishes conditions for identifiability when simultaneously inferring unknown parameters and functional terms in differential equation models, improving the interpretability and reliability of hybrid mechanistic–ML approaches. Second, we introduce efficient inverse modeling methods based on physics-informed neural networks that enable rapid parameter inference through an offline-online decomposition. Together, these approaches provide practical tools for integrating mechanistic knowledge with data-driven learning to support treatment response prediction and exploration of personalized dosing strategies.

Speaker: Mohammad Kohandel (University of Waterloo, Canada)

4:10 PM Personalizing Radiotherapy in HPV+ Oropharyngeal Cancer with Systematic In Silico Trials

RT for HPV+ oropharyngeal cancer has high cure rates, but this is often associated with significant toxicity. Despite broad interest in de-intensifying RT in this context, there isn’t a reliable biomarker to identify individual patients for safe de-escalation without sacrificing cure. We address this by creating a virtual cohort of head and neck cancer. The virtual cohort is based on two mathematical models: (1) a model of RT-response that simulates tumor volume dynamics during RT; (2) a model of tumor regrowth that simulates disease recurrence from post-treatment viable tumor burden dynamics. The virtual cohort’s RT response parameters are calibrated to weekly CT images from a cohort of 39 head and neck cancer patients that received fractionated RT. The recurrence/regrowth parameters are calibrated to 5-year locoregional recurrence data abstracted from a large cooperative group clinical trial that tested both standard and hyperfractionated RT (RTOG 9003). This outputs a calibrated virtual cohort of HNC patients that has the same recurrence patterns as its real counterparts in RTOG 9003, i.e. a digital twin of the trial. We then ran systematic in silico trials on this virtual cohort to determine patient-specific adaptive RT schedules that maximize locoregional control rates and minimizes both total RT dose and number of RT fractions.

Speaker: Mohammad Zahid (The University of Texas MD Anderson Cancer Center, US)

3:10 PM → 4:30 PM Game theory in ecology and evolution

3:10 PM Stackelberg evolutionary game theory: how to manage evolving systems

Stackelberg evolutionary game (SEG) theory combines classical and evolutionary game theory to frame interactions between a rational leader and evolving followers. In some of these interactions, the leader wants to preserve the evolving system (e.g. fisheries management), while in others, they try to drive the system to extinction (e.g. pest control). Often the worst strategy for the leader is to adopt a constant aggressive strategy (e.g. overfishing in fisheries management or maximum tolerable dose in cancer treatment). Taking into account the ecological dynamics typically leads to better outcomes for the leader and corresponds to the Nash equilibria in game-theoretic terms. However, the leader’s most profitable strategy is to anticipate and steer the eco-evolutionary dynamics, leading to the Stackelberg equilibrium of the game. In this presentation, we first introduce the concepts underlying SEG theory and follow with applications to fisheries management and cancer treatment, illustrating the benefit of taking eco-evolutionary dynamics into consideration.

Speaker: Alexander Stein (Universite Libre de Bruxelles & VIB-KU Leuven)

3:30 PM When policy shapes selection: anticipating evolutionary feedbacks in conservation

Evolutionary change is rapid, ubiquitous, and increasingly documented across managed ecological systems. Yet management decisions are still largely formulated as if ecological systems were static, with targets focused on abundance, habitat area, or harvest rates while evolutionary responses are treated as background processes or unintended side effects. This mismatch generates predictable outcomes: resistance to control, harvest-induced life-history shifts, and trait erosion under habitat simplification. Such responses are not anomalies but consequences of altered selection pressures created by policy itself. We argue that conservation should be reframed explicitly as an evolutionary decision problem in which management actions reshape fitness landscapes and populations adapt accordingly. Whether adaptation ultimately leads to persistence (evolutionary rescue) or collapse (evolutionary suicide) depends on how trade-offs are structured and how interventions modify ecological constraints. Through conceptual and mathematical examples, we show that policies designed to stabilise populations can inadvertently reduce evolutionary resilience, and that relocating evolutionary costs across demographic parameters can qualitatively shift system outcomes, revealing eco-evolutionary tipping points. Framing conservation as a hierarchical, leader–follower interaction between policymakers and evolving systems provides a principled way to anticipate adaptive feedbacks, identify extinction boundaries, and design interventions that balance short-term ecological stability with long-term evolutionary robustness. Integrating such eco-evolutionary foresight into conservation practice is essential for managing adaptive systems in a rapidly changing world.

Speaker: Maria Kleshnina (Queensland University of Technology)

3:50 PM Evolutionary Therapy in Non-Small Cell Lung Cancer

Resistance to targeted therapies remains a challenge in the treatment of metastatic non-small cell lung cancer (NSCLC). Standard Maximum Tolerated Dose (MTD) protocols often accelerate the competitive release of drug-resistant cell populations, leading to treatment failure. Evolutionary therapy (ET) offers an alternative approach, seeking to forestall resistance by exploiting density- and frequency-dependent competition between drug-sensitive and drug-resistant cells. The aggressive nature of NSCLC and clinical toxicity considerations motivate the exploration of dynamic dosing strategies.
In this study, we explore the theoretical efficacy of various treatment strategies in NSCLC using a data-driven mathematical modeling framework. Building on two-population ordinary differential equation (ODE) models validated against longitudinal tumour-burden data from NSCLC patients treated with Osimertinib, a tyrosine kinase inhibitor used as a first-line therapy, we compare different static and dynamic dosing protocols. Specifically, we focus on adaptive protocols where drug dosages are dynamically adjusted based on relative changes in tumour volume observed between clinical assessments. We also analyze how different clinical parameters, such as inter-test intervals and baseline doses, influence the Time to Progression (TTP).

Speaker: Kailas Honasoge (Delft University of Technology)

4:10 PM Exploiting evolutionary trade-offs in Anaplastic Large Cell Lymphoma though optimal targeted therapy

Anaplastic Large Cell Lymphoma (ALCL) is the most common peripheral lymphoma in children, with ~95% of pediatric cases driven by oncogenic ALK mutations [1, 2]. Although ALK inhibitors initially reduce tumor burden, continuous therapy (CT) leads to natural selection of resistant populations. Critically, this process in ALCL produces a strong reduction in cell viability in drug-free conditions (a phenomenon known as "drug addiction"), introducing an evolutionary trade-off that could be exploited with intermittent therapy (IT) [3]. However, this concept has found limited translation into clinical practice. In this work, we used patient-derived cell lines (PDCLs) and mathematical modeling to design an optimal treatment strategy based on evolutionary steering of drug resistance and addiction in ALCL.
Using a 180-day dose-escalation protocol, we confirm that PDCLs evolve resistance and addiction in vitro. We leverage the measure of the dose-response curve in time to calibrate a mathematical model recapitulating this process, and we simulate over 500 possible treatment schedules. An optimal strategy combining induction (60 days CT) followed by IT extended tumor control beyond one year, whereas CT alone predicted relapse within 150 days. To account for parameter uncertainty, we generated a virtual cohort by sampling 1000 parameter sets from estimated distributions. Across this cohort, the proposed schedule reduced tumor growth four-fold compared with CT, supporting the robustness of the strategy.
In conclusion, these results illustrate how integrating experiments with evolutionary modeling can identify treatment schedules that exploit adaptive trade-offs to prolong tumor control.
References
1. Lowe EJ, Woessmann W. Anaplastic large cell lymphoma in children and adolescents. Br J Haematol. 2025; 00: 1–14. https://doi.org/10.1111/bjh.20154
2. Brugières L, Le Deley MC, Rosolen A, Williams D, Horibe K, Wrobel G, Mann G, Zsiros J, Uyttebroeck A, Marky I, Lamant L, Reiter A. Impact of the methotrexate administration dose on the need for intrathecal treatment in children and adolescents with anaplastic large-cell lymphoma: results of a randomized trial of the EICNHL Group. J Clin Oncol. 2009 Feb 20;27(6):897-903. doi: 10.1200/JCO.2008.18.1487. Epub 2009 Jan 12. PMID: 19139435.
3. Amin, A. D. et al. Evidence Suggesting That Discontinuous Dosing of ALK Kinase Inhibitors May Prolong Control of ALK+ Tumors. Cancer Res. 75, 2916–2927 (2015).

Speaker: Franco Pradelli (Moffitt Cancer Center)

3:10 PM → 4:30 PM Heterogeneity in epidemic modelling

3:10 PM Genuine and spurious bistability in a simple epidemic model with waning immunity

We analyse an infection-age structured epidemic model where both infectivity and immunity loss depend on time since infection \cite{Scarabel2026}. The model can be formulated as a nonlinear renewal equation for the incidence or as a PDE for the infected population. Using ODE approximations and numerical bifurcation analysis, we study gamma-distributed infection durations and show that distribution shape critically affects endemic equilibrium stability, even when $R_0$ and the mean infectious period are fixed. We identify regions of bistability, where a stable endemic state coexists with a stable periodic orbit—providing, to our knowledge, the first example of such behaviour in models with waning immunity alone. Our analysis also shows how standard compartmental models, which impose implicit assumptions on infection duration, may yield to spurious dynamical outcomes.

Speaker: Francesca Scarabel (University of Leeds)

3:30 PM Network effect and behavioral feedback in epidemics

In recent years, there has been renewed interest in the modeling, analysis and control of epidemics. The classic SIR model presents limitations due to its assumption of fully mixed and homogeneous population. It is essential to consider network effects to account for heterogeneity in susceptibility, infectivity and interactions. In addition, different behavioral changes of the individuals may influence the epidemic. This talk first focuses on analyzing the SIR model on a network of interacting subpopulations. These subpopulations consist of homogeneously mixed individuals with differing activity rates, disease susceptibility and infectivity. In contrast to the classic SIR model, we show that infection curves can be multimodal in the single node. With rank-1 interaction matrix, we provide sufficient conditions for this multimodality and establish an upper bound on the number of monotonicity changes in the node-level infection curve. Additionally, we characterize the system's asymptotic behavior, with explicit expressions for limit equilibrium points and conditions for their stability. The second part of the talk analyzes a deterministic SIR model in which the transmission rate depends on the system state, reflecting behavioral adaptations in response to the epidemic. Under general conditions, we prove that the infection curve is unimodal. We then solve an optimal control problem to minimize intervention costs while keeping the infection curve below a desired threshold.

Speaker: Martina Alutto (KTH)

3:50 PM Modelling information-dependent protective behaviour in response to mosquito-borne epidemic outbreaks

We present a model for a mosquito-borne epidemic outbreak in which human hosts may adopt protective behaviour against mosquito bites according to the information they receive about disease prevalence. In line with the information index approach \cite{donofrio_information-related_2009}, we assume that individuals react to this information according to a memory kernel that is continuously distributed over the past.
Assuming that mosquitoes can also feed on noncompetent hosts, i.e. hosts that do not contribute to disease transmission, we revisit existing results \cite{demers_dynamic_2018, miller2016risk}, showing that behaviour-driven protection may either decrease or increase the reproduction number of the epidemic depending on several factors.
Furthermore, assuming that behavioural changes occur much faster than epidemic dynamics, it is possible to separate the timescales of the two mechanisms. By applying methods from Geometric Singular Perturbation Theory \cite{fenichel}, we derive an epidemic model with information index for a homogeneous host population.
The reduced system enables a detailed investigation of the impact of information-induced behavioural feedback on the transient dynamics of the epidemic, including scenarios in which protective measures lead to outbreaks with low attack rates \cite{ando_behavior-induced_2026}. Our analysis shows that behavioural responses may facilitate epidemic control, but may also prolong disease persistence, potentially generating recurrent damped epidemic waves. Numerical simulations are provided to illustrate and support the analytical findings.

Speaker: Simone De Reggi (Università di Trento)

4:10 PM SEIR Models With Host Heterogeneity: Main Properties And Applications To Seasonal Influenza Dynamics

Population heterogeneity strongly shapes epidemic dynamics, beyond age, space, or contact patterns.
We focus on host susceptibility differences within the SEIR framework, using the renewal equation approach of Diekmann and Inaba. Analytical results of SEIR models with heterogeneous susceptibility show that greater susceptibility variation reduces final epidemic size.

Speaker: Tamas Tekeli (University of Szeged)

3:10 PM → 4:30 PM Social dynamics and behavioural interactions in infectious disease modeling

3:10 PM Behaviour-driven epidemic phenomena in heterogeneous populations and networks

While realistic approaches have become increasingly important in epidemic modelling, behavioral factors and individual differences have historically been overlooked due to the lack of high-resolution data and appropriate mathematical methods. This gap became particularly evident during the recent pandemic, highlighting the need for large-scale data collection on individual-level epidemic-related behaviors across representative populations. These advancements have revealed several new and interesting spreading phenomena that challenge our previous understandings. In this talk, we will focus on two examples of such new insights, derived from data-driven and behavior-informed epidemic models. We will explore input-output inequalities in spreading dynamics \cite{Manna2024NatComms, Manna2024SciAdv}, and the paradoxical effects of awareness-driven adaptive behavior on epidemic outcomes \cite{Kolok2025PRR}. These findings highlight the role of behavioral factors, offering a more accurate understanding and modelling of real-world epidemic scenarios.

Speaker: Prof. Márton Karsai (Department of Network and Data Science, Central European University, Vienna, Austria; HUN-REN Rényi Institute of Mathematics, Budapest, Hungary)

3:30 PM Social Behaviour and Epidemic Dynamics: The Role of Imitation and Homophily

Epidemic dynamics are shaped not only by biological processes but also by how individuals perceive risk, adopt protective behaviours, and interact within socially structured populations. This talk explores how behavioural feedback and social homophily jointly influence the uptake of interventions and disease transmission dynamics. We will introduce a homophily-based modelling framework in which contact patterns and attitude change depend on vaccination beliefs. Individuals preferentially interact with others who share similar attitudes, while hesitant individuals may change their beliefs through social influence. We demonstrate how homophily reshapes epidemic outcomes by redistributing risk across attitudinal groups, creating localized pockets of high susceptibility and infection. Importantly, the results show that high overall vaccination coverage does not guarantee population-level protection when coverage is socially clustered, and that distinct homophily mechanisms or levels can produce similar vaccination coverage yet lead to vastly different epidemic outcomes. These results highlight the limitations of homogeneous mixing assumptions and underscore the need to integrate behavioural dynamics and social structure into network models of epidemics.

Speaker: Prof. Seyed M Moghadas (Agent-Based Modelling Laboratory, York University, Toronto, Ontario, Canada)

3:50 PM A Filippov Model Describing the Effect of Social Distancing in Controlling Infectious Diseases

Social distancing is now a familiar strategy for managing disease outbreaks, but it is important to understand the interaction between disease dynamics and social behaviour. We distinguished the fully susceptible from social-distancing susceptibles and proposed a Filippov epidemic model to study the effect of social distancing on the spread and control of infectious diseases. The threshold policy is defined as follows: once the number of infected individuals exceeds the threshold value, social-distancing susceptibles take more stringent social-distancing practices, resulting in a decreasing infection rate. The target model exhibits novel dynamics: in addition to the coexistence of two attractors, it also demonstrates the coexistence of three attractors. In particular, bistability of the regular endemic equilibrium and the disease-free equilibrium occurs for the system; multistability of the regular endemic equilibrium, pseudo-equilibrium and the disease-free equilibrium occurs for the system. Discontinuity-induced bifurcations, including boundary node, focus and saddle-node bifurcations, occur for the proposed model, which reveals that a small change in threshold values would significantly affect the outcome. Our findings indicate that for a proper threshold value, the infections can be ruled out or contained at the previously given level if the initial infection is relatively small.

Speaker: Prof. Stacey Smith? (Department of Mathematics and Faculty of Medicine, The Univeristy of Ottawa, Ottawa, ON K1N 6N5, Canada)

4:10 PM Impact of Avoidant Behavior on Influenza Dynamics Under Low Vaccine Efficacy

We present a comprehensive agent-based model designed to investigate the complex interplay between avoidant behavior and influenza transmission dynamics under varying levels of vaccine efficacy. The model’s architecture is grounded in an age-stratified contact matrix and stochastic transmission probabilities, where individual health outcomes are determined by their specific disease history. Crucially, we incorporate a behavioral component: while unvaccinated individuals tend to reduce social contacts—particularly with symptomatic peers—vaccination can paradoxically diminish perceived risk, leading to a reduction in such avoidant behaviors. Our simulations demonstrate that when vaccine efficacy is low, this 'behavioral compensation' can inadvertently increase the overall risk of infection. These findings underscore a critical public health message: seasonal vaccination campaigns for influenza and other airborne pathogens must look beyond immunization alone, actively promoting sustained precautionary measures, such as mask-wearing and hygiene, to mitigate the effects of reduced risk perception.

Speaker: Prof. Thomas Vilches (São Paulo State University, Botucatu, SP 18618-689, Brazil)

3:10 PM → 4:30 PM Mathematical and Computational Ophthalmology

3:10 PM Drug Release Dynamics from a Three-Layer Composite Contact Lens

Eye drops are typically used to deliver ophthalmic drugs that treat both acute and chronic eye disorders such as glaucoma. However, drugs delivered by this method quickly leave the tear film due to blinking and drainage. In contrast, drug-eluting contact lenses allow the drug to remain in the tear film much longer, thus serving as a potential drug delivery vehicle. Recently, such lenses have been designed by encapsulating drug-polymer films in contact lens hydrogels, where the drug-laden region takes an annular shape when viewed from the top down. Informed by in vivo data, we design a coupled partial differential equation three-layer model of contact lens drug release to mathematically investigate the effect of lens design characteristics on the time to 50% drug release (t50) in the vial, blister pack, and eye settings. In the eye setting, we incorporate our prior model that considers the effect of many blinks on the pre- and post-lens tear film drug concentrations. We simulate drug cumulative release profiles and study the variability of t50 across: (1) the ratio of the hydrogel to drug-polymer film diffusion coefficients, (2) the centerline of the polymer within the hydrogel, and (3) the polymer thickness. This work may help medical professionals better understand the mechanics of contact lens drug delivery and predict targeted tissue transport of drug.

Speaker: Dr Rayanne A. Luke (George Mason University)

3:30 PM A mathematical model of fluid and solute transport across the corneal endothelium

The cornea is the transparent tissue in front of the eye, composed of three main layers: endothelium (a monolayer of cells towards the anterior chamber), stroma and epithelium (towards the tear film). The cornea is kept at the correct hydration, essential for its
transparency, by the endothelium pumping water out of the stroma. In our previous work [1], we showed that local osmosis (water flux generated by the buildup of a concentration gradient in the channel between adjacent endothelial cells, called cleft) is the main driver of the endothelial pump. In this work, we refine our model to investigate another possible mechanism hypothesized in the literature, accounting for the presence of the lactate ion [2].

The model domain includes a well-mixed 0D compartment representing the cell and a 2D compartment representing the cleft. We consider 7chemical species (sodium, potassium, chloride, bicarbonate, carbon dioxide, protons, lactate) and a chemical reaction. We write
equations for fluid and ion balance, accounting for membrane channels and transporters, and for the tight junction closing the cleft on the anterior chamber side. Asymptotic analysis leads to a system of algebraic equations and ODEs, solved iteratively in MATLAB. We parametrize the model by optimizing the membrane permeability to ions against literature values.

With this model, we show the link between transendothelial lactate and water flux, and we investigate the role of bicarbonate [3] in their transport.

Speaker: Ms Federica Vanone (Gran Sasso Science Institute)

3:50 PM V-Cornea: A Multi-Scale In Silico Framework for Ocular Toxicology and IVIVE

Predicting injury severity and time-to-recovery after ocular chemical exposure is critical for chemical classification and risk assessment. Time-resolved in vitro data from localized injury on reconstructed corneal epithelium reveal concentration-dependent lesion evolution, including secondary propagation likely driven by necrotic cell rupture, yet these assays cannot alone predict tissue-level recovery. To address this gap, we extend V-Cornea, a published multi-scale agent-based model of epithelial homeostasis and recovery from slight to mild injuries \cite{Vanin2025}, with stochastic Boolean networks governing cell-fate decisions between survival, apoptosis, and necrosis \cite{Calzone2010} as functions of local chemical concentration. This extended framework serves as an in silico NAM and engine for in vitro to in vivo extrapolation (IVIVE). Leveraging the model as a computational hypothesis generator, we performed systematic sweeps of concentration and exposure duration, producing phase diagrams that map exposure conditions to outcome regimes ranging from containment to catastrophic spread. Without immune-mediated debris clearance, the damage loop lacks an off-switch, mirroring in vitro observations but diverging from in vivo recovery. This divergence defines the IVIVE boundary and motivates the introduction of immune dynamics to provide the missing recovery signals, enabling extrapolation to in vivo predictions of injury severity and recovery time.

Speaker: Dr Joel Vanin (Indiana University Bloomington)

4:10 PM Modeling the Ocular Immune Response to Seasonal Allergic Conjunctivitis and the Effects of Treatment

Seasonal allergic conjunctivitis (SAC) affects up to 40% of the population; however, the complex immune signaling processes that drive ocular inflammation are not fully understood. In this work, we present a quantitative mechanistic model of the cellular immune response during SAC. A system of 23 coupled ordinary differential equations is developed to represent interactions among allergens, immune cells, cytokines, chemokines, antibodies, and histamine in the conjunctiva.

To evaluate the model uncertainty, a local and global sensitivity analyses was conducted to identify the most influential parameters. Model validation was performed by comparing simulated cytokines concentrations to experimental cytokines concentrations in tears. Predicted histamine levels were further compared with clinical symptom scores, demonstrating a strong correlation.

The model highlights which pathways may be the most effective for therapeutic targets. We are currently working on extending the model to account for treatment of SAC using antihistamine drugs administered via eye drops or released by a pre-loaded contact lens. This modeling approach demonstrates potential applications in optimizing drug dosing, evaluating new therapeutic strategies, and predicting patient responses.

Speaker: Dr Lucia Carichino (Rochester Institute of Technology)

3:10 PM → 4:30 PM Data Science × Mathematical Modeling for Transforming Quantitative Life and Medical Sciences

3:10 PM Data and Modelling for Medical Inverse Problems

Electrical impedance tomography (EIT) is a medical imaging technique that uses electric currents and potential measurements on the surface of the body to infer the electrical conductivity within the body. To improve the reconstructed image, our models of biological tissues incorporate anisotropic conductivity, the electrophysiology of electrically active tissues, and the physics of ionic solutions. These partial differential equation models are solved numerically using boundary integral equation methods as well as biologically-informed neural networks. We take two parallel approaches to this medical inverse problem: numerical optimization and deep learning. Our approaches are validated against a large experimental dataset collected from our own EIT device. A second medical inverse problem is cardiography. The cells of the heart are electrically active and synchronized, which make measurement of the electrical activity of the heart readily observable in electrocardiograms (EKG). We model the electrical activity of the heart using the mono-domain model with detailed ionic current models and patient-specific heart geometry. We employ our simulation and vast collection of EKG recordings to pursue a variety of applications: a) visualize the shape of the heart as an indication of congestive heart failure; b) visualize the electrical conduction pathway within the heart to understand conduction disorders; and c) study circadian rhythms in the electrical activity of the heart.

Speaker: Adam Stinchcombe (University of toronto)

3:30 PM Multi-Omics–Driven Mathematical Framework for Integrating A Mechanistic Model and Data in Precision Medicine

Complex disease mechanisms in medical research are often inferred from limited patient samples, posing fundamental challenges in capturing inter-individual variability and selecting optimal therapeutic strategies. To address this limitation, I propose a new methodological framework, termed a multi-omics methodological framework, that systematically integrates mechanistic mathematical models with spatial transcriptomics data from patient biopsy samples, clinical trial outcomes, and virtual patients. Through the iterative integration of in silico simulations and data analysis based on the pathophysiology of virtual patients, this approach enables systematic analysis of disease mechanisms, therapeutic effects, and biomarker identification. As an application, I focus on inflammatory skin diseases to demonstrate how this framework uncovers latent structures underlying disease heterogeneity, particularly in terms of immune regulatory dynamics, and links them to variability in therapeutic responses.

Speaker: Sungrim Seirin-Lee (Kyoto University)

3:50 PM Towards Reliable Single-Cell Foundation Models: A Fully Data-Driven Framework for Signal Detection and Clustering via Mathematical Theories

The reliability of single-cell RNA sequencing (scRNA-seq) analysis is often hindered by subjective parameter tuning and stochastic inconsistencies, which pose significant challenges for the reproducibility of large-scale studies. To overcome these limitations and establish a rigorous foundation for single-cell foundation models, we propose a fully data-driven analysis framework based on mathematical and physical theories. Centrally, we introduce scLENS, which utilizes Random Matrix Theory (RMT) to distinguish biological signals from random noise. By employing RMT-based noise filtering and a signal robustness test, scLENS enables the objective determination of signal dimensions without manual intervention, ensuring high-fidelity feature extraction even in sparse datasets. Complementing this, scICE evaluates clustering consistency through the Inconsistency Coefficient (IC), providing a scalable and efficient way to identify stable cellular identities across tens of thousands of cells. By replacing subjective heuristics with robust, theory-based signal detection and evaluation, this integrated approach provides the essential high-quality, standardized data processing required to train and deploy reliable, large-scale single-cell foundation models in the era of artificial intelligence.

Speaker: JaeKyoung Kim (KAIST)

4:10 PM Equation Learning for Agent-Based Infectious Disease Models

Agent-based models (ABMs) capture heterogeneous contacts, stochastic transmission, and complex interventions in infectious disease dynamics but are computationally expensive, limiting parameter inference and policy analysis. We develop an equation-learning framework that derives interpretable ordinary differential equation (ODE) surrogates directly from stochastic ABM simulations. Using the COVID-19 ABM Covasim, we construct a 12-compartment ODE system incorporating testing and contact tracing while treating key epidemiological rates as state-dependent functions rather than constants. These functions are learned from ABM-generated trajectories using Biologically Informed Neural Networks (BINNs), which denoise state dynamics while enforcing epidemiological constraints. Sparse regression is then applied to obtain symbolic representations of the learned parameter functions to enable model interpretability. To quantify uncertainty arising from ABM stochasticity, we integrate Approximate Bayesian Computation to infer posterior distributions over model coefficients. The resulting ODE surrogates accurately reproduce ABM dynamics under constant and time-varying interventions and provide a fast, interpretable framework for analyzing complex epidemic models.

Speaker: Kevin Flores (North Carolina State University)

3:10 PM → 4:30 PM Differential modelling and numerics for human diseases

3:10 PM UQ analysis for cancer-on-chip experiments

In this talk, we will present our work to predict the dynamics of cancer-on-chip experiments using data-informed differential models \cite{article_bbbtz}.

We will consider a complex one-dimensional network along which tumor and immune cells evolve in response to chemotactic signals. This model is managed by coupled partial differential equations and solved by a Hybridized Discontinuous Galerkin method \cite{url_b}.

Synthetic data will be used to tune the parameters of the governing equations employing Bayesian inversion techniques. After this, we will assess the uncertainty on the predictions of the dynamics due to the uncertainty remaining on the parameters after the tuning procedure (i.e., their posterior distribution).

Finally, we will focus on surrogate models to make the analysis computationally affordable. Especially, we will exploit surrogates to approximate the mapping of the uncertain parameters to the quantities of interest of the system (e.g. the concentration of immune and tumor cells or the total amount of chemoattractant).

Speaker: Laura Rinaldi (CNR - IMATI)

3:30 PM HDG-Based Discretization of a Mathematical Model for Multiple Sclerosis

Multiple sclerosis is a complex neurodegenerative disorder whose progression can be described through nonlinear mathematical models accounting for both inflammatory and degenerative processes.
In this work, we investigate the application of the Hybridized Discontinuous Galerkin (HDG) method to the numerical approximation of such models.
The HDG framework retains the flexibility of discontinuous Galerkin schemes while significantly reducing the number of globally coupled degrees of freedom, thereby enhancing computational efficiency without sacrificing accuracy.
We consider the model introduced in \cite{desvillettes2022global}, derive the corresponding HDG discretization, and provide a rigorous convergence analysis of the proposed method.
The theoretical findings are validated by numerical experiments confirming the predicted convergence behavior. Overall, the results highlight the suitability of HDG methods for the simulation of multiple sclerosis dynamics and support their use as reliable tools for the numerical approximation of complex biomedical models.
This work is realized with the support of the Italian Ministry of Research, under the complementary action NRRP “D34Health - Digital Driven Diagnostics, prognostics and therapeutics for sustainable Health care” (Grant #PNC0000001).

Speaker: Micol Pennacchio (CNR - IMATI)

3:50 PM 1D/2D Coupling of HDG discretizations for the simulation of Cancer-on-chip devices

We present a framework for the simulation of Cancer-on-chip devices where independent software codes handling respectively the 2d chambers and the 1d channels are coupled by the approach proposed in \citations{bertoluzza2026abstract}. The 2D and 1D codes, that the coupling mechanism treats as black boxes and that can be therefore be individually replaced by the user’s preferred code, are presently both based on Hybridized Discontinuous Galerkin (HDG) discretizations \cite{bertoluzza2023hdg}. For the 2D chambers, an “in house” matlab code is used, while the 1D channels are handled using BioNetFlux, a python library for the simulation of biological fluxes in complex one-dimensional networks, that we developed in the framework of the “Digital Driven Diagnostics, prognostics and therapeutics for sustainable Heath care (D34Health)”.

This work is realized with the support of the Italian Ministry of Research, under the complementary action NRRP “D34Health - Digital Driven Diagnostics, prognostics and therapeutics for sustainable Health care” (Grant #PNC0000001).

Speaker: Silvia Bertoluzza

4:10 PM Numerical Study and Parameter Estimation on a Pressureless Euler-Type Model with Chemotaxis for Collective Cell Migration

The study of collective dynamics has attracted growing interest across multiple scientific fields due to its ability to describe self-organization and its broad range of applications. Many natural systems, including cell dynamics, display global patterns arising from local and nonlocal interactions. A distinctive feature of collective cell migration is its dependence not only on mechanical interactions but also on chemical signaling, which drives cells toward higher concentrations of specific substances \cite{bretti2021estimation}. Modeling such phenomena through mathematical models and numerical approaches has become increasingly important, enabling the development of in silico models to study complex processes. However, microscopic models of cell migration are computationally expensive, especially when dealing with large numbers of cells in high-dimensional settings.
In this talk we investigate a multidimensional pressureless nonlocal Euler-type model with chemotaxis, derived from hybrid ODE-PDE microscopic dynamics \cite{natalini2023mean}. The goal is to explore the role of nonlocal mechanical interactions, such as attraction-repulsion effects, and the extension to multi-population models \cite{menci2023microscopic, menci2026numerical}. Beyond the assumptions under which the limit has been rigorously derived, the validity of the macroscopic model and its agreement with the microscopic dynamics is assessed in more general scenarios. Finally, parameter estimation is performed to identify optimal values and enable comparisons with the underlying microscopic dynamics.
This is a joint work with Marta Menci (Universit`a Campus Bio-Medico di Roma) and Roberto Natalini (IAC-CNR).

Speaker: Tommaso Tenna (Università Sapienza Roma)

5:00 PM → 6:20 PM Modeling Avian Influenza Dynamics

5:00 PM Tracking the evolution, spread and reassortment patterns of avian influenza viruses using sequence data and phylodynamic modelling

Genetic reassortment, the exchange of gene segments between distinct influenza A virus genomes, is a key mechanism driving the emergence of novel variants. In avian influenza viruses, reassortment are extremely frequent and accompanies phenotypic changes. Since 2020, clade 2.3.4.4b H5 high pathogenicity avian influenza viruses (HPAIVs) have driven a global panzootic, causing mass mortality in wild birds, poultry and repeated spillover infections in a variety of mammalian species. This resurgence of H5 HPAIV has coincided with a dramatic increase in the number of circulating reassortant strains; however, the scale, impact and drivers of these reassortants remain unknown. Here, we combined statistical and phylodynamic modelling to reconstruct the global evolutionary dynamics of H5Nx viruses across four epizootic seasons. We identified over 200 genetically distinct reassortants, stratified into three transmission categories based on their phylogenetic and epidemiological profiles. Statistical modelling revealed that reassortant success was strongly shaped by ecological factors, including circulation in specific wild bird orders and the ability to infect a wider range of host niches. Collectively, our findings reveal reassortment dynamics in H5 HPAIVs and identify key virological and ecological. These insights support the importance of enhanced surveillance to track evolution of H5 HPAIV and identify traits relevant for consideration in pandemic risk assessment.

Speaker: Lu Lu (Roslin Institute, University of Edinburg)

5:40 PM A modelling assessment of the impact of control measures on highly pathogenic avian influenza transmission in poultry in Great Britain

Since 2020, highly pathogenic avian influenza (HPAI) H5N1 outbreaks in Great Britain have resulted in substantial poultry mortality and economic losses. There are additional concerns of increased HPAI circulation leading to a viral reassortment that causes zoonotic spillover. However, the mechanisms driving transmission between poultry premises and the impact of potential control measures in Great Britain, such as vaccination, are not fully understood. To enhance understanding of the disease transmission process and the potential measures that could be used to avert future infections, there is a need for mathematical models to be calibrated to outbreak data. I will present a spatial transmission model for the spread of HPAI in poultry premises calibrated using Markov chain Monte Carlo to infected premises data for the 2022–23 influenza season in Great Britain. The model formulation adapts existing spatial individual poultry premises-based models - such as Jewell et al. \cite{jewell2009novel} and Hill et al. \cite{hill2017modelling, hill2018impact} - for Great Britain. I will then overview model simulations investigating the potential epidemiological impacts of reactive enhanced control strategies that reduce susceptibility of poultry (e.g. enhanced biosecurity measures and/or vaccination). Our findings highlight thatenhanced control measures could limit the future impact of HPAI on the poultry industry and reduce the risk of broader health threats \cite{davis2026modelling}.

Speaker: Edward Hill (University of Liverpool)

6:00 PM Modelling H9N2 AIV transmission along poultry production and distribution networks in Bangladesh

H9N2 avian influenza viruses (AIVs) are endemic in Bangladesh and are consistently detected at high prevalence within live bird markets (LBMs). Despite its low pathogenic status, H9N2 AIV can hamper poultry meat and egg production. Moreover, its sheer prevalence in LBMs is concerning due to the associated risks of zoonotic spillover and viral reassortment with other co-circulating AIV subtypes (e.g. H5N1). In this presentation, I will first summarise recent modelling efforts leveraging observational data from a large, collaborative project to characterise H9N2 AIV epidemiology in LBMs. In particular, I will discuss the main drivers of virus persistence and diversity within LBMs. I will then show that within-LBM AIV dynamics cannot be fully understood without considering the rest of the production and distribution network (PDN) where LBMs are the terminal nodes. Indeed, upstream activities like poultry farming and transport are found to provide opportunities for the transmission and dissemination of infectious agents along the PDN. Finally, I will introduce a novel agent-based modelling framework to describe AIV transmission at the scale of the entire PDN. The model involves multiple actors and settings, including farms, mobile traders and LBMs, and uses extensive survey data to inform their behaviour. Our results demonstrate the importance of accounting for the entire PDN structure to implement more effective veterinary public health measures to reduce the burden of H9N2 AIV.

Speaker: Francesco Pinotti (INRAE, VetAgro Sup, UMR EPIA, Université de Lyon)

5:00 PM → 6:20 PM Reaction networks: Mathematical structures and concrete biochemical systems

5:00 PM Existence of a unique non-degenerate solution to parametrized systems of generalized polynomial equations

We consider solutions to parametrized systems of generalized polynomial equations (with real exponents) in $n$ positive variables, involving $m$ monomials with positive parameters; that is, $x \in \mathbb R^n_>$ such that ${A \, (c \circ x^B)=0}$ with coefficient matrix $A \in \mathbb R^{l \times m}$, exponent matrix $B \in \mathbb R^{n \times m}$, and parameter vector $c \in \mathbb R^m_>$ (and with componentwise product $\circ$).

We demonstrate that the existence of a unique nondegenerate solution for all parameters is equivalent to a specific moment map being a diffeomorphism. We characterize this property using Hadamard's global inversion theorem and establish sufficient conditions based on the sign vectors of the underlying geometric objects. This result represents a multivariate generalization of Descartes' rule of signs for exactly one nondegenerate solution.

Speaker: Abhishek Deshpande (International Institute of Information Technology, Hyderabad)

Existence of a unique non-degenerate solution for all parameters

5:20 PM Unbounded oscillations in the Selkov model of glycolysis with Michaelis-Menten kinetics

Glycolysis, the process by which energy is extracted from sugar, is known to exhibit oscillations and it has been shown experimentally that these arise in a reaction catalysed by the enzyme phosphofructokinase. Selkov introduced a simple model for this phenomenon which is a system of two ODE with mass action kinetics (in what follows the MA system). It is derived by a limiting process from a system with Michaelis-Menten kinetics (in what follows the MM system). Selkov claimed that the MA system has solutions with unbounded oscillations but that these are an artefact of the limiting process and are not present in the MM model. With Pia
Brechmann we gave a rigorous proof of Selkov's first claim. In this talk I present evidence that his second claim is not correct. A key step in the existence proof was showing that the MA system admits a heteroclinic cycle at infinity. I present a proof that the MM system also admits a heteroclinic cycle at infinity. I then explain what is needed to pass from this statement to the statement that there exist unbounded oscillations in the MM system.

Speaker: Alan Rendall (Johannes Gutenberg University Mainz)

5:40 PM Instabilities and pattern formation in distributive double phosphorylation

Reaction-diffusion equations provide a framework for understanding how spatial patterns emerge from biochemical networks. In quantitative biology, however, parameter values are frequently accompanied by large confidence intervals due to measurement uncertainty and limited experimental repetitions. This necessitates the study of entire families of parametrized PDEs to determine their qualitative behavior.

In this talk, we focus on a reaction-diffusion model of distributive double phosphorylation with unknown parameters. As numerical exploration of high-dimensional parameter spaces is often computationally prohibitive, we present an analytical approach to identify regions of the parameter space where the system exhibits Turing-like instabilities.

We derive a polynomial inequality — depending only on the catalytic constants and the diffusion constants of the enzyme-substrate complexes — that guarantees the existence of positive eigenvalues in the linearization of the PDE system, regardless of the values of the remaining constants. Notably, this description is structurally similar to the semi-algebraic conditions characterizing multistationarity in the corresponding ODE setting.

This is joint work with Maya Mincheva and Hannes Uecker.

Speaker: Carsten Conradi (Hochschule für Technik und Wirtschaft Berlin)

6:00 PM Asymptotic stability of delayed complex balanced reaction networks with general kinetics

Time delays are often present in natural and technological processes, and can be essential for the precise understanding and description of important phenomena. On the other hand, chemical reaction networks (CRNs) provide a general framework for describing general nonnegative nonlinear dynamics. It is known that complex balance is a property of fundamental importance, which guarantees a strong robust stability for CRNs. It was proved in the 2010's that delayed complex balanced CRNs with mass action kinetics are asymptotically stable for arbitrarily large discrete delays and also for any practically meaningful distributed delay. In this contribution, these results are extended to CRNs with general non-mass-action kinetics having a product structure. The applicable reaction rates include e.g., Michaelis-Menten and Hill kinetics. It is shown that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is locally asymptotically stable relative to the class. The stability of the equilibria is shown using appropriate logarithmic Lyapunov–Krasovski functionals both in the discrete and the distributed delay case. The results further underline the importance of complex balance in the theory of general dynamical systems.

Speaker: Gábor Szederkényi

5:00 PM → 6:20 PM Prospectives in HIV

5:00 PM Modelling longitudinal vaccine-elicited immune profiles in people living with HIV

The immune response to vaccination is highly heterogeneous and arises
from a dynamic interplay of immune components. In this talk, I will
discuss how we employed random forests (RFs) to classify differences
in immunogenicity between older people with HIV (PWH) on ART and
age-matched controls who received up to five SARS-CoV-2 vaccinations
[1]. Harnessing machine learning (ML) to learn immune
interdependencies offers the potential to decode immune signatures
linked to a specified comorbidity, and further reveal individualized
patterns laying the groundwork for precision-guided vaccination and
targeted clinical follow-up. Our data set contains an extensive range
of immune features, including serum and saliva IgG and IgA responses,
ELISpot IFNg and IL2 responses to SARS-CoV-2 spike peptides, ACE2
receptor displacement, and SARS-CoV-2 neutralization capacity; all
tracked longitudinally up to 104 weeks in each individual following
SARS-CoV-2 vaccine doses 1 through 5. In this biomarker space, RFs
identify highly important and unimportant combinations of features
that distinguish PWH from controls, and further reveal a subset of PWH
whose immune signatures resemble controls, suggesting near-complete
immunologic restoration from a vaccine perspective in these
individuals. Our results highlight the effectiveness in utilizing RFs
to identify complex immunological interdependencies.

Speaker: Chapin Korosec (University of Guelph)

5:20 PM Mathematical Modeling of HIV-Driven Accelerated Biological Aging via Long-Lived Cell Reservoirs

Suppressive antiretroviral therapy (ART) has been shown to only partially mitigate biological aging by plasma proteomic clocks in people living with HIV (PLWH). Despite effective viral suppression, treated individuals exhibit a measurable increase in biological age relative to uninfected controls, with more pronounced effects reported in younger populations.
In this talk, an eight-compartment ordinary differential equation (ODE) model is presented, in which a three-stage HIV viral dynamics sub-model is coupled with a long-lived cell (LLC) reservoir. This reservoir comprises tissue-resident macrophages and memory CD4+ T cell populations and is further linked to chronic inflammation, cellular senescence, and cumulative biological age advancement, denoted by Δ(t).
Mathematical analysis indicates that post-ART inflammatory decay is governed by the LLC reservoir half-life and that residual biological age accumulation is directly proportional to the reservoir size at treatment initiation. Under this framework, ART initiation at year 2 results in an estimated age advancement of Δ = 1.37 years, and initiation at year 4 yields Δ = 3.81 years. These results quantify the cumulative biological cost associated with delayed treatment initiation.

Speaker: Esteban Hernandez-Vargas (University of Idaho,)

5:40 PM A stochastic model of HIV viral rebound after treatment interruption

Human Immunodeficiency Virus (HIV) infections can be effectively controlled with the use of antiretroviral therapy (ART), which keep viral loads below detectable levels. Currently, individuals with HIV must adhere to treatment for the rest of their lives to manage the virus. This is due to the existence of the HIV reservoir – a population of cells that are latently infected by HIV – which can reactivate and cause viral rebound in individuals who stopped ART. Interestingly, the time to viral rebound is variable from weeks (in most individuals) to years. Mechanisms behind viral rebound or factors that could influence the timing of viral rebound remain largely misunderstood. We have developed a simplified model that simulates the seeding of the reservoir and viral rebound after treatment interruption. Using this model, we explore different factors that could be associated with extending the time to viral rebound.

Speaker: Jasmine Kreig

6:00 PM Investigating Heterogeneity in HIV Viral Rebound Times

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. While typically suspension of therapy is rapidly followed by rebound of viral loads to high, pre-therapy levels, there is an important nuance: in a small fraction of cases, rebound may be delayed by months, years, or even possibly, permanently. We will discuss modeling to investigate that heterogeneity in outcome of treatment suspension, focusing on time to viral rebound. We will first discuss our data-validated, mechanistically-motivated survival function for time-to-rebound using time-inhomogeneous branching processes. We show good agreement with data for both rapid and significantly delayed viral rebound. We will then use this model to characterize the impact of covariates such as treatment initiation time and pre-ART drug regimen on time to rebound.

Speaker: Jessica Conway (Penn State, USA)

5:00 PM → 6:20 PM Recent mathematical discoveries in Population Dynamics, Ecology and Evolution

5:00 PM Mathematical of pre-exposure prophylaxis and the quest to end the HIV epidemic

The use of pre-exposure prophylaxis (PrEP), where approved antivirals are administered to uninfected high-risk individuals, is universally regarded as a promising strategy to prevent susceptible high-risk individuals from acquiring HIV infection from their infected partners. A number of antiviral drugs (and their combinations) have been developed and are being used as prophylaxis against the HIV epidemic here in the U.S. and globally. We will first present a risk-structured mathematical model for assessing the population-level impact of PrEP in an MSM (men who have sex with men) population. An extended model, which considers several high-risk populations, will also be presented and used to assess the potential spillover effect, where the administration of PrEP to individuals in one risk group induces a reduction of disease burden in other risk group(s). The central aim is to determine whether the use of the aforementioned strategies can aid the End the HIV Epidemic initiative, aimed at eliminating the disease in the U.S. by 2030.

Speaker: Abba Gumel (University of Maryland)

5:20 PM How the Tulips get their Stripes

Tulips have captivated human interest for centuries, with their vibrant colors and unique shapes. Particularly striped tulips have been highly popular, leading to the “tulipomania” in the Dutch Golden Age. But how do the tulips get their stripes? Maybe Turing can help?

Speaker: Thomas Hillen (University of Alberta)

5:40 PM Changing Connectivity: A Spatial Understanding of Bistable Coral Dynamics

Modeling coral ecosystems in a theoretical framework typically focuses on tradeoffs between coral, algae, and grazing fish populations, highlighting its bistable dynamics; however, spatial understanding of this system is often suppressed. Analysis of models with spatial features is crucial, as degraded, patchy reef systems become more common, and the size, clustering, or overall connectivity of these patches play a key role in the persistence and the emergent dynamics. More broadly, the implications of spatial heterogeneity and connectivity in systems with alternative stable states are complex and underexplored. In this work, we explore the long term dynamics, through both numerical and mathematical analysis, of a spatial model of a coral ecosystem, extended to multiple reef patches. Our results explore the “mixed-blessing” that connectivity can have on coral metacommunities.

Speaker: Jennifer Paige (University of California, Davis)

6:00 PM Mathematical Models for evolutionary phenomena during range expansion

It has become increasingly evident that evolution can take place in ecological time scales. One such example is that of evolution of dispersal during range expansion. As individuals with higher motility get to the leading edge faster, if these individuals benefit from low competition therein, they reproduce, and their offspring are then equally able to colonize unexplored regions. Over time, individuals at the leading edge become much better at dispersal than their conspecifics at the range core, leading to faster spread of the population. This has been observed in nature for some species, most notoriously the cane toads in north Australia and red-shouldered soapberry bugs in Texas, USA, but also tested experimentally in bacteria, mites, bean bugs and thale cress. In light of such observations and the challenge they present in our understanding of range expansions, mathematical perspectives that once relied on describing population dispersal based on average phenotypes began to account for population variability in dispersal. In this talk, I plan to go over some of such models and some of our contributions, and show how evolution changes population asymptotic spreading speeds and leading edge population trait distributions during range expansion.

Speaker: Silas Poloni (Roskilde University)

5:00 PM → 6:20 PM Modeling of neural dynamics and neurodegeneration

5:00 PM Control treatments on surface-dependent formation and dissolution of amyloid plaques in Alzheimer's disease

The extracellular amyloid plaques, whose primary component is the amyloid-beta peptide (A$\beta$), are a key hallmark of Alzheimer’s disease. A four-compartment mathematical model for the A$\beta$ movements and aggregation processes has been proposed in [1]. The growth of the amyloid plaques is assumed to depend on their surface area, using an area-to-volume shape index. In this talk, at first, we refine the model proposed in Ficiarà 2023. In particular, we assume that also the possible dissolution of amyloid plaques is surface-dependent, analogously to their formation. Then, we incorporate terms modeling possible treatment actions to enhance A$\beta$ disaggregation and reduce A$\beta$ aggregation. Specifically, we take into account that a low A$\beta$ level in the cerebrospinal fluid is considered a positive biomarker of Alzheimer’s disease. In addition, we assume that treatments become increasingly inefficient as the disease progresses. Finally, we reformulate the refined model as an optimal control problem to reduce the amyloid plaques and minimize treatment actions and costs.

Speaker: Francesca Acotto (Dipartimento di Matematica "Giuseppe Peano", Università di Torino)

5:20 PM Tonic-clonic seizure transitions as bifurcations in a neural field model

Epilepsy is a dynamic complex disease involving a paroxysmal change in the activity of millions of neurons, often resulting in seizures. Tonic-clonic seizures are a particularly important class of these and have previously been theorised to arise in systems with an instability from one temporal rhythm to another via a quasi-periodic transition. We show that a recently introduced class of next generation neural field models has a sufficiently rich bifurcation structure to support such behaviour. This is used to seed a more exhaustive numerical bifurcation analysis that highlights the preponderance of the model to generate torus bifurcations. Since the neural field model is derived from a biophysically meaningful spiking tissue model we are able to highlight the neurobiological mechanisms that can underpin tonic-clonic seizures as they relate to levels of excitability, electrical and chemical synaptic coupling, and the speed of action potential propagation.

Speaker: Roberto Barrio (Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain)

5:40 PM A Functional Network Method for Monitoring State Changes in Neural Activity

Our lab uses multi-electrode probes to monitor the electrical activity from
populations of neurons in the gustatory cortex of the mouse as it drinks a liquid. We
simultaneously measure when licks occur. Is it possible to use the neural recordings
to determine when licks occur or what tastant is presented at various time points? We
describe a new method for doing this using functional networks and analysis tools from
network science. We demonstrate that this tool, NeuroSeq, is capable of determining
dynamic state changes in the activity of the neural ensemble, and that many of these
correspond to stimuli or mouse behavior. This functional network approach
is an alternative to Hidden Markov Models that allows the user more control in
determining what features of the data are used in the determination of states and state
changes. It is generally applicable to the analysis of spike trains from any
brain region.

Speaker: Richard Bertram (Florida State University)

6:00 PM Modeling the formation of perinuclear crowns made of agglutinated ATM proteins observed in fibroblasts from patients affected by Alzheimer’s disease

Alzheimer’s disease is a progressive neurodegenerative disorder characterized by the irreversible loss of neurons. Under normal conditions, ATM proteins exist as inactive homodimers in the cytoplasm. When oxidative stress occurs, these dimers dissociate into monomers that migrate to the nucleus, where they detect and repair double-strand DNA breaks. However, recent findings indicate that in all cells from Alzheimer’s patients, the ApoE protein, overexpressed and abnormally clustered around the nucleus, binds to ATM monomers. This interaction traps ATM–ApoE heterodimers at the nuclear envelope. As a consequence, the remaining ATM monomers, present at unusually high concentrations, rapidly re-dimerize before reaching the nucleus. These retained dimers accumulate at the perinuclear region, leading to the formation of a distinctive perinuclear crown. To better understand the mechanisms underlying this phenomenon and to explore potential therapeutic strategies, we developed two complementary modeling approaches: a compartmental model and a reaction–diffusion system that describes the physical and biochemical interactions between ATM and ApoE proteins. Both models integrate key processes such as protein transport, monomer aggregation, dimer and complex dissociation, and spatial constraints at the nuclear envelope. Using these models, we investigated how irradiation and antioxidant treatments influence the disintegration of the perinuclear crown. Our simulations show that while each strategy alone has a measurable effect, their combined application is significantly more effective in delaying or preventing the reformation of the crown. This synergy points toward a promising therapeutic direction for mitigating cellular dysfunction in Alzheimer’s disease.

Speaker: Laurent Pujo-Menjouet (Université Claude Bernard Lyon 1, France)

5:00 PM → 6:20 PM Plant models: mechanics, development and environment

5:00 PM Going underground: roots and rhizosphere hydraulic processes impacting plant response to drought

Plants respond to soil and atmospheric water deficits through strategies such as stomatal regulation and belowground adaptations. Root mucilage buffers erratic fluctuations in the rhizosphere water content, yet its influence on soil hydraulic properties, especially unsaturated hydraulic conductivity, and stomatal regulation remains unknown. We hypothesized that mucilage facilitates water uptake by attenuating the drop in matric potential at the root–soil interface during soil and atmospheric drying. We measured the impact of various maize (Zea mays) mucilage contents (0.0%, 0.05%, 0.2%, and 0.4%) on the water retention and hydraulic conductivity of a loamy soil. Leveraging a soil–plant hydraulic model, we investigated the effects of mucilage contents on transpiration and stomatal responses under soil drying and increased vapor pressure deficit (VPD). Higher mucilage contents prevented sharp declines in unsaturated hydraulic conductivity as soils dried. Simulations revealed that higher mucilage contents delayed the onset of hydraulic stress (the threshold transpiration rate beyond which a small increase in transpiration would result in a disproportionate decline in leaf water potential), broadened the hydroscape zone, and shifted stomatal behavior from isohydric to more anisohydric regulation, enabling plants to sustain stable transpiration and lower midday leaf water potentials under drought. The buffering effects on soil–plant hydraulics persisted across varying degrees of VPD, although high mucilage contents accelerated soil drying, indicating a trade-off between improved water uptake and faster moisture depletion during prolonged drought. Our findings underscore the important role of mucilage in modulating soil–plant water relations and stomatal regulation, offering insights into strategies for improving plant responses to soil and atmospheric drought.

Speaker: Mutez Ahmed (Root-Soil Interaction, School of Life Sciences, Technical University of Munich, Freising, Germany)

5:20 PM Geometry hidden in plain stress, Exploring the relationship between pressure-induced stresses and geometry in plant tissues.

Mechanical stresses play a central role during the morphogenesis of multicellular structures. Not only do they generate tissue deformations but they also provide cells with signals triggering differentiation and pacing development. This is especially true in growing plant epithelia where turgidity generates tremendous stresses within cell walls. From a systematic perspective, one can wonder what kind of signalling cues, turgor-induced stresses can provide growing cells with? In this presentation, we will first see how, in the case of symmetric and closed epithelia, such stresses can be related to a specific kind of geometrical descriptors: Killing vectors fields. We will then relax the symmetry assumption and evoke how this connection can be extended to pseudo Killing fields.

Speaker: Olivier Ali (Laboratoire Reproduction et Développement des Plantes (RDP), Université de Lyon, ENS de Lyon, Inria)

5:40 PM Fluid mechanics of the plant cell wall: from cellulose reorientation to twisting growth

Twisted shapes in plants, seen in helical roots, spiral grains and climbing vines, are both ubiquitous and consequential. They affect crop yield, impact lumber quality, and inspire biomimetic robotics. Understanding their mechanical origins begins at the single-cell level. The cell wall is a complex material: a pectin matrix reinforced by cellulose microfibrils that dynamically reorient during deformation. Under constant turgor pressure, anisotropic wall extension drives growth. We combine theories of transversely isotropic fluids, pressure-driven viscous sheets, and dynamic fibre-reorientation, developing a model for helical cell wall extension. The talk will present the model and semi-analytical solutions, including recent results on an internalised control mechanism for the growth and twist rates, and a generalised Lockhart equation that relates cell morphology to cellulose dynamics. This framework provides a key step towards explaining and controlling twisting morphology at the tissue and organ scales, which in turn underpins food security, sustainable development, and bio-inspired design.

Speaker: Galane Luo (School of Mathematics, University of Birmingham, UK)

6:00 PM The biomechanical basis of fixed handedness coiling in Cardamine fruit valves

While the rest of the plant does not show any twisting or coiling, the valves of Cardamine hirsuta coil with fixed right-handedness when released from the rest of the fruit at the end of its maturation. Through multi-scale biomechanical modeling of the valve, supported by live confocal imaging data of cortical microtubules (CMT), we show how CMT dynamics in the final phases of valve maturation can explain the coiling process. By coupling organ-level to tissue-level behaviour, we show the effect of a multi-layered cell wall structure and which hypotheses are required on the cell wall mechanical properties to quantitatively fit the coiling. Finally, we investigate the range of forces in the cell wall and tension on individual CMTs while the epidermal cells of the valve undergo a dramatic cytoskeletal reorientation from transverse to longitudinal — pivotal for the entire process — speculating on the possible causes of the consistent angular tilting ultimately achieved by the CMT.

Speaker: Gabriella Mosca (Center for Plant Molecular Biology, University of Tuebingen, DE)

5:00 PM → 6:20 PM Stochastic Dynamics and the Realities of Experimental Observation

5:00 PM Modeling mechanisms of neuronal microtubule dynamics and polarity

Microtubules are protein polymers comprised of tubulin, which are polarized and facilitate intracellular transport. A stable microtubule structure is important to ensure the long-term survival of neurons. However, microtubules also need to be dynamic and reorganize in response to injury events, which results in an increase in microtubule dynamics. How this complex balance is achieved on different scales remains an open question. Using experimental data and a stochastic mathematical model that limits microtubule growth, we seek to understand how nucleation, or new microtubules, can impact microtubule dynamics in dendrites of fruit fly neurons. We develop a partial differential equation (PDE) model that describes microtubule growth and nucleation dynamics to gain analytical insight to our stochastic model, and we compare analytical results to results from the complex stochastic model. Insights from these models can then be used to understand how microtubules can organize into polarized structures in neurons, where several mechanisms have been hypothesized to regulate microtubule polarity organization. Guided by experimental results, we implement our stochastic model with spatial polarity mechanisms to understand the efficacy of proposed biological mechanisms at establishing and maintaining the microtubule polarity observed in healthy neurons. Finally, we utilize our framework to explore mechanisms important in injury, where microtubule polarity is known to reverse.

Speaker: Anna Nelson

5:20 PM Three-Dimensional Modeling of Kinesin Mechanics in Optical Traps

Mechanical properties of molecular motors such as kinesin are often measured using optical traps. We develop three-dimensional stochastic models based on force and torque balances for two experimental setups: the single-bead assay and the three-bead assay. Our goal is to provide insight into how modeling choices in force–velocity and force–detachment relationships influence motion along the microtubule, and how these choices may fail to accurately represent experimentally observed displacements. We identify key misconceptions, particularly relating to the detachment times that arises when out-of-plane components are neglected. Finally, we discuss the limitations of these models and their discrepancies with experimental data.

Speaker: Christel Hohenegger (University of Utah)

5:40 PM Analyzing Partially Observed Stochastic Epidemic Networks

Understanding how epidemics spread on contact networks when the data are incomplete remains one of the central challenges in mathematical epidemiology. In this talk, I will describe a framework for analyzing stochastic epidemic models under partial observation, combining ideas from dynamical survival analysis (DSA), pairwise survival models, and recent exact closure results for SIR dynamics on random networks.

The starting point is to use DSA to estimate effective reproduction parameters directly from observed infection and recovery times, without requiring full knowledge of the underlying contact structure. These estimates are then combined with pairwise survival models, following Kenah and collaborators, to account for local dependence and correlations between connected individuals. To connect these approximations to large-network behavior, I will also discuss recent results on exact closure for configuration-model epidemics.

Taken together, these elements provide a tractable and interpretable approach to inference and uncertainty quantification in network-based epidemic models.

Speaker: Grzegorz Rempała (The Ohio State University)

6:00 PM Generative models for particle tracking microscopy

I will discuss the use of diffusion models for particle tracking microscopy images. The goal is to have a fully integrated generative model that connects stochastic models of particle motion to microscopy image data. Unfortunately, the observation likelihood function is too complex to explicitly model, and we do not know this function. Learning the likelihood function from a suitably large image set is the primary purpose of so-called diffusion models. We discuss the application of these neural network models for evaluating the log likelihood of image sets given particle positions.

Speaker: Jay Newby (University of Alberta)

5:00 PM → 6:20 PM Mathematical modelling of telomere dynamics

5:00 PM MS166-1

Speaker: Ana Portillo (University of Valladolid)

5:20 PM Stochastic modelling of telomere length dynamics in cell populations with ALT survivors

Telomeres are repetitive sequences of DNA at the end of linear chromosomes. Their length decreases at each cell division, leading to replicative senescence in the absence of elongation mechanisms. In some unicellular organisms, as the yeast Saccharomyces Cerevisiae, telomere length homeostasis is maintained by the enzyme telomerase [Martinez-Fernandez]. In liquid dilution experiments of yeasts with inactivated telomerase, emergence of cells presenting an alternative recombination-based mechanism (ALT) is observed after replicative senescence. The origin and dynamics of ALT cells are not yet well understood [Kockler] and the goal of this talk is to present a stochastic modelling approach to characterize the time of emergence of ALT cells and the variability of their telomere distribution. An asymptotic analysis under a relevant parameter scaling, inspired by [Champagnat], allows us to account for experimental observations.

References:

Champagnat et al. « Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer ». The Annals of Applied Probability, vol. 31, nᵒ 4, august 2021.

Kockler et al. « A Unified Alternative Telomere-Lengthening Pathway in Yeast Survivor Cells ». Molecular Cell, vol. 81, nᵒ 8, april 2021, p. 1816-1829.e5.

Martinez-Fernandez et al. « Life and Death without Telomerase: The Saccharomyces Cerevisiae Model ». Cold Spring Harbor Perspectives in Biology, vol. 17, nᵒ 5, may 2025, p. a041699.

Speaker: Juan Mardomingo-Sanz (University of Lorraine)

5:40 PM MS166-3

Speaker: Marek Kimmel (Rice University)

6:00 PM MS166-4

Speaker: Viviana Gavilanes (Sorbonne University)

5:00 PM → 6:20 PM Mathematical Modeling of Infectious Diseases: Classical Foundations to Contemporary Approaches

5:00 PM Optimizing HIV Antiretroviral Therapy Strategies: A Multi-Scale, Multi-Objective Framework for Reconciling Individual--Population Trade-offs

Existing single-scale HIV models often overlook conflicts between within-host and population-level treatment strategies. To resolve this, we develop a multi-scale model with infection-age structure to optimize antiretroviral therapy (ART) initiation timing and efficacy through multi-objective optimization. By reformulating initiation time as a control variable in the system, we establish the existence of Pareto-optimal solutions through variational analysis and provide a theoretical characterization of the optimal treatment schedule. Numerical analyses reveal that optimal ART strategies must dynamically adapt to evolving priorities between individual outcomes and population-level benefits: early high-efficacy ART maximizes individual benefits, while delayed initiation optimizes population outcomes under persistent post-treatment risks. Post-treatment behavioural shifts influence this balance: reduced sexual activity supports earlier initiation, while high-risk populations require precisely timed delayed administration to balance transmission control and treatment costs. This framework provides quantitative principles for reconciling scale-specific treatment priorities.

Speaker: Stacey Smith? (University of Ottawa)

5:20 PM The population-level implications of immune boosting and immunological priming

Vaccine-induced immunity is rarely static; rather, an individual's immune state is fundamentally shaped by their unique history of pathogen exposures. Silent exposures to the pathogen may lead to "immune boosting," reinforcing immunity without causing symptomatic infection. Moreover, because a primed immune system can respond to a lower dose of antigen than a naive one, immune boosting can be triggered by exposures that are too weak to lead to productive infection. Recent analyses of pertussis dynamics suggest that such extensive immune priming has significant implications for population-level vaccine effectiveness. Nevertheless, the population-level implications of immune boosting and immunological priming are not well understood and remain largely unexplored.

In this work, we incorporate a `strong' form of immune boosting and the mechanism of immunological priming into a leaky-vaccine SIR model. Our analysis reveals a fundamental relationship between the individual probability of boosting and the population-level impact of vaccination. As expected, we show that immune boosting enhances vaccine effectiveness in a wide range of scenarios. Surprisingly, we demonstrate that when immune priming is extensive, vaccine effectiveness can paradoxically decrease with increasing vaccine coverage. Furthermore, we show that in high-transmission settings, VE becomes independent of vaccine coverage. We elucidate these counterintuitive behaviors using a complementary analysis of repeated pathogen exposures and an analysis of direct and indirect effects. Our work sheds light on the complex interplay between individual immune history and herd immunity, emphasizing the importance of accounting for immunological priming when evaluating vaccine impact.

Speaker: Nir Gavish (Technion Israel Institute of Technology)

5:40 PM A Hybrid Networked SEIR Model with Generative-AI Driven Agents for Behavioral Heterogeneity in Epidemics

In this paper, we develop a hybrid, networked SEIR framework that integrates generative AI-driven agents to capture individualized protective behavior. Each agent is characterized by demographic and socioeconomic attributes, and a large language model (LLM) generated daily willingness-to-comply scores from prompts that encode personal traits, occupation, and income, local and global epidemic conditions, social influence, and policy strength. These AI-generated behavioral states modulate edge-level infection risk on dynamic physical contact networks, thereby linking individual decision-making to population-level transmission outcomes. We further embed the same behavioral mechanism into empirically measured temporal contact networks from six real-world scenarios (conference, hospital, workplace, high school, primary school, and college campus).

Speaker: Jia Zhao (The University of Alabama, USA)

6:00 PM The young shield: Mathematical modeling of the impact of age-targeted and dose-structured vaccination on malaria dynamics

Malaria, a parasitic disease spread to humans via effective bite by an infectious adult female Anopheles mosquito, continues to exude a major burden in endemic areas (causing in excess of 600,000 deaths annually, mostly in children under the age of five). Much progress was made over the last two or three decades in the fight against malaria, largely due to the heavy and large-scale use of chemical insecticides (particularly in the form of long-lasting insecticidal nets and indoor residual spraying) to kill the malaria mosquito, promoting a renewed quest for malaria eradication. Unfortunately, such heavy use has also resulted in widespread Anopheles resistance to all the main chemical insecticides used in vector control, posing challenges to the eradication objective. New anti-malaria vaccines have been approved recently and are being deployed in a number of countries in sub-Saharan Africa. In this talk, I will present a new mathematical model, in the form of a system of delayed-differential equations, for assessing the population-level impact of one of the approved vaccines (R21/Matrix-M vaccine) in curtailing the disease burden in the targeted (vaccinated) population.

Speaker: Arnaja Mitra (University of Maryland)

5:00 PM → 6:20 PM Discrete frameworks for modeling biological systems

5:00 PM Regulatory Motifs in C. elegans

For more than four decades, the nematode C. elegans has served as a key model organism in aging research, particularly at the cellular and molecular level. Recently single-cell time series studies have shown that different types of cells age at different rates and through distinct regulatory mechanisms. Using that published data, we identified transcription factors that are co-expressed in the same cells and constructed cell-specific models. The models were built using so-called minimal sets and are represented as directed graphs. The original goal was to identify a universal regulatory subnetwork conserved across multiple cell types, that when augmented within a specific type of cell would give rise to cell-specific behavior. Instead our work revealed similar motifs across cell types: we observed coordinated regulatory pairs, although the specific transcription factors involved vary by cell type. This suggests that aging regulation in C. elegans may be organized not around a single conserved subnetwork, but around motifs differentiated by cell type. We discuss how these motifs may contribute to robustness and maintenance of cellular dynamics during aging.

Speaker: Brandilyn Stigler (Southern Methodist University)

5:20 PM BoolForge: Controlled generation and analysis of Boolean functions and networks

Boolean networks are a widely used modeling framework in systems biology for studying gene regulation, signal transduction, and cellular decision-making. Empirical studies indicate that biological Boolean networks exhibit a high degree of canalization, a structural property of Boolean update rules that stabilizes dynamics and constrains state transitions. Despite its central role, existing software packages provide limited support for the systematic generation of Boolean functions and networks with prescribed canalization properties. In this talk, I introduce BoolForge, a Python toolbox for the random generation and analysis of Boolean functions and networks, with a particular focus on canalization. BoolForge enables users to (i) generate random Boolean functions with specified canalizing depth, layer structure, and related constraints; (ii) construct Boolean networks with tunable topological and functional properties; and (iii) analyze structural and dynamical features including canalization measures, robustness, modularity, and attractor structure. By enabling controlled generation alongside analysis, BoolForge facilitates ensemble-based investigations of structure-dynamics relationships, benchmarking of theoretical predictions, and construction of biologically informed null models for Boolean network studies.

Speaker: Claus Kadelka (Iowa State University)

5:40 PM Towards Complement-based Therapeutics: Opportunities for (Discrete) Mathematical Modeling

The complement system is a potent arm of the immune system, linking the adaptive and innate immune systems, and affecting many facets of human pathophysiology. Recent advances in the development of complement-specific drugs in several rare diseases have opened the gateways to apply complement interventions toward a broader array of pathologies. However, this goal remains elusive due to the complexity and the multifaceted roles of the complement system. Mechanistic mathematical models can provide an effective tool to integrate the different mechanisms, features, and feedback loops into a framework that allows the simulation of complement dynamics under different conditions and the prediction of the effect of interventions. In this talk, we provide an overview of the complement system and discuss open problems related to complement biology. We focus on how mechanistic mathematical modeling of the complement system can potentially alleviate some of the challenges in complement biology. In particular, we discuss how discrete modeling has largely been absent from the field and how it might provide some unique opportunities.

Speaker: Daniel Cruz (Cal Poly)

6:00 PM Prioritizing Control Strategies in Boolean Networks Using Mutation Scores and Network Modularity

Control of biological networks is often achieved by targeting a small number of regulatory nodes, but identifying optimal control strategies remains challenging. Existing control methods frequently yield multiple alternative control sets that satisfy the same objective, making it difficult to select among them. Optimality is typically defined by minimality or by minimizing a cost function. This talk presents a framework for prioritizing control strategies using mutation scores and the modular structure of Boolean networks. Within a stochastic Boolean network setting, mutation scores are computed by simulating the effects of available control interventions. We apply this approach to a pancreatic cancer model, where candidate controls are identified through network modularity and ranked using mutation scores to select an optimal control set. We assess the feasibility of these controls and discuss their biological relevance. Finally, we outline key challenges and potential extensions of this approach to broader classes of biological networks.

Speaker: David Murrugarra (University of Kentucky)

5:00 PM → 6:20 PM Recent Development on Digital Twins for Biology and Biomedical Sciences

5:00 PM Digital Twins of Morphogenesis

The regulation and maintenance of a tissue’s shape and structure is a major outstanding question in developmental biology and plant biology. In this talk, through iterations between experiments and multiscale model simulations that include a mechanistic description of interkinetic nuclear migration, we will show that the local curvature, height, and nuclear positioning of cells in the Drosophila wing imaginal disc are defined by the concurrent patterning of actomyosin contractility, cell-ECM adhesion, ECM stiffness, and interfacial membrane tension [1]. The biologically calibrated model describing both tissue growth and morphogenesis incorporates the spatial patterning of fundamental subcellular properties. Additionally, the model implements for the first time the dynamics of interkinetic nuclear migration within the simulated pseudostratified epithelium. This includes the basal to apical motion of the nucleus, mitotic rounding, and cell division dynamics. Key characteristics of global tissue architecture, such as the local curvature of the basal wing disc epithelium, cell height, and nuclear positioning, serve as metrics for model calibration. The experiments have shown how these physical features are jointly regulated through spatiotemporal dynamics in the localization of pMyoII, β-Integrin, and ECM stiffness. As the disc grows, there are progressive changes in the patterning of key subcellular features such as actomyosin contractility. The predictions made by the model simulations agree with the observed changes in contractility and cell-ECM adhesion during wing disc morphogenesis. AI techniques are incorporated in the model calibration to develop surrogate models to optimize model parameters. In the second half of the talk, aging of yeast cells will be discussed. Understanding the mechanisms of the cellular aging processes is crucial for attempting to extend organismal lifespan and for studying age-related degenerative diseases. Yeast cells divide through budding, providing a classical biological model for studying cellular aging. With their powerful genetics, relatively short cell cycle, and well-established signaling pathways also found in animals, yeast cells offer valuable insights into the aging process. A three-dimensional multi-scale chemical-mechanical model was developed and used to suggest and test hypothesized impacts of aging on bud morphogenesis [2]. Experimentally calibrated model simulations showed that during the early stage of budding, tubular bud shape in one aging mode could be generated by locally inserting new materials at the bud tip, a process guided by the polarized Cdc42 signal. Furthermore, the aspect ratio of the tubular bud could be stabilized during the late stage as was also observed in experiments [2]. The model simulation results suggest that the localization of new cell surface material insertion, regulated by chemical signal polarization, could be weakened due to cellular aging in yeast and other cell types, leading to the change and stabilization of the bud aspect ratio.

Speaker: Mark Alber (University of California, Riverside)

5:20 PM A Patient-Specific Digital Twin for Adaptive Radiotherapy of Non-Small Cell Lung Cancer

In this talk, we introduce a patient-specific digital twin framework termed COMPASS (COMprehensive Personalized ASsessment System) for adaptive radiotherapy of non-small cell lung cancer (NSCLC) patients based on fractional PET/KVCT imaging, radiomics, dosiomics, and biologically equivalent dose (BED) kinetics. Specifically, eight NSCLC patients treated with biology-guided radiotherapy (BGRT) were modeled with 99 organ-fraction observations across 24 organ trajectories. Organ specific time-series features were derived to preserve spatial dose heterogeneity and biological response. A gated recurrent unit (GRU) autoencoder was used to learn compact latent representations of evolving dose–response trajectories for critical organs, which were subsequently classified using logistic regression to predict eventual CTCAE grade ≥1 toxicity. Despite the limited cohort size, COMPASS achieved an AUC of 0.90 with 80% sensitivity and 78% specificity. Importantly, elevated toxicity risks were predicted several fractions prior to clinical symptom onset, defining an actionable window for early intervention for patients. Incorporation of BED kinetics and spatial dose-texture features sensitively captured transient metabolic and dosimetric perturbations not reflected by regular metrics. COMPASS provides a physics- and biology-informed framework for adaptive radiotherapy where organ toxicity and tumor dynamics are continuously updated based on delivered dose and images to guide radiotherapy.

Speaker: Jun Deng (Yale University)

5:40 PM Machine Learning-Enabled Digital Twins for Personalized Modeling of Alzheimer’s Disease

Digital twins are emerging as a powerful paradigm for modeling complex biological systems by integrating data-driven and mechanistic approaches. In this talk, we present recent developments in constructing machine learning-enabled digital twins for Alzheimer’s disease (AD), a highly heterogeneous neurodegenerative disorder characterized by diverse biomarker trajectories, progression rates, and treatment responses.
We develop a unified framework that combines mechanistic mathematical modeling with data-driven learning to build patient-specific digital twins capable of simulating disease progression and predicting individualized outcomes. This approach enables the integration of multimodal clinical and biomarker data, providing a more comprehensive representation of disease dynamics.
We demonstrate how these digital twins can be used to explore the underlying biomarker cascade, quantify patient variability, and evaluate personalized therapeutic strategies in silico. This work highlights the potential of digital twin technologies to advance precision medicine in AD and reduce the cost and time associated with clinical trials.

Speaker: Wenrui Hao (Penn State University)

6:00 PM Integrating Multimodal Patient Data with Biophysical Models for Predicting Patient-Specific Tumor Progression

Tumor progression is shaped by a complex interplay between genomic heterogeneity, biophysical interactions, and the tissue microenvironment. Computational models of tumor growth have historically struggled to incorporate the full richness of patient-specific data — from genomics and transcriptomics to medical imaging and tissue mechanics. Here, I will present a multi-scale computational approach designed to bridge this gap. The centerpiece is a stochastic state-space modeling framework that discretizes the tissue microenvironment into spatially resolved voxels characterized by resource availability, mechanical properties, vascular state, and clonal composition of tumor cells. Multi-modal patient data — medical imaging, bulk genomics, and digital pathology — parameterize and personalize model behavior, while cell proliferation, death, migration, and metabolic state are governed by microenvironmental conditions. Applied to glioblastoma, the framework integrates brain-scale atlases of oxygen, glucose, and tissue stiffness with patient MRI and whole-genome sequencing to simulate how ploidy-dependent resource sensitivity shapes clonal competition and spatial patterns of tumor recurrence. To complement this meso- to macroscale approach, I will briefly introduce a pipeline connecting RNA sequencing data to biophysical models of single-cell migration through cytoskeletal signaling networks — a path toward directly informing cell migration parameters from patient transcriptomic data.

Speaker: Parag Katira (San Diego State University)

5:00 PM → 6:20 PM Mathematical and Experimental Approaches to Retinal Degeneration and Visual Restoration

5:00 PM Numerical Modelling for Glucose Metabolization in the Retina

The buildup of toxic reactive oxygen species (ROS) is a significant contributor to retinal degeneration and cellular dysfunction. It has been shown that the glutathione (GSH) antioxidant system and nicotinamide adenine dinucleotide phosphate (NADPH) play an important role in the detoxification of ROS. Existing models describe these dynamics with system of ordinary differential-algebraic equations. However, ROS diffuses across retinal cells, which is not addressed in existing models. Understanding the spatial behavior of ROS could inform treatment strategies, but doing so requires the use of more advanced numerical tools. In this presentation, we address challenges and strategies for domain meshing, temporal discretization, and computational expense.

Speaker: Kohl James (Saginaw Valley State University)

5:20 PM Mathematical Models of Retinal Drug Delivery

Wet age-related macular degeneration (AMD) causes vision loss when vascular endothelial growth factor (VEGF) stimulates blood vessel growth into the light-sensitive retina. Anti-VEGF treatments such as ranibizumab are currently administered to treat wet AMD via intravitreal injections, which are unpleasant, expensive and risk complications. We explored the efficacy of topically administered ranibizumab, with cell penetrating peptides (CPPs).

Ex vivo pig eyes were divided into 3 groups and treated with 1. topical or 2. intravitreal ranibizumab and CPP, or 3. intravitreal ranibizumab. ELISAs measured ranibizumab and VEGF concentrations in the aqueous and vitreous at 20 min, 40 min, 1 hr and 3.5 hr (n = 3, per group). An ordinary differential equation model was formulated to describe the evolving concentrations of ranibizumab, VEGF and their compounds in the tear, aqueous and vitreal compartments.

CPP allows topical ranibizumab to penetrate the cornea but reduces ranibizumab availability and efficacy in neutralising VEGF for intravitreal treatment. Topical treatment may provide sustained, moderate suppression of vitreal VEGF levels, while intravitreal treatment provides strong suppression which lessens between treatments. Combined intravitreal/topical treatment presents a promising approach. Treatment efficacy would be enhanced if ranibizumab’s rate of binding to VEGF or tear residence time could be increased.

Speaker: Paul Roberts (City St George’s, University of London)

5:40 PM Mathematical analysis of photoreceptor changes in conditions of separation from the underlying retinal pigment epithelium

Photoreceptors (PR) are responsible for absorbing and converting light into electrical signals necessary to create vision. To accomplish that, they are in an intimate relationship and attached to the underlying retinal pigment epithelium (RPE). Separation of the PR from the underlying RPE is seen in many retina disorders and leads to PR cell death and subsequent vision loss. Separation of PR from the RPE (detachment) interferes with the normal phagocytosis and recycling of PR outer segments by the RPE, and disrupts nutrient and metabolite delivery, including glucose. All these factors contribute to cell dysfunction and eventual cell death. In this work, we sought to understand the importance of different factors in PR cell loss after detachment using mathematical modeling. We used known information of photoreceptor interactions in the healthy retina from the literature, and datasets for rod and cone degeneration after detachment. We also included three additional published datasets of PR cell death kinetics. A mathematical sensitivity analysis examined the impact of the parameters on the system over a detachment of 150 days and found that the parameters that significantly impact the rod and the cone population at the stages where “early intervention” happens (3-7 days after detachment) are not always the same ones that significantly impact the populations at 150 days. Additionally, some of the parameters negatively affected one population while having the opposite effect on the other. An increase in nutrient availability and efficiency of rod energy uptake were the only parameters that did not have a negative effect on either population. Similar results were obtained for reattachment. The interplay between these variables indicates that effective photoreceptor neuroprotection in retinal detachment may require multiple strategies. The prediction of these impactful parameters over time can be further assessed in experimental models and may provide guidance on the most effective ways to improve PR survival after their separation from RPE.

Speaker: Stephen Wirkus (The University of Texas at San Antonio)

6:00 PM Predicting the efficacy of optogenetic strategies for vision restoration

Optogenetic gene therapy enabled partial functional vision restoration in patients with retinal degeneration, but the achieved visual acuity remains below the threshold of legal blindness. Various modifications to these therapies have been proposed to improve acuity. However, existing reports typically quantify the light sensitivity of reactivated retinas, but rarely provide corresponding estimates of visual resolution, making it difficult to predict which strategies are most suitable for clinical translation. To address this gap, we developed a computational framework that translates electrophysiological recordings from optogenetically treated retinas into predictions of achievable visual resolution. Starting from a single-cell model fitted to MEA recordings of treated rd1 mouse retinas, we build a digital retinal population and simulate visual acuity tests. Maximum-likelihood decoding then provides an upper bound on achievable acuity for each strategy. This framework enables systematic comparison across optogenetic strategies, quantifying the impact of opsin kinetics on acuity and the potential benefit of bipolar-cell targeting.

Speaker: Chiara Boscarino (Institut de la vision)

5:00 PM → 6:20 PM Mathematical Modeling of Cross-Scale Biological Dynamics

5:00 PM MS178-1

Speaker: TBA

5:20 PM Stochastic Process and PDE Models for Cross-Scale Evolutionary Dynamics

Natural selection often operates simultaneously at multiple levels of biological organization, with evolutionary forces at each level potentially creating a tug-of-war between individual-level incentives to cheat and a collective incentive of maintaining cooperation. In this talk, we will discuss a stochastic framework for describing nested birth-death processes in group-structured populations with selection operating within and among competing groups, presenting simulations of the stochastic models and deriving ODE and PDE models that arise by successively taking the limit of an infinite number of groups and infinite group size. By comparing different possible update rules for individual-level and group-level replication events, we will be able to explore how forms of frequency-dependent competition at each level of selection can help shape the long-time support for cooperation by multilevel selection in both finite and infinite populations.

Speaker: Daniel Cooney (University of Illinois Urbana-Champaign)

5:40 PM MS178-3

Speaker: TBA

6:00 PM Cross‑Scale Drivers of Antimicrobial Resistance: Competition, Trade‑offs, and Landscape Structure

Antimicrobial resistance (AMR) is commonly framed as a genetic response to drug exposure, yet resistance reliably emerges from the ecological and spatial contexts in which microbes live. A growing body of theory and experiment suggests that competition can slow or even prevent the emergence of AMR, motivating intervention strategies that seek to enhance competitive interactions in clinical, agricultural, and environmental settings. However, our understanding of when and how competition could constrain resistance remains limited. Here, we develop a cross‑scale mathematical framework linking genetic costs of resistance to population‑level competition and landscape‑scale spatial structure. Using a classical growth–efficiency trade‑off from ecological theory, we examine competition between drug‑sensitive and drug‑resistant strains in which increasing resistance incurs a cost in reduced growth rate or resource efficiency. We ask how anthropogenic land‑use change, particularly spatial and environmental homogenization, alters the ecological conditions under which these strains compete. By embedding AMR within a broader ecological theory of resource competition and life‑history trade‑offs, this work reframes resistance as an emergent property of coupled ecological and evolutionary dynamics rather than a purely pharmacological phenomenon. More broadly, the framework helps identify general principles governing when and why resistance genes emerge, persist, and spread.

Speaker: Jessica Hite (University of Wisconsin -- Madison)

Mathematical Society Abstract.docx

5:00 PM → 6:20 PM Data-Driven Modeling of CAR T-Cell Dynamics in cancer

5:00 PM Spatiotemporal dynamics of tumor - CAR T-cell interaction

The success of chimeric antigen receptor (CAR) T-cell therapy in treating hematologic malignancies has generated widespread interest in translating this technology to solid cancers. However, issues like tumor infiltration, the immunosuppressive tumor microenvironment, and tumor heterogeneity limit its efficacy in the solid tumor setting. Recent experimental and clinical studies propose local administration directly into the tumor or at the tumor site to increase CAR T-cell infiltration and improve treatment outcomes. We develop a simplified spatiotemporal model for CAR T-cell treatment of solid tumors and demonstrate that the model can reproduce tumor and CAR T-cell data from small imaging studies of local administration of CAR T cells in mouse models. Our results suggest that locally administered CAR T cells will be most successful against slowly proliferating, highly diffusive tumors. In our simulations, low average tumor cell density is a better predictor of treatment success than total tumor burden or volume doubling time. These findings affirm the clinical observation that CAR T cells will not perform equally across different types of solid tumors, and suggest that measuring tumor density may be helpful when considering the feasibility of CAR T-cell therapy and planning dosages for a particular patient.

Speaker: Ivana Bozic (University of Washington)

5:20 PM Predicting CAR T-cell Therapy Outcome and Cytokine Release Syndrome Through Data-Driven Mathematical Models

Chimeric Antigen Receptor (CAR) T-cell therapy represents a frontier in treating leukemias and lymphomas, with recent clinical approvals worldwide. Despite its potential, therapeutic outcomes remain heterogeneous due to factors such as limited in vivo persistence, impaired migration, exhausted phenotypes, and tumor-mediated immunosuppression. Mathematical modeling offers a robust framework to predict these outcomes and elucidate biological mechanisms that are otherwise inaccessible through direct measurement. Our group has developed models incorporating diverse CAR T-cell phenotypes—including effector, exhausted, and memory cells—calibrated with data from public clinical trials. Furthermore, our models account for the roles of healthy B-cells and macrophages in clinical outcomes and the development of Cytokine Release Syndrome (CRS). Finally, we analyze antigen expression dynamics as a proxy for predicting antigen-positive and antigen-negative relapses. Overall, our multiscale models integrate in vitro and in vivo data to enhance the predictive understanding of CAR T-cell therapy in hematological malignancies.

Speaker: Luciana Barros (Universidade de São Paulo)

5:40 PM Quantifying target antigen-dependent CAR T-cell performance against AML

Antigen Receptor (CAR) T-cell therapy has transformed cancer immunotherapy by genetically engineering T-cells to target tumor antigens. Acute myeloid leukemia (AML) presents unique challenges due to resistance mechanisms, especially in patients with TP53 loss mutations.
The complex dynamics of CAR T-cell expansion remain poorly understood. The field lacks validated quantitative frameworks to systematically evaluate different CAR T-cell target constructs, such as CD33, CD123, and CD371, against resistant AML variants. We address this gap by combining mathematical modeling with in vitro assay data and Bayesian inference. We select, train, and validate a two-compartment deterministic mathematical model that describes the nonlinear dynamics of target AML and CAR T cells, accounting for expansion, killing, and exhaustion. Using Bayesian inference, we train and select the best-performing functional form for CAR T expansion, and then validate it on unseen data. Our framework selects a model that accounts for handling time and T-cell self-interference. Thus, expansion is a complex and dynamic process in which the handling time of target cells and T-cell crowding negatively affect T-cell expansion. Analysis of posterior parameter distributions reveals target-antigen-specific responses against TP53-deficient AML. For instance, CD33-targeting CARs have reduced attack rates against TP53-deficient cells, while CD123- and CD371-targeting CARs show moderately increased attack rates; however, the former exhibit higher death rates, and the latter have increased handling times, impeding efficacy. This target-dependent form of resistance challenges the assumption of uniform performance and reveals a unifying nonlinear expansion model for integrated, yet antigen-specific, experimental and theoretical predictions of efficacy.

Speaker: Philipp Altrock (Cancer Modeling & Evolution UKSH Campus Kiel)

6:00 PM Synergistic interplay of morphology and metabolic activity rule response to CAR T-cells in B-cell lymphomas

CAR T-cell therapy, based on genetically engineered T-cells, has demonstrated significant potential in treating hematological malignancies, including B-cell lymphomas. This treatment has complex longitudinal dynamics due to the interplay of different T-cell phenotypes (e.g. effector and memory), the expansion of the drug and the cytotoxic effect on both normal and cancerous B-cells, the exhaustion of the immune cells, the tumor immunosupressive environments, and more. Thus, the outcome of the therapy is not yet well understood leading to a variety of responses ranging from sustained complete responses, different types of partial responses, or no response at all. We developed a mechanistic model for the interaction between CAR T- and cancerous B-cells, accounting for the role of the tumor morphology and metabolic status. The simulations showed that lesions with irregular shapes and high proliferation could contribute to long term progression by potentially increasing their immunosuppressive capabilities impairing CAR T-cell efficacy. We analyzed 18F-FDG PET/CT imaging data from 63 relapsed/refractory diffuse large B-cell lymphoma receiving CAR T-cells, quantifying radiomic features including tumor sphericity and lesion aggressiveness through standardized uptake values (SUV). Statistical analyses revealed significant correlations between these metrics and progression-free survival (PFS), emphasizing that individual lesions with complex morphology and elevated metabolism play a critical role in shaping long-term treatment outcomes. We demonstrated the potential of using data-driven mathematical models in finding molecular-imaging based biomarkers to identify lymphoma patients treated with CAR T-cell therapy having higher risk of disease progression.

Speaker: Soukaina Sabir (UC3M)

5:00 PM → 6:20 PM Temporal Fluctuations in the Tumor Microenvironment and Their Influence on Cancer Progression

5:00 PM Exploring the connection between hypoxia and intra-tumour heterogeneity through mathematical modelling

In solid tumours, the presence of regions of abnormally low oxygen levels (i.e., hypoxia) is recognised as a major driver of tumour progression and therapeutic resistance. Yet, how exactly oxygen levels shape cancer cell responses and disease dynamics in vivo remains poorly understood. While in vitro models of hypoxia exist, they often fail to capture the complex oxygenation dynamics of real tumours. In this talk, I will discuss how mathematical modelling can be used to address the gap between in vitro and in vivo experimental conditions. As an example, I will present our work on cell-cycle dysregulation in cancer cells exposed to fluctuating oxygen environments – namely cyclic hypoxia. In this work, we have integrated mechanistic mathematical modelling and cell culture experiments to explore and predict cell responses to a wide range of (cyclic) hypoxia conditions. Our results uncover the possible multifaced role of hypoxia in shaping the heterogeneous composition of vascularized tumours.

Speaker: Giulia Celora

5:20 PM The role of hypoxic memory on tumor invasion under cyclic hypoxia

Tumor growth and angiogenesis drive complex spatiotemporal variation in micro-environmental oxygen levels. Previous experimental studies have observed that cancer cells exposed to chronic hypoxia retained a phenotype characterized by enhanced migration and reduced proliferation, even after being shifted to normoxic conditions, a phenomenon which we refer to as hypoxic memory. However, because dynamic hypoxia and related hypoxic memory effects are challenging to measure experimentally, our understanding of their implications in tumor invasion is quite limited. Here, we propose a novel phenotype-structured partial differential equation modeling framework to elucidate the effects of hypoxic memory on tumor invasion along one spatial dimension in a cyclically varying hypoxic environment. We incorporated hypoxic memory by including time-dependent changes in hypoxic-to-normoxic phenotype transition rate upon continued exposure to hypoxic conditions. Our model simulations demonstrate that hypoxic memory significantly enhances tumor invasion without necessarily reducing tumor volume. This enhanced invasion was sensitive to the induction rate of hypoxic memory, but not the dilution rate. Further, shorter periods of cyclic hypoxia contributed to a more heterogeneous profile of hypoxic memory in the population, with the tumor front dominated by hypoxic cells that exhibited stronger memory. Overall, our model highlighted the complex interplay between hypoxic memory and cyclic hypoxia in shaping heterogeneous tumor invasion patterns.

Speaker: Dr Gopinath Sadhu (Indian Institute of Science Bangalore)

5:40 PM Population-level and agent-based models for a quantitative understanding of the tumor-immune interaction

Cancer populations evolve in response to dynamic microenvironments, and the adaptive immune system responds by attempting to recognize and eliminate cancer cells by targeting tumor-associated antigens. The interplay between an evading cancer and recognizing immune compartment is quite dynamic and results in cancer elimination or ultimate immune escape preceded by a period of sustained equilibrium.  In this talk, I will discuss our group’s efforts at understanding the role of the adaptive immune system, surrounding extracellular matrix, and alterations in immune activity in contributing to ultimate tumor escape or elimination. This work introduces both population dynamics and agent-based modeling frameworks to better understand the resultant co-evolution of cancer populations.

Speaker: Jason Thomas George (Texas A&M University)

6:00 PM Growth and adaptation mechanisms of tumour spheroids with time-dependent oxygen availability

Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used to understand cancer progression and develop cancer therapies, have been routinely performed for the past fifty years in constant external environments. Furthermore, spheroids are typically grown in ambient atmospheric oxygen (normoxia), whereas most in vivo tumours exist in hypoxic environments. Therefore, there are clear discrepancies between in vitro and in vivo conditions. We explore these discrepancies by combining tools from experimental biology, mathematical modelling, and statistical uncertainty quantification. Focusing on oxygen variability to develop our framework, we reveal key biological mechanisms governing tumour spheroid growth. Growing spheroids in time-dependent conditions, we identify and quantify novel biological adaptation mechanisms, including unexpected necrotic core removal, and transient reversal of the tumour spheroid growth phases.

Speaker: Ryan Murphy (Adelaide University)

5:00 PM → 6:20 PM Biology at the Interfaces: Data-Informed Multiscale Modelling

5:00 PM Drug dosing design guided by response and resistance convexity

We explore the practicality of guiding treatment scheduling based on the convexity (or concavity) of dose-response curves, which provides a straightforward comparison of continuous treatment and high-dose / low-dose alternatives. Concave dose-response functions predict that the daily administration of a dose of x may be less efficacious than a regimen that switches equally between 120% of x and 80% of x (every other day). Convex dose-response provide the opposite prediction (high / low dosing is best). However, treatment fails due to the evolution of resistance, indicating that dose-response is changing in time with mutation or plasticity driven resistance mechanisms. Drug holidays have been suggested as re-sensitization method for tumors.
Using mathematical modeling integrated with in vivo data, we predict the dose-dependent rate of resistance onset for targeted therapy, which we show is a concave function of dose. Our integrative modeling framework predicts a trade-off between maximizing response (continuous protocols) and maintaining drug sensitivity (high / low protocols), suggesting re-sensitization is possible. Thus, we propose alternative switching treatment protocols to balance this trade off: continuous followed by high / low (or vice versa), subsequently validated in a non-small cell lung cancer in vivo model. This convexity-based approach to treatment scheduling illustrates the effectiveness of incorporating principles of convexity into protocol design.

Speaker: Jeffrey West (Moffitt Cancer Center)

5:40 PM Mathematical modeling of tissue morphogenesis and regeneration

In this talk, we investigate how organs acquire functional structure and rebuild after injury using Individual Based Models (IBM) confronted with experimental data. We first study simple 2D and 3D models for architecture emergence, with cells appearing and growing in a dynamic network of cross-linked fibers. Cells and fibers interact via mechanical repulsion. When applied to adipose tissue, the model reproduces experimental structures and suggests that cell clusters could spontaneously emerge from simple cell–fiber interactions. By implying that vasculature could be secondary to tissue architecture, this simple model therefore proposes a new view of tissue development. In the second part of the talk, we extend the model to account for tissue repair, exploring mechanisms of adipose tissue regeneration. The model successfully generates regeneration or scar formation as functions of few key parameters and indicates that injury outcomes largely depend on ECM rigidity. Via a combined in vivo/in silico approach, the model enables to identify a therapeutically validated target enabling regeneration in mouse adipose tissue. Altogether, these studies point to the essential role of mechanics in tissue structuring and regeneration, and bring a comprehensive view on the role of ECM crosslinking on tissue architecture emergence and reconstruction.

Speaker: Diane Peurichard (INRIA Paris)

6:00 PM Leveraging spatial data analysis to provide robust, model-agnostic, and accurate measurements of pattern formation

Understanding how groups of cells robustly coordinate their behavior represents a key question in developmental biology. Mathematical modeling helps to address this problem by enabling researchers to investigate hypotheses in an abstract setting, yet it remains challenging to link these theoretical frameworks to experimental data. Here, we present a novel computational pipeline that addresses this issue and illustrate its application to the case of zebrafish stripe pattern formation. The pipeline generates labeled point clouds from experimental and theoretical images and extracts information about their spatial patterns by applying tools from spatial data analysis. We demonstrate that statistics which measure spatial organization across multiple length scales are robust to experimental and synthetic replicates, even when synthetic data are sampled from a nearly spatially uniform initial state. Unsupervised clustering of images based on pipeline-derived statistics yields biologically interpretable clusters based on the presence of stripes, spots, or maze-like structures. We envision that our spatial analysis pipeline, which is agnostic to data source and not limited to models of zebrafish pattern formation, will enable future researchers to robustly and accurately link dynamic models of spatially heterogeneous phenomena to experimental data.

Speaker: Duncan Martinson (The Francis Crick Institute)

5:00 PM → 6:20 PM Mechanistic Model Inference for Stochastic Single-Cell Dynamics

5:00 PM Stochastic Gene Expression: Modeling and Inference from Single-Cell Data

Gene expression is intrinsically stochastic, leading to substantial cell-to-cell variability in mRNA and protein levels, now routinely quantified with single-cell technologies. In this talk, I will discuss extensions of the classical two-state telegraph model to incorporate salient features of single-cell biology, including cell division, DNA replication, mRNA maturation, gene dosage compensation, growth-dependent transcription, cell-size control strategies and cell-cycle duration variability. I will also present our statistical inference and machine learning approaches for fitting both classical and complex gene-expression models to single-cell data (smFISH, live-cell imaging, and scRNA-seq). These frameworks provide principled ways to separate biological from technical noise, estimate transcriptional parameters, and infer the mechanisms most compatible with observed transcriptional dynamics.

Speaker: Ramon Grima (The University of Edinburgh)

5:40 PM Clone wars: understanding clonal diversity in resistance to CAR-T cell immunotherapy

Chimeric Antigen Receptor (CAR)-T cell therapy is revolutionising immunotherapy, and has shown significant efficacy in cancers of the blood. Experimental collaborators have observed that patterns of clone-agnostic and clone-specific resistance change sharply with immunologic pressure. We have leveraged mathematical modelling to determine which mechanisms can give rise to the experimentally observed clonal resistance profiles. We develop our models under a branching process framework, considering features such as CAR-T expansion, cytotoxic action, tumour competition, and stochastic extinction. Our modelling suggests that the observed clonal distributions are only possible in the presence of cellular competition. Calibrating the models to experimental data has presented numerous challenges. We conclude by sharing our ambitions for model calibration and highlighting the value of mathematical modelling as a framework for exploring mechanisms in the absence of explicit model calibration.

Speaker: Adriana Zanca (The University of Melbourne)

6:00 PM Detection Noise Renormalizes Apparent Kinetic Rates in Stochastic Gene Regulatory Networks

Imperfect molecular detection in single-cell experiments introduces technical noise that can distort the observed dynamics of gene regulatory networks, hence complicating the inference of the true kinetic parameters from single-cell data. We extend binomial capture models from simple gene-expression systems to general, possibly time-dependent, regulatory networks, using both chemical master equation and piecewise-deterministic Markov process descriptions. Our main result is that the effects of technical noise can be absorbed into the renormalization of a subset of the kinetic rates. This occurs when transcription factor abundance is not too small. In this regime, imperfect capture leads to apparently smaller mean burst sizes of gene products and apparently larger transcription factor binding rates. Together, these results provide a systematic framework for interpreting noisy single-cell measurements.

Speaker: Iryna Zabaikina (Comenius University)

5:00 PM → 6:20 PM Mathematical and Computational Ophthalmology

5:00 PM A coupled fluid-dynamics-heat transfer model for 3D simulations of the aqueous humor flow in the human eye

Understanding the behavior of the human eye is challenging due to the complex interactions between various physical phenomena, such as heat transfer, fluid dynamics, and tissue deformation. Although medical data can offer valuable insights into ocular physiopathology, the available information can be scarce and noisy. Moreover, in experimental studies, multiple factors come into play and it is difficult to isolate the contributions of individual mechanisms. Therefore, developing a robust and accurate model for ocular applications can enhance our understanding of this complex system, by integrating governing mechanisms and data variability.

This talk presents our ongoing efforts in this direction, focusing on the thermo-fluid dynamics governing aqueous humor flow and its coupling with heat transfer throughout the eyeball ~\cite{SCPS_2026}. Our methodology involves developing a comprehensive mathematical and computational model based on the finite element method, rigorously validated against experimental data and numerical studies. To facilitate real-time feedback, we derived a reliable reduced-order model using the certified reduced basis method. We performed forward uncertainty quantification studies with the reduced model, utilizing experimental based stochastic inputs, and conducted global sensitivity analysis to address variability and noise ~\cite{SPS_2024}. We will illustrate these developments, discuss their applications, and address the remaining challenges.

Speaker: Prof. Marcela Szopos (Université Paris Cité)

5:20 PM Modeling the impact of venous collapsibility on retinal blood flow

Glaucoma is a leading cause of blindness worldwide that is characterized by irreversible vision loss. In addition to elevated intraocular pressure (IOP), impairments in retinal blood flow and oxygenation have been shown to contribute to the progression of glaucoma. We extend our existing model of the retinal vasculature, which includes blood flow and oxygen transport mechanisms, to incorporate venous collapsibility. Venules are modeled as Starling resistors, allowing collapse when external pressure exceeds intravascular pressure. Retinal blood flow and tissue oxygenation are predicted as intraluminal pressure and IOP are varied. At baseline IOP, blood flow remains relatively constant across a physiological pressure range (autoregulation plateau). Elevated IOP shifts this plateau to higher pressures, reducing autoregulatory capacity. At elevated IOP, the oxygen extraction fraction decreases sharply as arterial pressure increases. This suggests that venous collapse alters microvascular flow distribution and limits effective oxygen utilization despite increased perfusion pressure. Ultimately, the inclusion of venous collapsibility in the model yields more accurate predictions of the impact of IOP on autoregulation and hemodynamic dysfunction in glaucoma. This model framework will allow for future comparisons to sectorial-specific clinical data to assess the role of impaired blood flow regulation in ocular disease.

Speaker: Ms Tajkera Khatun (Indiana University Indianapolis)

5:40 PM Untangling abnormal retinal blood vessels: Integrating computational modelling, image analysis and in vivo imaging

Abnormal retinal neovascularisation is a hallmark of many retinopathies, including diabetic retinopathy (DR), Age-related macular degeneration (AMD) and retinopathy of prematurity (ROP). It is still unclear how the altered conditions in these diseases, drive cells to construct these vessels, which exacerbate disease progression and in some cases sight loss. Current therapies focus on anti-vegf or laser to limit further damage, but complications, risks and a large proportion of poor responders mean greater understanding of the disease mechanism is required to reveal new strategies.

We are developing integrated computational methods to integrate with state-of-the-art retinal imaging modalities in preclinical mouse, patient and post-mortem human eyes to reveal the dynamic mechanisms governing abnormal vessel growth towards identifying new/adapted therapeutic strategies to improve patient outcomes.

I will give an overview of our tools development and insights to date on 1) our 3D image analysis tool to quantify abnormal retinal vessel and cell-scale morphology and signalling patterns and 2) our predictive cell-based mechanistic simulations integrating with imaging at Moorfields Eye Hospital.

Speaker: Dr Katie Bentley (The Francis Crick Institute and Kings College London)

6:00 PM Mathematical modelling to explore the role of metabolic dysfunction in retinal disease

The retina is the light-detecting tissue layer which lines the back of the eye. There is an increasing awareness of the central importance of metabolic dysfunction in driving a range of currently incurable blinding retinal conditions. The retinal metabolic network is highly nonlinear with multiple feedback mechanisms, necessitating a mathematical modelling approach to accompany ongoing experimental studies for full understanding. We developed a novel mathematical model of retinal metabolism to explore how the retina maintains healthy metabolic homeostasis and how this breaks down in disease.

An ordinary differential equation (ODE) model was formulated to describe and predict the evolving concentrations over time of respiratory metabolites in outer retinal cells. The model accounts for the passage and transformation of metabolites through key respiratory pathways. The model was parameterised using data from the literature and through fitting to data from ongoing experimental studies. The full model was solved computationally, while reduced models were solved analytically.

Our model demonstrates behaviour in agreement with experimental studies, showing metabolites moving through the metabolic pathways in the established fashion. Further, simulations predict key metabolites and processes for maintaining metabolic homeostasis, indicating potential treatment strategies where this breaks down in disease.

Speaker: Dr Paul A. Roberts (City St George’s, University of London)

6:30 PM → 9:30 PM SMB Reception

Speaker: TBA

6:30 PM → 8:30 PM Poster Presentations

6:30 PM Evaluating and developing models for survival extrapolation

Survival analysis is the study of time-to-event data. In a clinical trial, this could be the time to death, or the end of the trial, along with an indicator of whether or not death occurred. Common non- and semi-parametric survival models can only predict survival for at most as long time as a clinical trial is run. Here, we implement survival extrapolation models that extend the survival prediction beyond the trial time window. We train and test the models on a dataset consisting of approximately 10 million individuals from the Swedish general population. From these, we model survival for those who were diagnosed with cancer between 2003 and 2018, and who were at least 30 years old at the time of diagnosis. Follow-up data is available until 2023, and we have access to 10 years lookback for previous diagnoses. This dataset is randomly split into training and testing sets. We investigate how the models perform on different subpopulations.

Speaker: Maiya Tebäck (Uppsala University)

6:50 PM Hopf Bifurcations Unravel Complex Antibody Dynamics in COVID-19 Patients

The introduction of vaccines during the later phases of the 2019-2022 coronavirus pandemic (COVID-19) emphasized the importance of understanding our immune response and the dynamics of antibody production. We improved a model that previously concentrated on viral replication and T-cells to illustrate the antibody dynamics seen in COVID-19 patients. Our analysis revealed the existence of Hopf bifurcations, where changes in the virus-positive equilibrium point (VPE) stability correspond with limit cycles. These bifurcations illustrated a more complex immune response than suggested by our earlier model. When T-cell immunity is compromised, resulting in the emergence of VPE, moderate antibody levels can facilitate pathways to manage prolonged infections through an unstable VPE. Our findings show that while T-cells can eliminate the infection by achieving a stable virus-free equilibrium, antibody responses are crucial when T-cells become overwhelmed.

Speaker: Prof. Alexis Erich Almocera (University of the Philippines Mindanao)

7:10 PM Developing a digital twin of 3D vascular systems to study haemorrhagic viral diseases

Disruption of the microvascular barrier is a hallmark of severe haemorrhagic diseases such as Dengue, while the mechanisms leading to acute vascular leakage and hypovolaemic shock remain incompletely understood. We are developing a cell-based digital twin of 3D microvascular organoid culture systems to investigate how endothelial cells and pericytes self-organise and how this organisation is altered in disease. In particular, we focus on the interplay between differential adhesion and cell contractility within vascular organoids. By exploring how changes in pericyte and endothelial mechanical properties affect spheroid architecture, we aim to provide mechanistic explanations for microvascular dysfunction in haemorrhagic disease, including Dengue-associated barrier failure. This digital twin complements experimental organoid studies from Dr Campagnolo’s lab (University of Surrey).

Speaker: Jiale Miao (UCL)

7:30 PM FEM Simulation of STING Pathway Activation for Glioblastoma Immunotherapy

Glioblastoma (GBM) creates an immunosuppressive microenvironment that renders current therapies largely ineffective. The STING (Stimulator of Interferon Genes) pathway has emerged as a potent target to remodel this environment and stimulate local immune responses. This study presents a Finite Element Method (FEM) framework to investigate the therapeutic impact of the STING agonist ADU-S100 on glioma growth. We implemented a coupled reaction-diffusion system on a realistic brain mesh, incorporating tissue heterogeneity by assigning distinct diffusion coefficients to gray and white matter. The model simulates the diffusion of injected ADU-S100 and subsequent intracellular signaling that triggers the production of Type I interferons (IFN-β), leading to tumor cell death. Simulation results demonstrate that while the control (PBS) group shows rapid tumor expansion along white matter tracks, the ADU-S100 treatment group exhibits significant tumor suppression driven by STING-mediated immune activation. Our results are in good agreement with experimental data (Sean Lawler group, Legorreta Cancer Center, Brown University). This work bridges the gap between computational modeling and mechanistic immunotherapy, providing a predictive tool for optimizing treatment strategies in GBM.

Speaker: Minjong Kim (Konkuk University)

7:50 PM A forecasting pipeline for triple-negative breast response to neoadjuvant chemotherapy: combining MRI and PK/PD-informed modeling with a mechanical constraint on proliferation.

We present an image-driven computational model to enable patient-specific forecasting of triple-negative breast cancer (TNBC) response to neoadjuvant chemotherapy (NAC). Our approach integrates longitudinal magnetic resonance imaging (MRI) data with a biologically-based mechanistic model of tumor growth and therapy response.

Building upon our previously published model that couples drug pharmacokinetics/pharmacodynamic with a reaction-diffusion equation for tumor cell density, we introduce a key enhancement: a mechanical constraint on tumor cell proliferation, motivated by recent experimental evidence. The model's reduced parameter set, identified via global sensitivity analysis, is calibrated for each patient using Gauss-Newton iterations informed by early-treatment MRI scans. Forward simulations then generate spatiotemporal forecasts of tumor response for the remainder of the NAC regimen.

Global biomarkers are computed at regular intervals. The pipeline produces volumetric exports, time‑series summaries, and calibration histories to support reproducible evaluation of model fidelity and predictive performance in a unified imaging‑calibration-to‑forecast workflow. This work outlines our unified imaging-to-forecast-to-prediction workflow, which will be validated on a cohort of TNBC patients to assess its ability to forecast tumor dynamics and accurately identify pCR status.

Speaker: Thomas Gallagher Romero (Universidade da Coruña)

8:10 PM A double-dose vaccination model for COVID-19: Insights from three types of global sensitivity analyses

According to the WHO, the implementation of potent double-dose vaccination programs helped significantly reduce COVID-19 case numbers and disease-acquired deaths during the pandemic. Thus, understanding the most efficacious control parameters of a double-dose vaccination strategy can be helpful in the control of emerging and re-emerging infections. To this end, we extended the traditional SEIR model framework to incorporate a double-dose vaccine. We focused on three specific outputs of the model: disease reproduction number, peak of infection trajectories, and cumulative cases. Our methodology encompassed three global sensitivity analysis (GSA) approaches: partial rank correlation coefficient (PRCC), distance correlation (DC), and Sobol' indices. Both PRCC and DC methods are dependence-based GSA approaches, while the Sobol' method is a variance-based GSA approach. Collectively, these techniques provided valuable insights into various aspects of infection control. Specifically, high rates of partial vaccination as well as a highly effective and long-lasting immunity upon full vaccination can remarkably mitigate the disease burden.

Speaker: Indunil Hewage (West Virginia University Institute of Technology)

8:10 PM A Mathematical Model for Determining the Treatment Order in Catheter Treatment with Multiple Stenoses

Vascular stenosis caused by plaque can lead to life-threatening conditions such as stroke and heart attack. Catheter therapy is one method used to treat plaque and does not require open surgery. In this study, we assumed that a drug is released from specific points of a catheter to treat stenosis. Based on this assumption, we constructed a mathematical model to determine the treatment time.
We determined the blood flow rate using the Navier–Stokes equations and performed simulations using a fitted equation. The fitted equation was introduced to simplify the simulation because the vascular network is complex and the Navier–Stokes equations require high computational cost.
We also constructed a differential equation describing the relationship between the height of stenosis and time. In this model, we assumed that when the blood flow rate is large, the drug tends to be washed away before acting sufficiently on the plaque. Therefore, the reduction of stenosis becomes slower when the flow rate is high. Conversely, when the flow rate is smaller, the drug can act more effectively on the plaque. We also assumed that larger stenoses are more easily reduced by the drug.
As a result, when two stenoses exist in a blood vessel, treating the smaller stenosis first is more effective because the treatment time becomes shorter and the required amount of drug decreases. These results suggest that determining an appropriate treatment order is important for catheter therapy.

Speaker: Ms Haruka Suga (Kyushu University)

8:10 PM A Score-Based Bayesian Data Assimilation for High-Dimensional Jansen–Rit Models Using EEG Measurements

Advances in experimental techniques allow brain activity to be measured at scale, for example using electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). Alongside experimental advances, computational platforms for simulating brain dynamics have also shown meaningful progress. Together, they have created new opportunities to understand spatiotemporal patterns of brain activity underlying diverse physiological and cognitive processes, including sleep and working memory. However, optimally integrating computational models with experimental data remains an open challenge. Data assimilation is challenging because the brain is high-dimensional system governed by strongly nonlinear dynamics. To address these challenges, we propose a score-based Bayesian data assimilation method for high-dimensional Jansen–Rit models using EEG measurements. Based on the measurement equation of the EEG forward model, we construct a forward process from latent states to measurements. This formulation enables closed-form computation of the likelihood score for posterior sampling of latent brain states, and learning the prior score with a score model allows the method to scale to high-dimensional settings. Numerical experiments on EEG-based state estimation in the Jansen–Rit model support the effectiveness of the proposed method.

Speaker: Eunbi Yoon

8:10 PM Adaptive Finite Element method for reconstructing dielectric properties of malign melanoma in 3D

This poster concerns the coefficient inverse problem for Maxwell's equations, related to finding the space-dependent dielectric permittivity and effective conductivity functions using backscattered time-dependent electrical field in three dimensions. The aim is to reconstruct the dielectric properties of Malignant Melanoma tissue, both shape and values.
The forward problem is solved using a Domain Decomposition method developed in \cite{BL1, BR, LB1}, where both the Finite Element Method and the Finite Difference Method is used. The inverse problem is solved using Lagrangian approach and the Conjugate Gradient Descent method, and numerical examples are performed in a homogeneous and non-homogeneous setting while adaptively refining a finite element mesh using a posteriori error estimates of \cite{BL2}.

This method was applied for breast phantoms in \cite{BL1,BL2} and for malignant melanoma detection in a homogeneous setting in \cite{KLB}.

Speaker: Georg Kyhn (Department of Mathematical Sciences, University of Gothenburg, and Chalmers University of Technology)

8:10 PM AI-based multiomics profiling reveals complementary omics contributions to personalized prediction of cardiovascular disease

Genomics, metabolomics, and proteomics offer complementary insights into cardiovascular disease (CVD) risk. In this published work, we introduce the CardiOmicScore, a multitask deep learning framework, to learn disease-specific proteomic (ProScore) and metabolomic (MetScore) risk scores for the six most common CVDs by profiling 2920 proteins and 168 metabolites. Experiments demonstrate that ProScore and MetScore are strong sole CVD risk predictors (C-index range: 0.69–0.82 for ProScore and 0.64–0.74 for MetScore), and can significantly enhance risk prediction across CVDs up to 15 years prior to disease onset when combined with clinical data, increasing the C-index by 0.005–0.102. These findings suggest that incorporating multiomics profiling into clinical practice can improve personalized risk assessments at early stages. CardiOmicScore also identifies important CVD-related proteins and metabolites, which represent promising data-driven pathways, calling for further external validation, to develop novel biomarkers and targeted therapies, facilitating precision medicine for primary prevention of CVDs.

Speaker: Qingpeng Zhang (The University of Hong Kong)

8:10 PM Antigenic drift and therapy resistance in CAR T-cell treatment: insights from a cellular automata model

Chimeric antigen receptor T-cell (CAR T) therapy has demonstrated remarkable efficacy in hematological malignancies. However, resistance remains a major clinical challenge, as it can compromise treatment response and promote relapse. Among the mechanisms that may underlie resistance, loss or downregulation of the target antigen is particularly relevant, since it enables tumor cells to escape immune recognition.
In this work, we develop a spatial agent-based model based on cellular automata to investigate the role of tumor phenotypic heterogeneity and antigen-dependent cytotoxicity in the emergence of resistance. The model represents interactions between tumor cells and CAR T-cells on a lattice and incorporates experimental measurements of antigen expression obtained from flow cytometry. Tumor proliferation includes a stochastic phenotypic inheritance mechanism that allows antigen levels to vary across generations.
Simulations reproduce sequential co-culture experiments and show that reduced cytotoxicity against low-antigen cells promotes the clonal selection of resistant subpopulations. This process can be interpreted as a therapy-driven drift in antigen expression, analogous to resistance dynamics described in other targeted therapies, and reveals evolutionary dynamics of the antigen under treatment pressure. These findings highlight the importance of accounting for treatment-specific efficacy when designing more effective therapeutic strategies.

Speaker: Pablo Sanz Galarreta (Mathematical Oncology Laboratory (MOLAB), Universidad de Castilla-La Mancha (UCLM))

8:10 PM Asymptotic problems for the Keller-Segel system with density cut-off

We consider the asymptotic problems of the Keller-Segel system with the nonlinear diffusion of porous medium type and logistic sensitivity. We classify three possible distinguished limits and reveal the relations between the Keller-Segel system and the limit systems. We prove that our model converges to three various limits as the parameters are chosen adequately: a porous medium equation when the chemotactic sensitivity is small and the chemical diffuses slowly; a hyperbolic Keller-Segel system when the cell diffusion vanishes; a surface-tension-driven free boundary problem when the chemical diffuses slowly and attracts the cells strongly. Unlike previous works, the strong convergence of the density is necessary due to the nonlinearity of the sensitivity. The mathematical methods employed vary for the three different cases, including the energy formulation, the entropy equality, the kinetic formulation, and $L^1$ compactness.

Speaker: Dr Mingyue Zhang (Vienna University of Technology)

8:10 PM Benchmarking of the robustness of mechanistic generative models in cellular trajectory and gene regulatory network joint inference

Cellular models based on single-cell RNAseq data have emerged as a common tool for a system-level exploration of cell mechanisms, especially relevant for tasks such as gene regulatory network (GRN) inference or cell trajectory prediction. Some early mechanistic models allow dataset simulation from GRNs, thus using underlying biological knowledge and offering greater interpretability. However, these models cannot be calibrated from scRNAseq data to formulate predictions. In contrast, multiple generative models fitted on temporal snapshots of scRNAseq data can predict cell trajectories, but most until recently were based on non-mechanistic models lacking explicit GRN formulation. Yet since a GRN encodes the regulatory interactions driving gene expression dynamics, GRN structure and cell trajectories are two facets of the same process. Addressing this, new generative models calibrate a GRN from temporal data and use it to constrain trajectory inference, exploiting this coupling so that both tasks reinforce each other. In our recent work, we evaluate this joint modeling performance gain by benchmarking recent GRN-driven generative models (including \cite{Zh, Be, Is, Ma, Ri}) against state-of-the-art methods performing these tasks separately. We evaluate their ability to reconstruct gene networks from simulated and curated datasets, assess the biological coherence of reconstructed trajectories, predict cell states at held-out timepoints, and generalize to unseen perturbations.

Speaker: Yann Maugé (Aix-Marseille University - CRCM)

8:10 PM Beyond Markovian Assumptions: A History-Dependent Framework for Epidemic Inference

Epidemic models commonly assume Markovian disease progression, in which transitions between infection states occur at constant, memoryless rates. However, real infectious diseases are inherently history-dependent: the probability of becoming infectious depends on time since exposure, and latent and infectious periods rarely follow exponential distributions. This mismatch can bias epidemic inference, leading to overestimation of key transmission parameters and mischaracterization of hidden initial conditions.

Here, we present two data-driven, history-dependent frameworks for more accurate epidemic inference. The first incorporates gamma-distributed latent and infectious periods to improve estimation of epidemiological parameters, including the reproduction number, directly from reported case data. The second reconstructs hidden exposure histories to more accurately infer the initial exposed population, even under noisy or rapidly changing outbreak conditions. Together, these approaches move epidemic inference beyond conventional Markovian assumptions, reduce systematic bias in both parameter and initial-condition estimation, and provide a more reliable foundation for epidemic analysis and prediction.

Speaker: Dr Sunhwa Choi (National Institute for Mathematical Sciences)

8:10 PM Bifurcation analysis of a distributed-delay Wilson–Cowan model for sleep spindle dynamics

Sleep spindles are hallmark thalamo-cortical oscillations of non-REM sleep implicated in memory processing and emotion regulation. We develop and analyze a Wilson–Cowan mean-field model of a corticothalamo-reticular circuit comprising cortical pyramidal and inhibitory populations, thalamic relay cells, and reticular thalamic populations, to capture spindle-like dynamics at the population level. Particular emphasis is placed on neuroprocessing times within the circuit, modeled through weak Gamma-distributed delayed feedback. We study the system with and without distributed delays to determine how temporal effects interact with coupling architecture to reshape the underlying dynamics. Using stability and bifurcation analysis, we characterize the impact of delayed feedback and connectivity strengths on equilibria, oscillatory regimes, and transitions into and out of spindle-like activity. Our results show that timing acts jointly with connectivity to govern the emergence and modulation of spindle-generating dynamics. The model provides a mathematically tractable framework for investigating mechanisms underlying sleep spindle activity in thalamo-cortical networks.

Speaker: Anca Stanoev (West University of Timisoara)

8:10 PM Bridging Reaction–Diffusion Models and Empirical Data: Reparameterization for Transporter Kinetics

Transporter-mediated drug delivery is a crucial factor in pharmacokinetic and pharmacodynamic (PK/PD) studies. Transporter kinetics are typically evaluated using the Michaelis–Menten (MM) model, which estimates the maximum reaction rate($V_{\max}$) and the Michaelis constant($K_M$). However, the MM model assumes a well-mixed environment, whereas transporters operate in localized spatial settings, which can lead to estimation inaccuracies. While previous studies addressed this spatial discrepancy, they introduced an additional spatial parameter that is difficult to determine experimentally. To overcome this practical limitation, we reformulated the reaction–diffusion equations in terms of more accessible parameters. Furthermore, we rigorously evaluated the accuracy and practical identifiability of these transformed parameters with real experimental data. By transitioning to practically measurable variables, this study bridges the gap between complex spatial models and empirical laboratory data, offering a robust and experimentally interpretable framework for analyzing transporter kinetics.

Speaker: Se Jun Ahn (Graduate School of Data Science, KAIST, Daejeon, Republic of Korea)

8:10 PM Catalyst: Fast and flexible modeling of reaction networks

Chemical reaction networks (CRNs) are a commonly used model type in biology and chemistry (with applications in e.g. systems biology, pharmacology, and epidemiology). Here, we demonstrate Catalyst.jl, a flexible and feature-filled Julia library for the creation, simulation, and analysis of CRN models. Models can be created both using the Catalyst DSL (which enables the implementation of CRNs in their native reaction format), or built programmatically. Next, they can be simulated using ODE, SDE, and jump process (e.g. Gillespie simulation) approaches. Internally, models are represented symbolically, enabling e.g. automatic symbolic simplifications and Jacobian constructions to improve simulation performance. Finally, Catalyst’s internal CRN model representation enables it to compose with many additional modelling packages. This facilitates features such as steady state computations, bifurcation analysis, identifiability analysis, and parameter fitting.

Speaker: Torkel Loman (University of Oxford)

8:10 PM Cellular- and Subcellular-Scale Modeling of Cardiac Excitation Propagation with Dynamic Extracellular Cleft Concentrations

In cardiac electrophysiology, ionic currents at the subcellular scale drive electrical activity at the tissue scale, making accurate cellular modeling essential for understanding cardiac function. Experimental inaccessibility of subcellular compartments in intact tissue positions mathematical models as essential tools for studying excitation propagation and motivates the development of multiscale frameworks. We present a biophysically derived computational model for action potential propagation in linear strands of cardiac myocytes that explicitly couples gap junction and ephaptic mechanisms. The model incorporates a biophysically detailed ionic model (Luo-Rudy dynamic) with intracellular concentration dynamics, coupled to a continuum PDE–DAE system governing transmembrane voltage and cleft ion concentrations. Cleft concentration dynamics, governed by conservation of mass, balance spatially localized transmembrane ionic currents at intercalated discs from adjacent myocytes with Goldman-Hodgkin-Katz electrodiffusive exchange to the bulk extracellular space. Equations are discretized using finite volume methods to preserve conservation and integrated using operator splitting with a multirate GARK method to resolve the multiple temporal scales. This framework enables mechanistic investigation of ephaptic coupling through dynamic ion concentrations in the extracellular cleft and demonstrates stable propagation with recovery of known conduction limits in ventricular tissue.

Speaker: Nicholas Cantrell (The University of North Carolina at Chapel Hill)

8:10 PM Challenging the standard protocol: Mechanistic mathematical model for ¹⁷⁷Lu-PSMA therapy optimization

Radiopharmaceutical therapy with $^{177}$Lu–PSMA has emerged as an effective treatment for metastatic prostate cancer, yet current clinical protocols rely on empirically fixed and non-personalized schedules. A mechanistic mathematical model based on ordinary differential equations is introduced to integrate tumor growth dynamics, radiation damage and organs pharmacokinetics. Radiopharmaceutical activity in tumor and organs at risk is described through compartment-specific effective decay rates combining physical and biological clearance, while injected activity is distributed according to uptake-weighted mass fractions. The toxicity is quantified using biologically effective dose thresholds, enabling a quantitative assessment of efficacy–toxicity trade-offs \cite{2025RPT}.
Virtual patient cohorts generated through stochastic sampling of biologically grounded parameter ranges allow in silico trials. Model predictions reproduce published dosimetry and survival outcomes from independent clinical studies, showing good agreement in absorbed doses and Kaplan–Meier survival distributions.
Exploration of treatment schedules reveals a clear efficacy–toxicity landscape: consolidated regimens with fewer, higher-activity injections increase median overall survival but raise renal toxicity, whereas excessive cycle delays markedly reduce therapeutic efficacy. Notably, a nine-week cycle preserves survival comparable to the standard six-week protocol while significantly reducing toxicity.

Speaker: Silvia Bordel-Vozmediano (Mathematical Oncology Laboratory (MOLAB), University of Castilla-La Mancha)

8:10 PM Characterisation of the function of tumor vascular networks

Angiogenesis is a hallmark of tumor growth. Strikingly, tumor vascular networks present a non-hierarchical, dense, high-permeability vascular structure. To better design personalised treatment strategies, it is important to characterise and understand the function of these altered vascular networks in different scenarios - namely, how does oxygen perfusion depend on vessel density.

In this work we simulate two and three-dimensional vessel networks to investigate how the progressive addition of vessels between pre-existing ones alters the fluid flow through the network and tissue perfusion. The proposed method consists in the implementation of an algorithm that builds a denser vessel network by introducing new vessels in a controlled manner.

We introduce a novel measure to describe how tissue perfusion depends on vessel density for different flow, pressure and vessel permeability constraints. The differences observed suggest that tumour neo-vessel networks present a wide range of perfusion extents depending on network morphology and vessel integrity. We proceed to propose strategies to probe the function of tumor vascular networks in patients.

Speaker: Matilde Palmeira (University of Coimbra)

8:10 PM Codifying the rules of microbial community physiology for biotechnology designs: fighting natural biochemistry with its own sword

We are still actively searching for principles and recipes to design scalable, robust, efficient, and modular microbial bioproduction processes. Engineering natural microbes, however, also means balancing between the interests of the microbe, hardwired in natural biochemistry, and the biotechnologist who aims to upcycle poorly accessible, abundant feedstocks. Could we unlock alternative feedstocks for synthetic biotechnology by rational engineering of microbial communities? I argue that we should seek inspiration from metabolism(s) from natural environments, and codify their physiology, as we did with “cellular economics” of single microbes in isolation. For this we propose to blend multiple meta-omics data with mechanistic, stoichiometric modeling of metabolic networks. We are continuously developing a library of metabolic “jigsaw parts” by reconstructing metabolic networks from metagenome-assembled genomes of environmental microcosms. In parallel, we use metatranscriptomics data generated from the same samples to identify mutually compatible jigsaw parts, i.e. metabolic networks which are co-expressed in multiple microorganisms forming natural microbial communities. In the long run, we aim to design a “rulebook” of synthetic metabolic networks, based on the insights of our current data-driven approach.

Speaker: Pranas Grigaitis (Karlsruhe Institute of Technology)

8:10 PM Decoding Cis-Regulatory Information Underlying Gene Expression in Forest Trees Using Field Transcriptomes from Natural Environments

Regulation of gene expression is essential for organisms to survive and reproduce in fluctuating environments. Machine learning has increasingly been used to understand relationships between non-coding sequences and gene expression. However, most studies rely on data from a limited set of model organisms under controlled laboratory conditions, restricting our understanding of gene regulation in natural environments. Here, we applied machine learning-based cis-regulatory motif detection to two species of Fagaceae, a family of dominant forest trees, using field transcriptome data collected across a two-year seasonal cycle in leaf and bud tissues. First, we trained a convolutional neural network (CNN) to predict the presence or absence of gene expression from 2-kb flanking sequences. The model achieved high predictive accuracy (ROC-AUC > 0.8) for most genes, except those related to photosynthesis, suggesting distinct regulatory mechanisms in these pathways. We then extracted DNA motifs based on importance scores and identified motifs corresponding to several known transcription factors, including the BBR/BPC family, a transcriptional repressor in maize and Arabidopsis. These results suggest that binding sites of transcriptional repressors known across a wide range of plants may also contribute to gene expression in forest trees and provide candidates for future experimental validation.

Speaker: Shuichi Kudo (Kyushu University)

8:10 PM Doubly Structured Models of Tumour-Immune Cell Reactions

Tumour progression is shaped by a dynamic interaction between tumour cells and the immune system. One specific immunosuppressive mechanism to study tumour evasion causes cytotoxic T-cells, a major driving force of the immune system, to differentiate to an ‘exhaustive’ state where they have reduced immune effectiveness due to increased tumour interactions. While this is incorporated in existing mathematical models, we now extend this framework by introducing a doubly structured tumour-immune model in which tumour cells are additionally structured by accumulated damage due to immune attacks. Initially considering binary structure variables helps us build intuition, before then examining larger compartment numbers towards the continuum limit.

Speaker: Fenora David (UCL)

8:10 PM Dynamical paths to depolarization block and back

Depolarization block (DB) occurs when strong depolarization prevents neurons from generating action potentials. It is critically involved in several brain disorders, including epilepsy, migraine, and stroke, but also serves physiological roles, for example in odor encoding. Despite the relevance of DB for brain function and dysfunction, relatively few modelling studies directly address its underlying mechanisms. At the same time, DB states systematically emerge in models of neuronal spiking, bursting, or seizure activity when parameters are varied, suggesting that DB is a robust component of neuronal dynamics.

Here we exploit a rare dataset of whole-cell patch-clamp recordings that reveals a progression of transition patterns from baseline excitability to DB and back. Using dynamical systems theory, we unfold the minimal dynamical structures that enable Type I excitability as in the recorded pyramidal neurons. Coupling this minimal neuron model to slow variables representing collective homeostatic processes naturally reproduces the observed progression. The framework explains DB ubiquity in neuron models and predicts distinct dynamical types of DB with different experimental signatures and responses to perturbations. This frames depolarization block as a nuanced dynamical phenomenon and provides constraints for both experimental and modelling design.

Speaker: Marisa Saggio (Aix-Marseille University, Institut de Neurosciences des Systèmes (INS, UMR1106))

8:10 PM Dynamics and stability of microbial communities under community-level selection

There is growing interest in designing microbial communities that perform collective functions, with potential applications ranging from human health to pollutant degradation and crop production. However, attempts to artificially select communities have reported limited success, with modest improvements in performance and a lack of ecological or evolutionary stability.

Here, we approach this challenge from an organismal perspective. We propose that microbial communities can be engineered to behave more like integrated organisms by imposing a coordinated stress response as a required feature. We develop a theoretical framework to describe microbial populations interacting under selection for community-level traits. Using differential equation models, we analyze the stability and dynamics of multi-species communities subjected to perturbations.

We identify common sources of instability and derive a set of minimal trait requirements for engineering communities that maintain their function. In particular, stress responses at the community level can stabilize functional outputs despite environmental fluctuations or shifts in species abundances. Our results suggest potential design principles for the construction of microbial communities with more stable and reliable collective behavior.

Speaker: Sofia Almirante (Umeå University)

8:10 PM Epidemiological model under vaccination regime and non-permanent immunity driven by time-changed Lévy noise

Stochastic version of Susceptible-Infected-Recovered-Vaccinated (SIRV) epidemiological model is observed. The model is constructed from the ordinary differential SIRV model by introducing the additive time-changed Levy noise in the transmission coeffcient. The noise is constructed in terms of a conditional Brownian motion and a doubly stochastic Poisson random field. The structure of these noises can be strongly related to the corresponding time-changed Brownian motion and the time-changed Poisson random measure, when the time-change is independent of the Brownian motion and Poisson field. The existence of a unique global positive solution of this system of stochastic differential equations is proved. The conditions under which the infectious disease in the population of non-constant size extincts and persist are given in terms of the parameters of the model and the time-change processes from the noise.

Speaker: Nenad Šuvak (School of Applied Mathematics and Informatics, University of Osijek)

8:10 PM Explaining differential influenza viral kinetics on treatment with Oseltamivir versus Baloxavir

Influenza viruses remain a global health concern; thus, we examine the interplay of host-pathogen interaction using math models. Using human challenge data (Hayden 1999, 2000), we fit our model to analyze the heterogeneity of the observations. We tested hypotheses of immune factors influencing viral kinetics and distinguished the immune components between those who cleared and those who experienced prolonged viral shedding. Key findings revealed different immunological signatures of individuals that exhibited rapid expansion of immune effector cells and facilitating a quicker viral clearance than high shedders with delayed adaptive immune responses, correlating to their prolonged infection.
Further, we incorporated treatment effects into our viral dynamics model to analyze the mechanisms of action of Oseltamivir (Tamiflu®) and Baloxavir (Xofluza®). Simulations explained the qualitative differences of virus kinetics when treated with Oseltamivir, a neuraminidase inhibitor, versus Baloxavir, a cap-dependent endonuclease inhibitor. Oseltamivir prevents the release of newly formed virions from infected host cells. In contrast, Baloxavir, blocks viral mRNA transcription early in replication. Our results explained that alleviation of infection symptoms occurs more rapidly when treated with Baloxavir as the antiviral stops new viral production early leading to a rapid reduction, whereas Oseltamivir resulted in gradual decline of viral load reducing the spread of virus to new cells.

Speaker: Angela Tower (Washington State University)

8:10 PM Fluctuating Trait-Switching Opportunities Generate Bistable Cultural Dynamics in the Absence of Conformist Bias

In cultural evolution, the frequency of a cultural trait often exhibits a nonlinear relationship with its frequency in the previous time step: a trait held by the majority tends to become increasingly common even in the absence of any advantage over the minority trait. This pattern has been attributed to conformist bias, which has been shown to generate a sigmoidal relationship between past and present frequencies. However, recent studies suggest that other mechanisms, including sampling biases, can produce similar patterns. Here, we identify a novel mechanism: fluctuations in the proportion of individuals allowed to switch traits. Consider the discrete-time dynamics of two cultural traits, A and B. Let $p_t$ denote the frequency of trait-A carriers at time $t$. At each time step, a fraction $k^+_t$ of trait-A carriers and a fraction $k^-_t$ of trait-B carriers update their traits based on their observations of the frequencies of the two traits. The values of $(k^+_t, k^-_t)$ change periodically with period $n$. For $n=2$, we analytically obtain the following results. Only the trivial equilibria, $p=0$ and $p=1$, can be locally stable. The sigmoidal relationship between $p_t$ and $p_{t-n}$ can arise when the changes in $p_t$ at two consecutive steps occur in opposite directions; in this case, an unstable internal equilibrium exists, and $p=0$ and $p=1$ are simultaneously locally stable. We confirmed analytically or numerically that these properties also hold for $n \geq 3$.

Speaker: Rinto Yoshizaki (Kyushu University)

8:10 PM From Flickering to Dynamical States: A Data-Driven Analysis of Nonequilibrium Dynamics in Red Blood Cells

Active biological systems often operate far from thermodynamic equilibrium, leading to violations of detailed balance and irreversible stochastic dynamics. Red blood cells provide a model system to study nonequilibrium phenomena through membrane flickering, spontaneous fluctuations driven by thermal noise and active intracellular processes. The statistics of these fluctuations reflect the mechanical and dynamical state of the membrane.
The aim of this work is to determine whether the observed dynamics depart from thermodynamic equilibrium. Classical approaches detect nonequilibrium behaviour by estimating entropy production or temporal irreversibility from stochastic trajectories. However, these methods require an explicit discretization of the state space and reliable statistical estimation, which is challenging in noisy experimental data.
We propose a data-driven machine-learning framework that learns tokenized stochastic time-series embeddings, transforming continuous trajectories into sequences of discrete latent states (tokens) through vector quantization. This representation provides a data-driven coarse-graining of the dynamics. Token distributions are analysed using a Self-Organizing Map, yielding a topological embedding of the learned dynamical states. The method is validated on Brownian dynamics simulations and applied to erythrocyte membrane fluctuations, enabling identification of dynamical states associated with nonequilibrium behaviour.

Speaker: Irene Alférez Gómez (Universidad Francisco de Vitoria)

8:10 PM Global Dynamics of Two-prey-one-predator Models with Direct Competition between the Prey : The Mathematical Parts

In this work, we revisit classical three-dimensional Lotka-Volterra two-
prey-one-predator models with direct prey competition. Employing a rescaling technique, we reduce the system to a simpler model with eight key parameters. With minimal assumptions, all parameters are grouped into four generic categories with a total of nine subcases, which are further refined into 56 sub-items to explore diverse dynamical behaviors, including the globally asymptotically stability, bistability of boundary equilibria, the existence and stability of the positive equilibrium, the existence of periodic solutions, and the complex dynamics of some solutions. Many results are novel; most findings are shown analytically; some are verified numerically; and some are open.

Speaker: Tinghui Yang (the department of applied mathematics and data science, the college of science, Tamkang University)

8:10 PM Global Dynamics of Two-prey-one-predator Models with Direct Competition between the Prey:The Biological parts

In this work, we revisit classical three-dimensional Lotka-Volterra two
prey-one-predator models with direct prey competition. Employing a rescaling technique, we reduce the system to a simpler model with eight key parameters.With minimal assumptions, all parameters are grouped into four generic categories with a total of nine subcases, which are further refined into 56 sub-items to explore diverse dynamical behaviors, including the globally asymptotically stabilities and bistabilities of boundary equilibria, the existence and stability of the positive equilibrium, the existence of periodic solutions, and the complex dynamics of some solutions. Many results are novel, most findings are shown analytically, and verified numerically.
Fromabiological perspective, we find three competition interactions among species: the resource, apparent, and trade-off competitions. These explore how the interplay between direct competition for resources, apparent competition mediated by a shared predator, and trade-off competition dictates species survival and ecosystem diversity. By symmetry and without loss of generality, we assume that one prey species (e.g., u1) is superior in its birth-to-consumption ratio, the apparent competition. Biological implications are provided to interpret the origin of the dynamics

Speaker: MING CHIEH HUANG (the department of applied mathematics and data science,the college of science,TamKang UNIVERSITY)

8:10 PM Graph-Based Nonequilibrium Analysis of RNA Polymerase Transcription from Optical Tweezers Time Series

RNAPolII transcription is a stochastic process where efficiency and fidelity emerge from nonequilibrium dynamics. We present a methodology to quantify the transcriptional efficiency of RNAPII using time series obtained from dual-bead optical tweezers experiments.

Our approach combines stochastic thermodynamics and graph-based time-series analysis. Probability fluxes along the inferred transcriptional states are estimated and used to quantify the breaking of detailed balance associated with transcriptional progression. To characterize the dynamics of RNAPII motion along the DNA template, the experimental TS are mapped into Horizontal Visibility Graphs, allowing the evaluation of the efficiency–precision trade-off in terms of the structural properties of the corresponding graphs.

Special attention is devoted to transcriptional pauses, which appear as dynamical regimes where entropy production increases significantly, suggesting enhanced nonequilibrium dissipation during these events. Finally, we incorporate hydrodynamic coupling between the two beads of the optical tweezers setup as a potential mechanism of energy transfer within the experimental system, and assess its influence on the inferred thermodynamic and graph-theoretic observables.

This framework provides a quantitative link between transcription dynamics, nonequilibrium thermodynamics, and graph-theoretical descriptors of experimental time series.

Speaker: Diego Herraez Aguilar (Universidad Francisco de Vitoria)

8:10 PM Increasing group size can cause catastrophic collapse of cooperation

In many biological and social systems, cooperation depends on collective actions that generate benefits only when a minimal number of individuals coordinate to contribute. These interactions are often modeled using threshold public goods games, in which public goods are produced only if participation exceeds a critical threshold. Cooperative groups vary greatly in size across species, with some very large groups allowing sophisticated types of cooperation, such as division of labor. But how increasing group size influences the evolutionary stability of cooperation remains poorly understood. In this study, we investigate how increasing group size affects the evolutionary dynamics of cooperation, especially when cooperation depends on reaching a certain threshold. Previous work has shown that cooperation can collapse due to increasing costs \cite{pena2014gains}. Our model reveals that a similar collapse can arise even when costs and benefits remain fixed. Specifically, increasing group size alone can alter the stability of cooperative equilibria and can cause a saddle-node bifurcation that eliminates the stable cooperative states. As group size exceeds a critical value, the stable cooperation equilibrium can disappear abruptly, leading to an abrupt transition to full defection. These findings show that increases in group size may destabilize cooperation in threshold public goods systems, explaining how cooperative behavior breaks down when benefits require coordinated effort.

Speaker: Rokeya Rahman (University of Kentucky)

8:10 PM Integrative Modelling of Innate Immune Response Dynamics during Virus Infection

Positive-sense RNA viruses employ various strategies to suppress host immune defenses. Understanding the dynamic interaction between the viral life cycle and immune signaling is crucial for designing effective antiviral strategies. Here, we develop a mathematical model integrating the intracellular viral life cycle with key innate immune pathways, including RIG-I-mediated detection and JAK-STAT signaling. The model captures both virus-specific dynamics and innate immune responses driving their coupled behavior. Comparing viruses, we show how the Japanese Encephalitis virus undergoes a dramatic reduction in viral load due to rapid replication that robustly activates the RIG-I pathway, in contrast to the poor immune control seen in HCV. Our model demonstrates that virus-host interactions exhibit sharp bifurcation behavior, where minor differences in immune strength or viral suppression capacity determine whether infections resolve or persist. We propose that ISG mRNA translation and viral replication predominantly dictate these bimodal infection outcomes. The model also recapitulates molecular players involved in IFN desensitization and predicts optimal timing and dosing strategies for interferon-based prophylactic therapies. Our approach reveals fundamental features governing the balance between infection establishment and immune control in RNA virus infections.

Speaker: Ramya Boddepalli (Indian Institute of Science Bangalore, India)

8:10 PM Ladderpath: A Compression-Based Hierarchical Framework for Biological Sequence Analysis

Ladderpath is a compression-based framework, grounded in Algorithmic Information Theory, for extracting repeated, nested, and hierarchically organized structure from symbolic sequences. Rather than treating biological sequences as flat strings, it reconstructs reusable building blocks and their dependency relations, yielding interpretable representations together with quantitative measures of complexity, hierarchical reuse, and sequence distance.

This poster presents Ladderpath as a unified mathematical and computational framework for biological sequence analysis. I introduce its core formalism, including ladderons, laddergraphs, and indices of repetition and compressibility, and show how the same representation supports multiple problems in mathematical biology. For example, Ladderpath-derived distances provide an alternative to purely alignment-based similarity measures for phylogenetic and comparative sequence analysis, enabling the study of duplication, modular reuse, and evolutionary innovation; Ladderpath-based tokenization offers a compression-guided alternative to amino-acid-level and BPE-style segmentation in protein and DNA language models, with the potential to capture longer-range regularities and biologically meaningful reusable units.

Overall, the poster argues that compression-based hierarchical decomposition provides an interpretable analytical tool and a mathematical interface connecting sequence complexity, evolution, and learning.

Speaker: Yu Liu (Beijing Normal University)

8:10 PM Learning Population Dynamical Models in Systems Biology with Mixed-Effect Gaussian Process ODEs

Ordinary differential equation models are central to systems biology and computational biology because they provide interpretable descriptions of regulatory, signaling and population-level dynamics \cite{ma}.

In many biological applications, however, longitudinal data are sparse, noisy, irregularly sampled and heterogeneous across individuals or experimental units. Classical nonlinear mixed-effects ODE models capture such heterogeneity, but rely on a fixed parametric vector field and can therefore be sensitive to model misspecification \cite{me}.

We present a Bayesian nonparametric mixed-effect ODE framework in which each subject is described by a shared population vector field together with an individual-specific deviation, both modeled with Gaussian process priors. Building on GP-ODE \cite{gpode} and Mixed-Effects GPs \cite{magma}, the proposed approach combines state-space trajectory priors with collocation-based ODE constraints, yielding tractable inference without repeated numerical ODE solves during training.

We evaluate the method on synthetic heterogeneous dynamical systems, including classical biological oscillators, and on real post-vaccination antibody kinetics data. The results show improved recovery of shared and subject-specific dynamics, better forecasting and adaptation to new subjects, and reliable uncertainty quantification, supporting the use of mixed-effect GP-ODEs as flexible data-driven dynamical models for heterogeneous biological systems.

Speaker: Julien Martinelli (Aalto University)

8:10 PM Mathematical and Mouse Models Identify T Regulatory Cell Influx as A Key Determinant of Acquired Resistance to PD-1 Immunotherapy

The immune system can eradicate cancer, but various immunosuppressive mechanisms active within a tumor curb this beneficial response. Unraveling the effects of multimodal interactions between tumor and immune cells and their contributions to tumor control using an experimental approach alone is time- and resource-intensive. To identify key immunological features associated with tumor control and escape, we built a mathematical model of the interactions between CD8+ T cells, Tregs, DCs, and tumor cells. A distinguishing feature of our model is that it captures Treg accrual occurring after checkpoint blockade immunotherapy. After fitting the model to data from an immunogenic melanoma mouse model showing resistance to αPD-1, we generated hundreds of parameter sets, each representing a unique ‘virtual mouse’ to capture individual variability. Our model indicates that the initial tumor and immune conditions instruct cancer control or progression. Increasing the initial number of CD8+ T cells alone does not always yield better outcomes; instead, the model implies there exist optimal initial immune cell ratios that result in improved tumor control. The model also predicts Treg influx as a key determinant of αPD-1 resistance. All predictions were experimentally validated. Overall, this integrated approach of modeling and experimental validation identified key determinants of resistance to immunotherapy and can be used to guide the development of more effective therapeutic strategies.

Speaker: Rachel Sousa (University of California, Irvine)

8:10 PM Mathematical model of excitation and contraction in cardiomyocytes for simulation of in vitro systems for Heart Failure drug development

Heart failure with preserved ejection fraction (HFpEF) is growing in prevalence, often attributed to an ageing and obese population. It lacks effective treatments due to poorly understood pathophysiology and absence of translationally relevant animal models \cite{gao_animal_2024}. The aim of this work is to couple an in vitro system of strip-based engineered heart tissue (EHT) with a mathematical model of excitation-contraction coupling. This is used to gain a translational model of heart failure for investigation of potential drug targets. The mathematical model integrates the ODE-based “ORd” \cite{ohara} electrophysiology model of dimension 41 with the ODE-based “HMT” \cite{hmt} contractile force model of dimension 6. The physiological coupling of the models is through calcium binding to troponin, which initiates the muscle contraction. The model is calibrated against twitch force data from EHTs consisting of human stem cell-derived cardiomyocytes and primary fibroblasts. The model reproduces baseline twitch force and captures the sigmoidal dependence of peak force on extracellular calcium concentration (0.2–1.8 mM). Experiments with administration of the well characterized calcium channel blocker verapamil (0.1, 0.5 and 1 µM) produced a dose dependent decrease in twitch force in the EHTs, which was in close agreement with model predictions. Ongoing work couples this model to a cardiac mechanics framework, enabling simulation of in vivo cardiac function and drug effects.

Speaker: Jacob Bendsen (Roskilde University. Novo Nordisk a/s)

8:10 PM Mathematical modeling of drug delivery by intra-vaginal rings, with application to trans-species ring designs

An alternative to daily or on-demand methods (pills/gels), intravaginal rings (IVRs) provide long-term, topical drug delivery for contraception, HIV prophylaxis, and hormone therapy. Current IVR designs are based on empirical interpretations of in vitro and in vivo experiments in animals and humans. We developed a deterministic mathematical model of IVR-based drug delivery, to enhance rational IVR design. This multi-compartmental model is a set of coupled PDEs and ODEs embodying conservation of mass that predicts drug diffusion across the ring and into target compartments in the female reproductive tract – vaginal fluid, epithelium, stroma, and bloodstream. Model parameters specify designer-controlled IVR (e.g. ring size, drug properties, initial drug load) and host (e.g. anatomy, histology, drug-cell interactions) characteristics. IVR parameter estimation uses a simplified one compartment model, fit to in-vitro release-into-sink data. We created scaling rules to connect ring designs and experimental data across animal and human trials. This equates/scales biologically relevant model outputs by conserving volume- and time-averaged drug concentration in target regions like the stroma . MCMC simulations captured sensitivity of model outputs to varying IVR sizes, drug loads, and biological variations within/across species. This method is robust to target Islatravir (anti-HIV) drug delivery, and is a step toward comprehensive pharmacokinetic modeling and scaling for diverse IVRs.

Speaker: Bhavana Morankar (North Carolina State University)

8:10 PM Mathematical Modeling of ECM-Targeted Therapy to Enhance Drug Delivery in Solid Tumors

Drug delivery in solid tumors is a major challenge due to the complex tumor microenvironment. Abnormal vasculature, a dense extracellular matrix (ECM), and elevated interstitial fluid pressure (IFP) hinder the penetration of therapeutic agents [1]. ECM-modifying therapies have been proposed to overcome these barriers by altering the structure of the ECM and improving drug transport in tumor tissue [2].
In this study, we develop a dynamic mathematical model of the tumor microenvironment to examine how ECM-targeted therapies influence drug delivery. The model incorporates key components of the tumor microenvironment, including tumor cell density, vascular dynamics, IFP, oxygen transport, and drug distribution. Within this framework, we investigate PEGPH20, a hyaluronan-depleting agent, to determine how hyaluronan (HA) degradation modifies the tumor microenvironment and affects drug transport.
Model simulations show that combining ECM-targeted therapy with chemotherapy improves intratumoral drug penetration compared with chemotherapy alone. Furthermore, the results suggest that appropriate treatment dosing and scheduling can enhance therapeutic outcomes. The proposed model provides a computational framework for exploring ECM-targeted treatment strategies and identifying conditions that improve drug delivery in solid tumors.

Speaker: Elif Basak Sisman (Özyeğin University)

8:10 PM Mathematical Modelling of the Tumour Microenvironment and $\gamma\delta$ T cells in Ovarian Carcinoma

Ovarian epithelial cancer still claims the highest mortality rates of all \nobreakdash{gynaecological}
cancers to date, in part due to its complex tumour immune microenvironment (TIME) \cite{Veneziani2023}. The lymphocyte $\gamma\delta$ T cell subset has emerged as a promising target in cancer-related disease, such as ovarian carcinoma, due to its immunological plasticity \cite{Schadeck2024}. Cytotoxic properties of \mbox{$\gamma\delta$ T cells} can be enhanced using bi-specific antibodies, but are subjected to the modulation of other TIME components \cite{Gonnermann2020, Schadeck2024}. One key modulator is the immuno-suppressant galectin-3, which binds $\beta$-galactoside on the cell surface \cite{Gilson2019}. \
In this mathematical modelling approach, we develop a set of ordinary differential equations (ODE) which explores the system dynamics of $\gamma\delta$ T cells and galectin-3 in ovarian cancer. More specifically, we analyse characteristic T cell behaviour including exhaustion, proliferation and tumour cell killing by assessing the functional response models.

Speaker: Cedrik Neber (University Hospital Schleswig-Holstein, Kiel)

8:10 PM Mechanistic Integration of Longitudinal RNASeq Data to Reveal Novel Biomarkers in Parkinson's Disease

Parkinson's disease (PD) is a progressive neurodegenerative disorder whose underlying molecular mechanisms remain poorly understood, hindering development of targeted therapeutics. While 10% of cases are linked to mutations in over 20 genes, the majority are idiopathic, reflecting the disease's complexity. Recent approaches use multi-OMICS characterization of patient-derived neurons obtained through differentiation of induced pluripotent stem cells (iPSC), however, identifying underlying mechanisms of PD remains challenging. We addressed this challenge by a Non-negative Matrix Tri-Factorization (NMTF) framework that mechanistically integrates longitudinal RNASeq data from patient-derived dopaminergic neurons carrying PD-associated mutations in the PINK1 and SNCA genes. Single-cell RNA sequencing, proteomics, and metabolomics data — spanning iPSC differentiation across seven timepoints — are processed via a high-performance computing pipeline and enriched with biological knowledge from the BioGrid database. The NMTF decomposes data into genotype and phenotype embedding spaces, enabling comparison of genotype-phenotype coupling matrices across conditions to identify impaired regulatory pathways. Applying this pipeline to the iPSC derived neurons, reveals both common and mutation-specific disease mechanisms that extend our knowledge about PD development and progression beyond the classical differentially expressed gene analysis.

Speaker: Cyrille Lorenz-Dittmar (University of Luxembourg)

8:10 PM Metabolic Bacterial Game

Bacteria interact in different ways, from competition to cooperation, depending on resource availability in the environment.
Identifying environments that foster these dynamics is both important and challenging, as the outcomes often depend on subtle alignment between the dynamic metabolic needs of species.
A common community approach to this challenge has been metabolic modeling.
Genome-scale metabolic models can identify interactions between species, but they are computationally expensive when applied to large communities.
In fact, metabolic modeling often cannot fully capture the discrete nature of species, as these models typically optimize the total biomass of the system rather than the behavior of individual organisms.

We propose a simpler and more tractable alternative, the Metabolic Bacterial Game (MetaBGame), in which bacteria strategically consume or produce environmental compounds according to their metabolic needs.
The framework employs multi-agent reinforcement learning and can operate under perfect or imperfect information, reflecting whether agents fully observe or only infer each other’s metabolic states.
Our results demonstrate that in MetaBGame we can scale and learn communities up to thousand agents in 34 hours. On top of that, our simple design allows easily identifying competitive and cooperative strategies. MetaBGame is implemented in JAX, allowing scaling across different hardwares, including CPUs and GPUs.

Speaker: Oleksandr Cherednichenko (Umeå University)

8:10 PM Modeling Neurovascular Coupling

The brain critically depends on a continuous vascular supply of oxygen and glucose. Cerebral blood flow is locally regulated by neuronal activity through neurovascular coupling (NVC), a mechanism that optimizes energy delivery to active brain regions via coordinated vasodilation and vasoconstriction. NVC arises from interactions between neurons, astrocytes, and blood vessels. While vasodilation has been extensively studied, the mechanisms underlying vasoconstriction remain less understood.

To address this gap, we developed minimal differential equation models describing changes in arteriole diameter during vasoconstriction induced by different stimuli. These models were fitted to experimental data from mouse brain slices and accurately reproduced arteriole contraction dynamics across conditions.

We specifically analyzed vasoconstriction induced by Prostaglandin E2 (PGE2) and Neuropeptide Y (NPY). Beyond reproducing experimental responses, the model enables estimation of free parameters, supporting its predictive capacity. We further extended this framework to capture the bidirectional interaction between neuronal activity and vasomotion, coupling a neuronal activity variable to arteriole diameter dynamics and forming a closed feedback loop between neuronal demand and vascular tone.

Speaker: Léa Benyakar (Sorbonne Université, CNRS, INSERM, Neurosciences Paris Seine - Institut de Biology Paris Seine (NPS-IBPS))

8:10 PM Multi-Scale Mathematical Modelling of Prostate Cancer Response to Iron-Supplemented Ferroptosis

Prostate cancer (PCa) has been widely studied, yet new strategies are needed to mitigate resistance and recurrence. Ferroptosis, an iron-dependent form of regulated cell death, is emerging as a promising therapeutic strategy, yet its mathematical modelling in PCa remains limited \cite{Maccarinelli2023}. This is especially relevant for castration-resistant prostate cancer (CRPC), where hormonal control fails and new therapies are needed. In this work, we developed a hybrid multi-scale framework to investigate the response of PCa to iron-supplemented, RSL3-induced ferroptosis. We use an ABM to represent the growth and treatment response dynamics of normal and cancer cells (e.g. proliferation, necrosis, phenotypic switching, and ferroptotic death), PDE reaction-diffusion equations for nutrients and drugs in the tumour microenvironment, and ODEs for the intracellular dynamics of key ferroptosis factors (e.g. iron, lipid hydroperoxides, and GPX4). Simulations of this hybrid ABM-PDE-ODE system calibrated to in vivo experiments reasonably capture tumour progression, treatment response, spatial patterns of the cellular species and drug-combination effects. Thus, by coupling intracellular biochemistry with spatial tumour dynamics, our framework enables investigation of how iron availability and GPX4 inhibition govern ferroptotic sensitivity, and how treatment scheduling and dosing can be optimised to maximise tumour elimination and prevent progression to CRPC.

Speaker: Ms Eisha Arif (University of Sussex)

8:10 PM Multiscale Analysis of Gut Dysbiosis Identifies Time-Adaptive Immune Augmentation as an Inflammatory Flare Suppression Strategy

Chronic inflammatory disorders, such as inflammatory bowel disease (IBD), are characterized by unpredictable transitions between disease remission and debilitating flare-ups driven by gut dysbiosis. Despite extensive research, the mechanistic drivers of these relapse-remission cycles and the optimal strategies to restore stability remain elusive. Here, we introduce a minimal mechanistic ordinary differential equation model coupling bacterial burden and innate immune activity, which we calibrated to longitudinal in vivo infection data and validated against an independent chemically induced colitis dataset. Using steady-state control maps, we delineate distinct disease regimes and demonstrate that increasing immune recruitment capacity can shift flare-prone dynamics into a stable recovery state. To operationalize this finding, we applied Computational Singular Perturbation (CSP) to dissect the multi-scale dynamics of the system, pinpointing a critical "explosive" time window preceding flare peaks. CSP diagnostics identified immune decay as the dominant driver of oscillation growth, enabling the design of a time-adaptive, threshold-triggered intervention protocol that systematically suppresses recurrent flares. Ultimately, this analysis challenges the strictly immunosuppressive paradigm of current therapies, providing a mathematically grounded framework for stabilizing dysbiosis through targeted immune augmentation.

Speakers: Haya Mayoof (Khalifa University), Dr Dimitris Manias (Khalifa University), Haralampos Hatzikirou (Khalifa University)

8:10 PM Non-Periodic Steady State in a Closed Ferroin-Catalyzed Belousov–Zhabotinsky Reaction induced by High Stirring Rates

It is intuitive that stirring homogenizes and increases the efficiency of liquid chemical reactions. However, in complex nonlinear systems, stirring can also alter intrinsic dynamics. Such systems may show bistability, excitability, or periodicity. A prominent example is the Belousov-Zhabotinsky reaction, where stirring effects have long been studied \cite{menzinger_concentration_1990,strizhak_stirring_1996,ruoff_excitability_1982}. In a closed ferroin-catalyzed batch reaction, high stirring rates within the periodic regime suppress oscillations \cite{ruoff_excitability_1982}. Experiments show that oscillations reappear once stirring stops or the stirring rate is decreased. For moderate stirring rates, oscillations remain, but amplitudes increase after stirring stops. The effect also depends on reaction volume, geometry, and the phase at which stirring begins.
Due to the complex interplay of reaction, diffusion, and convection, theoretical explanation is challenging \cite{noszticzius_hydrodynamic_1991,kalishyn_stirring_2010}. We aim to model the effect using diffusion-controlled reactions where the diffusion is affected by the turbulence created by the process of stirring. We conjecture that the stirring rate acts as a bifurcation parameter and present a detailed overview of our experimental findings and discuss a first version of the proposed model.

Speaker: Mihnea Hristea

8:10 PM ON A MODIFIED LESLIE-GOWER MODEL WITH PREY DEFENSE AND PREDATOR CANNIBALISM

Recent experiments show that cannibalism in predators and de-
fense in prey can both occur concurrently. Motivated by this, we investigate
a predator-prey system where cannibalism occurs in predators and defense in
prey simultaneously. System analysis show that depending on the prey defense
(µ) and predator cannibalism (c) parameters respectively, one can have global
stability of the coexistence and prey free states, bi-stability dynamics or up
to three interior equilibria. Local stability analysis shows that, the combined
effects of c and µ cannot drive both populations to extinction and for certain
parameter choices can destabilize the system. After varying the parameters µ
and c, the system undergoes standard co-dimension one bifurcations includ-
ing Hopf bifurcation, transcritical bifurcation and saddle-node bifurcation. In
addition, the system undergoes co-dimension two bifurcations such as cusp bi-
furcation and Bogdanov-Takens bifurcation. For the spatially explicit model,
we observe that in the absence of both µ and c, the system cannot exhibit Tur-
ing instability, whereas the system can produce Turing instability depending
on system parameters when present. We support our results with numerical
experiments and discuss their ecological implications.

Speaker: Gloria Botchway (AIMS, Ghana)

8:10 PM Optimal control approach to obesity reduction

This study numerically investigates optimal intervention strategies for reducing overweight and obesity using a compartmental dynamical model with three classes: normal-weight, overweight, and obese individuals. Two time-dependent controls are considered: a preventive strategy promoting healthy lifestyles and a treatment intervention targeting obese individuals. The optimal control problem is solved using Pontryagin’s Minimum Principle and implemented numerically through the Forward–Backward Sweeping Method with a fourth-order Runge–Kutta scheme.
Simulations are performed over a 10-year horizon, assuming a constant population and initial prevalence levels consistent with reported data. Three intervention scenarios are examined: prevention only, treatment only, and a combined strategy. Results show that preventive measures significantly reduce the overweight population and indirectly lower obesity prevalence, whereas treatment directly reduces obesity but has a weaker impact on overweight individuals. The combined strategy yields the best outcomes, increasing the proportion of normal-weight individuals while reducing both overweight and obesity levels.
Optimal control profiles indicate sustained preventive effort and gradually decreasing treatment intensity over time. Overall, the numerical analysis highlights the importance of integrating preventive lifestyle campaigns with treatment programs to achieve effective long-term control of obesity.

Speaker: Olga Vasilieva (Universidad Del Valle)

8:10 PM Optimizing cell-cycle–targeted drug combinations for high-grade serous ovarian cancer: An integrated approach

High-grade serous ovarian cancer (HGSOC) is the leading cause of gynecologic cancer mortality. Late diagnosis, widespread disease, and frequent relapse limit the effectiveness of current therapies. p53 deficiency indicates HGSOCs are vulnerable to cell-cycle inhibitors; however, currently available agents have shown less clinical benefit than expected. We hypothesize that maximizing the efficacy of these drugs requires treatment schedules that exploit HGSOC cell-cycle dynamics.

Experimental results showed the CDC7 inhibitor Simurosertib (active in G1 and S) and the PKMYT1 inhibitor Lunresertib (active in G2 and M) have strong synergy, even with sequential administration. Our associated ODE model, incorporating mechanistic knowledge of the cell cycle and drug action, showed that cell-cycle dynamics were key to this synergy. Subsequent time- and cell-cycle-resolved tracking data revealed cell-line-specific differences in cell-cycle distribution, motivating an expansion of the model that better integrated drug effects across phases and cell lines.

The calibrated model predicts schedule-dependent differences in cell death and tumor burden driven by cell-cycle dynamics and pre-existing mutations. These results highlight the potential of quantitative modeling to guide scheduling of cell-cycle inhibitors and support the development of personalized treatment strategies for HGSOC.

Speaker: Agata Xella (Moffitt Cancer Center)

8:10 PM Optimizing enzyme inhibition analysis: precise estimation with a single inhibition concentration

Enzyme inhibition analysis is essential in drug development and food processing, necessitating precise estimation of inhibition constants. Traditionally, these constants are estimated through experiments using multiple substrate and inhibitor concentrations, but inconsistencies across studies highlight a need for a more systematic approach to set experimental designs across all types of enzyme inhibition. Here, we address this by analyzing the error landscape of estimations in various experimental designs \cite{jang2025optimizing}. We find that nearly half of the conventional data is dispensable and even introduces bias. Instead, by incorporating the relationship between IC50 and inhibition constants into the fitting process, we find that using a single inhibitor concentration greater than IC50 suffices for precise estimation. This IC50-based optimal approach, which we name 50-BOA, substantially reduces (>75%) the number of experiments required while ensuring precision and accuracy. Additionally, we provide a user-friendly package that implements the 50-BOA.

Speaker: Hyeong Jun Jang (Graduate School of AI for Math, KAIST, Daejeon, Republic of Korea)

8:10 PM Percolation theory and Voronoi geometry for modeling protein-ligand interactions

In the field of structure-based drug design, there is enormous interest in determining the binding characteristics and physical orientations of putative therapeutic ligands within the binding sites of the proteins they target. A primary tool to investigate this binding interaction involves characterizing the structure of the protein bound to its ligand, typically using X-ray crystallography and Cryo-EM as structural methods. In this work, we take a modeling approach to the problem, using tools from spatial stochastic processes and stochastic geometry to understand the dynamics and shape configurations underlying this problem. We use percolation theory to model aspects of ligand contact with the protein target, coupled with Voronoi geometry (and its dual, Delaunay tessellation) to capture protein pocket geometry and ligand orientation effects. Percolation theory is a mathematical formalism that deals with how connected clusters occur in random graphs/networks. It is employed for modeling a wide array of problems involving disordered or porous media, such as protein crystalline arrays used in ligand structural studies. Our work addresses new challenges in applied percolation, including comparing diffusional versus invasive percolation, and specific problems arising from definition of boundary conditions for the percolation process.

Speaker: Dr Miranda Lynch (University at Buffalo/Hauptman-Woodward Institute)

8:10 PM Physics-Informed Neural Networks for Mathematical Models on Alzheimer's Disease Dynamics

Mathematical models can be used in order to verify medical hypotheses and quantify the mechanisms of the progression of neurological pathologies like Alzheimer's disease. Here we consider a model based on ordinary differential equations incorporating dynamics of toxic proteins like Amyloid $\beta$ species and tau tangles and describing their spread on a brain graph based on the human connectome, where brain regions are connected by edges representing fiber tracts.\cite{Bianchi2024MCA}
In order to solve the differential equation and compare the results with clinical data, Physics-Informed Neural Networks (PINNs\cite{Raissi2019CP}) can be leveraged. The deep-learning framework has shown to be powerful by combining previous physical knowledge with sparse or noisy data\cite{Zhang2024CMAME}, in this case tau concentrations inferred from PET scans of subjects with Alzheimer's disease \cite{Petersen2010N}. Choosing the best suited hyperparameters and the weights of the individual loss function terms is delicate, but even with a quite simple network architecture, results have been achieved that are comparable with those given by standard numerical methods in a steady-state setup.
Future applications and extensions of the approach will involve model parameters estimation by setting specific variables trainable within the PINN. Identifying the most suitable parameter values will allow further assessment of the model’s ability to reproduce observed patterns of pathology.

Speaker: Samira Breitling (PhD student)

8:10 PM Quantifying the Impact of Healthcare Accessibility on Non-COVID Excess Mortality During the COVID-19 Pandemic in South Korea

Spatial accessibility to healthcare can influence population health outcomes during large-scale public health crises. However, its contribution to excess mortality beyond directly reported COVID-19 deaths remains insufficiently quantified. This study evaluates the relationship between regional healthcare accessibility and excess mortality across South Korea during the COVID-19 pandemic.

Regions were grouped using hierarchical clustering based on average travel time to medical facilities, producing high- and low-accessibility clusters. A counterfactual mortality baseline was estimated using a machine-learning prediction model trained on pre-pandemic mortality data from 2014–2019. Excess mortality during the pandemic period (2020–2022) was calculated as the difference between observed and predicted deaths. The association between accessibility and excess mortality was then assessed using multiple linear regression.

Regions with lower healthcare accessibility showed substantially higher excess mortality, particularly during the Omicron wave when healthcare demand was highest. In high-accessibility regions, excess mortality largely aligned with reported COVID-19 deaths, whereas low-accessibility regions exhibited additional excess mortality not explained by COVID-19 fatalities. These findings highlight how spatial healthcare accessibility may amplify indirect mortality during pandemics.

Speaker: Soyoung Kim (National Institute for Mathematical Sciences)

8:10 PM Reaction Kinetics of Ryanodine Receptors in a Closed–Open–Inactivated Model

Calcium-induced calcium release plays a significant role in mammalian skeletal and cardiac cell excitation. The ion channels responsible for this process are called ryanodine receptors (RyRs), which can exist in several conformational states, including open, closed and inactivated. Transitions between these states are regulated by concentrations of ligands, particularly calcium and magnesium. Recently, Zahradníková and colleagues proposed a structurally-informed allosteric model for this system, that reproduces the steady-state probabilities of RyR channels being open across a range of ligand concentrations~\cite{zahradnikova2025structure}. In this work, we develop a continuous-time Markov chain model for the Closed–Open–Inactivated (COI) gating scheme corresponding to this framework, allowing the kinetic behaviour of RyR channels to be studied beyond steady-state thermodynamics. The model enables the calculation of experimentally observable quantities such as open- and closed-time distributions and burst statistics, providing a link between structural models of RyR regulation and single-channel experimental recordings.

Speaker: Ms Anna Hlubinová (Comenius University Bratislava)

8:10 PM Real-time detection of aberrant physiological changes from wearable data using Kalman Filtering and Autoencoder

Consumer-grade wearables enables continuous monitoring and early detection of aberrant physiological signals associated with diverse health issues. However, substantial measurement noise and natural physiological variability in wearable data have prevented reliable identification of physiological anomalies, limiting their deployment in real-world and clinical settings. Here, we propose a real-time anomaly detection framework that first estimates latent physiological dynamics using a Kalman filter and subsequently detects anomalies using an autoencoder-based model. By explicitly modeling physiological dynamics, our approach projects out known sources of variation such as circadian rhythms, intrinsic biological fluctuations, and measurement noise, leaving anomalies visible in the residual. We tested our method on real-world wearable body temperature data from cancer patient and showed that it can detect early signals of impending fever events. Applying anomaly detection after physiological filtering outperforms an existing method of directly applying the autoencoder to raw data, including LSTM-autoencoder based models previously used for wearable anomaly detection. This indicates the importance of incorporating physiological structure and filtering into machine learning pipelines.

Speaker: Yejoon Wang (KAIST)

8:10 PM Risk-aware mechanistic framework for early detection of post-radiotherapy biochemical relapse in prostate cancer

Patient monitoring after radiotherapy for prostate cancer relies on population-based thresholds of rising prostate-specific antigen (PSA), ignoring patient-specific tumor dynamics and uncertainty. To avoid delays in recurrence detection and treatment, we propose a personalized Bayesian mechanistic framework to forecast post-radiotherapy PSA dynamics. These forecasts enable the definition of risk-aware biomarkers of biochemical relapse, such as surviving tumor cell proliferation rate and time to progression. The mechanistic model is calibrated using longitudinal measurements, yielding posterior distributions of PSA over time and the model-based biomarkers. To quantify biochemical relapse risk, we summarize posterior distributions using α-superquantiles to capture adverse tail behavior and evaluate them using leave-one-out cross-validated ROC analyses and comparison across post-treatment time horizons. The most informative model-based biomarkers achieve high discriminative performance, which is superior to standard PSA-based metrics (e.g., PSA nadir, time to PSA nadir). To further assess clinical relevance, we introduce a days gained metric, representing the time gained by model-based relapse detection compared with standard-of-care PSA-based criteria (e.g., nadir+2 ng/mL). Pareto front analyses reveal trade-offs between classification accuracy (sensitivity/specificity) and early detection, enabling risk-aware selection of biomarker thresholds for clinical decision-making.

Speaker: Miguel Anxo Vicente Pardal (University of A Coruña)

8:10 PM Social information under restricted observations

Observing the decisions and actions of others within a group (such as running from a predator) provides social information that can inform actions such as whether to follow. We consider a model where all agents simultaneously gather stochastic private information (weighted towards an unknown preference), coming to a decision once sufficiently confident. These observing agents infer the state of the private information from these decisions and use this as social information that they incorporate with their private information; they will follow the observed decision if they are sufficiently confident with this new social information. Unlike previous models, we assume that agents can only observe the decisions of some (but not all) other agents at any one time. Consequently, first decisions are unseen by many, meaning decisions instead spread through a `network of observation' and that the first decision seen by an agent could be the result of social information acquired by earlier hidden decisions. We will explore how the properties of the network of observation affect how social information and decisions spread, as well as how this affects decision accuracy and consensus within the group.

Speaker: Andrew Bate (University of Leeds)

8:10 PM Structural inference over reaction network spaces

Dynamical systems in biochemistry are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing time-series of species concentrations, the unknown reactions between the species. Most frequentist approaches to CRN inference focus on identifying a single, most likely CRN, without addressing uncertainty about the network structure. On the other hand, Bayesian treatments of CRN inference typically involve trans-dimensional and multimodal posterior distributions, which are computationally challenging to deal with. This poster illustrates how Bayesian CRN inference can be tackled with tempered spike-and-slab distributions, with applications to population models in ecology. Results are benchmarked against approaches that exhaustively consider all networks to evaluate how well our method explores the relevant networks.

Speaker: Elijah Foo (University of Melbourne)

8:10 PM SymScore: Machine Learning Accuracy Meets Transparency in a Symbolic Regression-Based Clinical Score Generator

Self-report questionnaires are widely used in healthcare to assess disease risk and symptom severity. However, their length can burden respondents and compromise data quality. While machine learning models have enabled the development of shortened questionnaires with high predictive performance, they often operate as black boxes, limiting transparency and requiring specialized expertise that hinders clinical adoption.
To address this, we have developed the Symbolic Regression-Based Clinical Score Generator (SymScore), a framework designed to produce score tables for shortened questionnaires while maintaining accuracy comparable to machine learning approaches. SymScore employs symbolic regression to optimize response grouping and assign predictive weights that capture the relationship between questionnaire responses and disease severity. The resulting score tables provide a transparent and practical tool for clinical use.
SymScore achieves performance comparable to high-accuracy machine learning-based instruments, including MCQI-6 (MAE = 9.94, R² = 0.82) and SLEEPS (AUROC = 0.88–0.94), developed for assessing sleep disorders. Beyond these applications, SymScore has also been applied to questionnaires evaluating sleep-related cognitive dysfunction in patients with cancer.
By combining predictive performance with interpretability, SymScore offers a practical pathway for translating advanced computational methods into trustworthy and accessible tools for healthcare professionals.

Speaker: Olive Cawiding (Department of Mathematical Sciences, KAIST, Daejeon, 34141, Republic of Korea)

8:10 PM Turing Instability in a Reaction-Diffusion Predator-Prey Model with Prey Infection and Intraspecific Predator Competition

This study investigates a predator–prey system incorporating a transmissible disease that spreads exclusively within the prey population and intraspecific competition among predators. The dynamics are modeled using a system of reaction–diffusion equations to account for both local interactions and spatial movement. In this system, we focus on the occurrence of diffusion-driven instability, or Turing instability. Using linear stability analysis, we determine parameter regimes under which diffusion destabilizes the stable homogeneous interior equilibrium. This instability can lead to the emergence of spatially heterogeneous structures known as Turing patterns, which may correspond to clustering phenomena observed in ecological systems. Numerical simulations are performed in a two-dimensional spatial domain in order to illustrate these dynamics. The results demonstrate the emergence of complex spatial patterns and emphasize the significant role of diffusion coefficients in shaping spatial heterogeneity. These findings provide insight into the mechanisms underlying spatial pattern formation in predator–prey interactions influenced by prey infection and predator competition.

Speaker: Mark Lois Fortin (University of the Philippines Diliman)

Fri, July 17

10:40 AM → 12:00 PM Modeling Avian Influenza Dynamics

10:40 AM Co-circulation of low and highly pathogenic avian influenza viruses in poultry farms: an integrated experimental and modeling framework

Emergence of high-pathogenicity avian influenza virus (HPAIV) H5 or H7 variants, following infection with low-pathogenicity avian influenza (LPAIV) of several poultry flocks or directly after infection of a single of few flocks within a poultry farm, emphasizes the need for understanding co-circulation dynamics of LPAIV and HPAIV in poultry farms to develop adequate control strategies. Although the transition from LPAIV to HPAIV is a well-documented phenomenon, limited knowledge exists on the epidemiological processes leading to selection of the HPAIV variant following its emergence in a flock. We performed transmission experiments in chickens to assess transmission of field sample containing a mix of both LPAIV and HPAIV and experiments with purified LPAIV and HPAIV variants. We derived quantitative estimates of key epidemiological parameters and developed a mechanistic stochastic Susceptible-Infectious-Recovered model, based on these estimates. We found that if HPAIV randomly emerges within an LPAIV infected chicken within the first 10 days following the start of LPAIV outbreak in a flock, a large fraction of chickens in the flock will become infected with the HPAIV (“major outbreak”) with a probability of 0.9, followed by a gradual decline over subsequent days, resulting in a probability of less than 0.1 at 17 days post-mutation. We discuss the implications for control and surveillance measures of the HPAIV in poultry farms, and how these findings can support policymakers.

Speaker: Hadi Taghvafar (Wageningen Bioveterinary Research)

11:00 AM Mapping avian influenza risk across the ecological niches of HPAI and the wild–poultry interface

Since 2020, highly pathogenic avian influenza (HPAI) H5N1 clade 2.3.4.4b has spread rapidly and widely, affecting a growing diversity of avian species across five continents and increasingly spilling over into mammals. Addressing this challenge requires characterising both where environmental conditions are suitable for viral circulation and where the wild bird reservoir poses the greatest spillover risk to poultry. These represent two complementary but distinct modelling problems.

Using an ecological niche modelling approach, we investigate which environmental predictors are associated with the post-2020 surge in H5N1 and H5Nx cases, whether the ecological niche of HPAI has shifted over time, and whether models trained on pre-2020 data retain predictive transferability to the current epidemiological situation \cite{dupas2025global}. Models were fitted separately for wild and domestic bird occurrences across two periods (2015–2020 and 2020–2022). Post-2020, intensive chicken population density emerged as the dominant predictor, alongside cultivated vegetation, suggesting a transition toward farm-to-farm transmission dynamics rather than wild bird-driven spillover.

We further develop a modelling framework based on reservoir distribution, combining a systematic meta-analysis of AIV prevalence in wild birds \cite{dupas2026patterns} with species-richness maps weighted by host abundance and prevalence, providing a basis for spatially explicit introduction-risk modelling.

Speaker: Marie-Cécile Dupas (Université Libre de Bruxelles)

11:20 AM Ecological and environmental predictors of highly pathogenic avian influenza risk in wild birds across Europe: a Bayesian machine learning approach

Highly pathogenic avian influenza (HPAI) represents a serious threat to animal and human health, with the ongoing H5N1 outbreak within the H5 2.3.4.4b clade being one of the largest on record. Although wild birds are known to be a key reservoir of HPAI, the factors driving prevalence within this reservoir remain poorly understood. In this study we use Bayesian additive regression trees, a machine learning method designed for probabilistic modelling of complex nonlinear phenomena, to construct species distribution models (SDMs) for HPAI presence and identify factors driving geospatial patterns of infection in wild birds across Europe. Our models are time-stratified to capture both seasonal changes in risk and shifts in epidemiology associated with the succession of earlier strains by H5N1 within the clade. While previous studies aimed to model HPAI presence from physical geography, we explicitly consider wild bird ecology by including estimates of bird species richness, abundance of specific taxa, and “abundance indices” describing total abundance of birds with high-risk behavioural traits. Our model projections indicate a shift in persistent, year-round risk towards cold, low-lying regions of northwest Europe associated with H5N1. Methodologically, we demonstrate that while most variation in risk can be explained by climate and physical geography, adding host ecology is a valuable refinement to SDMs of HPAI.

Speaker: Joe Hilton (University of Manchester)

11:40 AM The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

Previous research efforts on highly pathogenic H5N1 avian influenza (HPAI) suggest that different avian species exhibit a varied severity of clinical signs after infection. Waterfowl, such as ducks or geese, can be asymptomatic and act as silent carriers of H5N1, making detection harder and increasing the risk of further transmission, potentially leading to significant economic losses. For backyard hobby farmers, passive reporting is a common HPAI detection strategy. We aim to develop a computational, mechanistic model to quantify the effectiveness of this strategy by simulating the spread of H5N1 in a mixed-species, small-population backyard flock. Quantities such as detection time and undetected burden of infection in various scenarios are compared. Our results indicate that the presence of ducks can lead to a higher risk of an outbreak and a higher burden of infection. If most ducks within a flock are resistant to H5N1, detection can be significantly delayed. We find that within-flock infection dynamics can heavily depend on the species composition in backyard farms. Ducks, in particular, can pose a higher risk of transmission within a flock or between flocks. Our findings can help inform surveillance and intervention strategies at the flock and local levels.

Speaker: Steve Wu (University of Warwick)

10:40 AM → 12:00 PM Reaction networks: Mathematical structures and concrete biochemical systems

10:40 AM Automatic initial estimates of reaction rate coefficients

Fitting functions to data with nonlinear parameter dependence is challenging, particularly for differential equations common in chemical kinetics, due to the need for good initial estimates. We propose a method to automatically generate robust initial estimates for mass-action kinetic ODEs (where the right-hand side is linear in parameters). Illustrative examples show these estimates often yield highly accurate final fits.

Speaker: János Tóth (Eötvös Loránd University Budapest)

11:00 AM Turing instability in reaction networks with one diffusing species

Conditions for Turing instability in reaction networks involving two interacting species are well understood and typically require self-activation or autocatalysis. However, general criteria for the emergence of Turing instabilities in large-scale reaction networks are less studied. We consider a reaction network with an arbitrary number of species, in which only a single species diffuses. We establish a novel condition for Turing instability, which arises when a spatially homogeneous equilibrium loses stability via a pair of complex conjugate eigenvalues.

Speaker: Maya Mincheva (Northern Illinois University)

11:20 AM Buffering Structures and Factorization of the Jacobi Determinant in Biochemical Reaction Networks

In the bifurcation analysis of biochemical reaction networks, the determinant of the Jacobian of the corresponding ODE system plays a crucial role. When network parameters are treated symbolically, computing this determinant becomes challenging, even for moderately sized systems. This computation can be simplified if one decomposes the network into subnetworks such that the Jacobi determinant factorizes into a product of determinants associated with these subnetworks. One such known decomposition is based on so-called buffering structures. In this talk, we show that buffering structures are not only sufficient but also necessary for a factorization of the Jacobi determinant. Furthermore, we present an effective computational method for detecting buffering structures in a given reaction network.

Speaker: Máté László Telek (Budapest University of Technology)

11:40 AM Autocatalysis in Reaction Networks with Explicit Catalysis

In the practical analysis of chemical reaction networks, it is often assumed that no explicit catalysts exist, i.e., that species appear both as a reactant and a product in the same reaction.
In this case, the stoichiometric matrix uniquely identifies the corresponding reaction network (RN), and methods from matrix theory naturally apply. However, catalysis plays an important role, in particular for biochemical reactions. We, therefore, adapt here the concepts derived for autocatalytic cores, the minimal units accounting for the emergence of autocatalysis, to RNs with explicitly catalyzed reactions. In this setting, we confirm that an inspection of the stoichiometric matrix alone is inconclusive concerning the presence and number of autocatalytic cores, and that a more delicate algebraic analysis is required. Nevertheless, this generalization demonstrates that, up to certain subtleties, both the graph and matrix representations of autocatalytic cores are preserved. We additionally show that in the common case of unit stoichiometries (0 and 1), autocatalytic cores containing explicitly catalyzed reactions always have a spanning subgraph that is composed of a single loop with a simple metabolite-to-reaction chord.

Speaker: Richard Golnik (University Leipzig)

10:40 AM → 12:00 PM Prospectives in HIV

10:40 AM Tracking and predicting the dynamics of HIV-1 epidemics in France using virus genomic data

Understanding the dynamics of HIV epidemics is important to control them effectively. Classical methods that mainly rely on occurrence data are limited by the fact that an unknown part of the epidemic eludes sampling. Since the early 2000s, phylodynamic methods have enabled the estimation of key epidemiological parameters from virus genetic sequence data. These methods have the advantage of being less sensitive to sampling bias and to track the epidemic history even before the date of the first samples. In this study, we analysed 2,205 HIV sequences from the French ANRS PRIMO C06 cohort. We identified and were able to reconstruct the history of two large clades that reflect key features of the HIV-1 epidemics in the country. Using Bayesian phylodynamic inference models, we found that the first clade, from subtype B, originated in the end of 1970s, grew rapidly during the 80s before decreasing from 2000 to 2015 and stagnating since then. The second clade, from CRF02_AG, emerged and spread in the 80s, grew again in the early 2000s, before declining slightly. Finally, using numerical simulations, we investigate prospective scenarios for future epidemic trends. This study is one of the first to analyse the HIV epidemic in France using phylodynamics methods. It demonstrates the historical and public health value of routine HIV sequence data in epidemiological surveillance.

Speaker: Louis Colliot

11:00 AM Elucidating the mechanism of synergy between latency reversal agents and broadly neutralizing antibodies for HIV remission

Recent studies have shown that the administration of combinations of latency reversal agents (LRAs) and broadly neutralizing antibodies (bNAbs) at the time of antiretroviral therapy (ART) cessation significantly enhances the chances of eliciting long-term control of HIV post treatment over that with ART alone. Surprisingly, neither LRAs nor bNAbs succeed independently, implying strong synergy between them. The mechanism(s) underlying the synergy remain unknown, precluding optimal deployment of the drug combinations. Here, we posit a mechanism of synergy and evaluate it using mathematical modeling. When ART is successful, productive viral replication is nearly completely halted. Under these circumstances, LRAs reactivate latently infected cells, triggering bursts of viral production. bNAbs bind to these virions and enhance antigen presentation to immune cells, stimulating HIV-specific CD8 T-cells. The combination, administered towards the end of ART, thus leaves a reduced latent reservoir and a primed CD8 T-cell population. The smaller reservoir size suppresses the magnitude of the viral rebound post ART. The primed CD8 T-cell population proves adequate to exert lasting control of the rebounding virus. Our model, based on the above mechanism of synergy, recapitulated clinical data of long-term remission following the LRA/bNAb combination therapy. The model offered insights into the role of CD8 T-cells in eliciting and maintaining viremic control and presented a route to identifying optimal dosages of LRAs and bNAbs for achieving this control, informing ongoing clinical trials.

Speaker: Narendra Dixit (Indian Institute of Science)

11:20 AM Simulating adaptive within-host HIV sequence evolution

Simulating within-host virus sequence evolution allows for the investigation of factors such as the role of recombination in virus diversification and the impact of selective pressures on virus evolution. Here, we describe a new software to simulate virus within-host evolution called wavess (within-host adaptive virus evolution sequence simulator), a discrete-time individual-based model and a corresponding user-friendly R package. The underlying model simulates recombination, a latent infected cell reservoir, and three forms of selection: conserved sites fitness and replicative fitness in comparison to a reference sequence, and immune fitness including cross-reactivity imposed by a co-evolving immune response. We applied this model to investigate the selection pressures on HIV-1 env sequences longitudinally collected from 11 individuals. The best-fitting immune cost differed across individuals, mirroring the real-world expectation of heterogeneous immune responses among human hosts. Furthermore, the phylogenies reconstructed from these simulated sequences were similar to the phylogenies reconstructed from the real sequences for all summary statistics tested. The wavess R package can be downloaded from https://github.com/MolEvolEpid/wavess.

Speaker: Narmada Sambaturu

11:40 AM Binding mediated clearance of anti-HIV-1 broadly neutralizing antibodies in viremic individuals

Due to their long-half life and breadth of coverage, broadly neutralizing antibodies (bnAbs) are increasingly studied for both treatment and prevention of HIV-1 infection. Recent clinical studies have shown potent neutralization with corresponding multiple log-declines following single or multiple administrations of bnAbs in viremic participants. While bnAb concentrations typically exhibit biphasic decline during these trials, bnAb pharmacokinetics significantly differ between HIV-1 positive and negative individuals during phase I trials. These differences are hypothesized to be driven by nonlinear interactions between bnAb and circulating virus that result in increased clearance of bnAb-virus complexes. I’ll discuss a series of mechanistic models that quantify these nonlinear effects across three phase I clinical trials of distinct bnAbs. I’ll show how the dynamics of these bnAb-virus complexes can explain nonlinear viral dynamics during early bnAb treatment and implicate the immune system in the viral dynamics following bnAb treatment.

Speaker: Tyler Cassidy (University of Leeds)

10:40 AM → 12:00 PM Recent mathematical discoveries in Population Dynamics, Ecology and Evolution

10:40 AM Mixed Contact–Pheromone Feedback in Ant Foraging: Thresholds, Oscillations, and Multistability

Ant colonies regulate foraging via nest-entrance contacts and short-lived pheromone cues. We propose a mechanistic mathematical model tracking an entrance pool, outbound foragers, successful and unsuccessful returners, and a transient pheromone signal. Analytic reductions connect equilibrium geometry to colony-level regimes. In the contact-only limit, a forager generation number and a quadratic balance law predict either forward onset or fold-induced bistability. In the pheromone-only limit, equilibria follow a cubic in cue intensity, yielding a sharp threshold between collapse and sustained activity. With mixed feedback, simple algebraic conditions classify equilibria and their stability. Bifurcation maps show that combining contacts and pheromone can lower persistence thresholds, create oscillatory foraging via Hopf bifurcation, and produce multistability across activity levels.

Speaker: Tao Feng (Yangzhou University)

11:00 AM Self-organisation through nonlocal movement: patterns and multistability in spatial population models

Understanding the mechanisms underlying the self-organisation of mobile organisms is a central question in spatial ecology and population dynamics. In many biological systems, individuals - from cells to animals - sense their environment before moving, leading naturally to nonlocal movement responses. Empirical evidence increasingly supports the importance of such nonlocal interactions, and mathematical models incorporating them provide a richer and more realistic description of collective behaviour.

In this talk, I will present a class of nonlocal advection-diffusion equations modelling population movement driven by spatially extended species interactions. Combining analytical and numerical approaches, I will show how the interplay between sensing range, interaction strength, and diffusion gives rise to a wide spectrum of spatio-temporal dynamics, including aggregation, segregation, time-periodic behaviour, and chase-and-run phenomena. I will discuss the emergence of multistability and hysteresis, and describe bifurcation mechanisms organising transitions between different spatial patterns. Overall, the talk will illustrate how nonlocal movement processes lead to qualitatively new dynamical regimes and mathematical challenges in models of spatial population dynamics.

Speaker: Valeria Giunta (Swansea University)

11:20 AM Impact of Network Variation on Metapopulation Dynamics

Spatiotemporal population dynamics are often modeled using reaction–diffusion equations, yet analytical insight into the role of movement and network structure remains limited. In this talk, we present a metapopulation framework based on coupled ordinary differential equations on networks, focusing on regimes where dispersal is faster than local growth. Using tools from matrix analysis and perturbation theory, including new rank-one results for group-invertible matrices, we quantify how local changes in movement affect the dominant eigenvalue, which governs population persistence. In particular, we show that increasing symmetric connectivity in weight-balanced networks can inhibit growth under fast dispersal.

Speaker: Zhisheng Shuai (University of Central Florida)

11:40 AM When Systems Tip: Predicting Critical Transitions and Uncovering Frequency-Induced Tipping

Tipping points (critical transitions) are abrupt, often irreversible shifts in dynamical systems that can be triggered by small changes. This talk tackles two questions: how to predict tipping early and why tipping occurs. In this talk, I will demonstrate how combining tipping-point ideas with machine learning can enhance early-stage outbreak prediction using limited epidemic data. I will then present a new mechanism, frequency-induced tipping, where a system can be driven to a critical transition by subthreshold periodic forcing at particular frequencies, even in the absence of noise and without crossing a static bifurcation threshold.

Speaker: Shan Gao (University of Alberta)

10:40 AM → 12:00 PM Modeling of neural dynamics and neurodegeneration

10:40 AM A Multimodal Mathematical Model of Iron and Amyloid-β in Alzheimer’s Disease

Alzheimer’s disease (AD) is a complex, multifactorial, and currently incurable neurodegenerative disorder. Existing treatments can only slow disease progression, highlighting the urgent need for reliable biomarkers for early diagnosis. Among the most promising candidates are iron and amyloid-beta 42 (Aβ42), which can be measured both in blood and cerebrospinal fluid (CSF).
One of the hypothesized contributing mechanisms in AD is the formation of amyloid-beta plaques in the brain. However, this process remains difficult to observe and quantify in vivo. To address this limitation, several mathematical models have been proposed by our group to describe the temporal accumulation of iron and amyloid-beta in the brain (Ficiarà et al. 2022, 2023). Despite their relevance, these models are constrained by simplifying assumptions, most notably the representation of the brain as a single homogeneous compartment rather than a complex, spatially structured system.
In this work, we propose an integrated mathematical framework that combines existing models of iron and Aβ dynamics into a more comprehensive description of their interaction and evolution. Model validation is performed using multimodal data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI («ADNI | Alzheimer’s Disease Neuroimaging Initiative», s.d.)), including PET and T2-weighted imaging, CSF measurements of iron and Aβ, and cognitive assessment scores such as the Mini-Mental State Examination (MMSE).

Speaker: Ilaria Stura (Dept. of Neurosciences, Università degli Studi di Torino, Italy)

11:00 AM Folded node canard dynamics as a mechanism for delay in astrocytic evoked-Ca2+ responses

Astrocytic calcium responses under glutamate or ATP stimuli are highly heterogeneous, ranging from oscillatory dynamics to sustained plateau-like signals [1]. In the case of multi-peaks-type responses, experimental observations consistently report a delay preceding the onset of large amplitude cytosolic calcium oscillations (LAO). This delay is captured by a novel astrocyte model based on [2], which exhibits a phase of small amplitude oscillations (SAO) before the onset of LAOs. Our computational results demonstrate that the duration of the delay depends on the number of SAOs, which is strongly modulated by the calcium concentration in the endoplasmic reticulum (ER): ER overload prolongs the delay, whereas depletion shortens it. To explain this behaviour, we analyse the model using slow–fast and canard theories, revealing its geometric structure and the presence of a folded node. The latter explains the origin of SAOs and provides a mechanistic explanation for discussing the duration of the delay. Guided by this insight, we design an in silico experiment to reactivate SAOs by exploiting the identified folded node structure. Specifically, we suggest that the low-affinity calcium chelator TPEN could restore transient SAOs by elevating the ER calcium concentration following TPEN wash-out. Overall, this study illustrates how slow–fast and canard theories can uncover the origins of delayed calcium signalling in multi-peaks responses.

Speaker: Matteo Martin (University of Padova, Department of Information Engineering)

11:20 AM How neuromodulation shapes breathing: from cellular dynamcis to network rhythmogenesis

Breathing is a vital, involuntary behavior that must remain robust while adapting to changing physiological demands. This poses a challenge for the control of breathing. The preBötzinger complex (preBötC) is a heterogeneous neuronal network responsible for driving the inspiratory rhythm. While neuromodulators such as norepinephrine (NE) allow it to be both robust and flexible for all living beings to interact with their environment, the basis for how neuromodulation impacts neuron-specific and network-level properties remains poorly understood. In this talk, I will present our recent work on neuromodulatory control of respiratory rhythms, with a focus on NE. By modeling NE effects on key intrinsic parameters, we show how it differentially modulates different neuronal subtypes. At the network level, we demonstrate that both the organization of intrinsic properties and synaptic interactions critically shape population activity. Together, these results provide a multiscale perspective on how neuromodulation regulates network state underlying respiratory rhythm generation in the preBötC.

Speaker: Yangyang Wang (Brandeis University)

11:40 AM A Chemical Reaction Network-based approach to mTOR signaling dysregulation in drug-resistant epilepsy

Chemical Reaction Networks (CRNs) provide a rigorous mathematical framework to represent molecular interactions along signaling pathways by large systems of ordinary differential equations, exploiting the mass-action law. This framework enables a deeper understanding of the mechanisms underlying different diseases by analyzing the dynamics of the concentrations of the involved chemical species [1], capturing the steady-state behaviors through specific accurate root-finding methods [2], and observing the perturbation effects induced by genetic mutations and pharmacological treatments by implementing their action on the network [3].
We will present an application of this approach to the PI3K-AKT-mTOR axis to investigate the synergistic effect of two somatic activating mutations - MTOR p.S2215F and RPS6 p.R232H - documented in a patient with brain malformations and drug-resistant epilepsy [4]. Single and combined mutations are implemented as parameter perturbations within the CRN to capture how altered signaling dynamics propagate along the pathway and shift the system toward pathological steady states. Furthermore, we simulate pharmacological inhibition via mTOR inhibitors to explore whether and how their administration attenuates the dysregulation of key cellular pathways that may be involved in aberrant neuronal migration, proliferation, and electrical activity, potentially providing new therapeutic avenues for patients refractory to conventional anti-epileptic drugs.

Acknowledgments
This research was partially found by Hub Life Science - Digital Health (LSH-DH) PNC-E3-2022-23683267 - Progetto DHEAL-COM - CUP: D33C22001980001, founded by Ministero della Salute within “Piano Nazionale Complementare al PNRR Ecosistema Innovativo della Salute - Codice univoco investimento:
PNC-E.3”

Speaker: Silvia Berra (LISCOMP lab, IRCCS Azienda Ospedaliera Metropolitana Ospedale Policlinico San Martino, Genova, Italy and Dipartimento di Matematica, Università di Genova, Genova, Italy)

10:40 AM → 12:00 PM Plant models: mechanics, development and environment

10:40 AM Three-dimensional multiscale modelling of plant tissue mechanobiology

The genetic underpinnings that define tissue shape and function are still an open question. Part of the answer is in the biomechanics of cells and tissues and in the cross-talk between biomechanics and biochemistry. In particular, plants exhibit differential growth mediated by the viscous and plastic properties of the cell wall and the spatial distribution of chemical patterns.
We are working on a 3D version of the plant modelling package VirtualLeaf, i.e., a quantitative multiscale three-dimensional vertex model of plant development. The final goal is to combine cell wall mechanics with known models of growth, genetic regulation, and water transport, to model plant tissues developing through regulated cell divisions and growth.
We will present first results, in which we validate a simulation of uniaxial cell elongation with well-established models and solutions (the Lockhart equations). We will show that our model is capable of capturing the mechanical frustration arising naturally from models of plant cell growth, when accounting for spatial heterogeneity of mechanical parameters and multicellularity. We also explore the possible three-dimensional structures arising from different cells division rules, and whether the three-dimensionality and cell division rules change known relationships between cell volume, pressure and number of neighbours, typically measured only on the epidermis.

Speaker: João R. D. Ramos (Mathematical Institute, Leiden University, NL)

11:00 AM A framework for modelling auxin signalling pathways in plants

Auxins are a group of plant hormones which are involved in various processes across plant tissues and species. The auxin signalling pathway (ASP) consists of interacting transcription factors and repressors, and governs an individual cell's response to changes in auxin concentration. Alongside its role in plant growth (through both cell division and cell growth) this pathway determines cell fates, and is implicated in processes such as root-hair formation, phototropism, and other responses to environmental stimuli. Different responses to different auxin concentrations at different timescales are governed by different subnetworks, where the dominant signalling components vary. This profound diversity in response is reflected by the many copies of each signalling component found in different species. We present a general framework for ODE-based models of auxin signalling networks with the flexibility to model the promotion and repression of genes by any combination of transcriptional regulators. Using this framework, we present examples of plausible emergent behaviour and discuss the effect that network dynamics have on the response genes to different auxin signals.

Speaker: Joey Shuttleworth (School of Mathematical Sciences, University of Nottingham, UK)

11:20 AM Busse balloon Barbapapa

Spatial self-organisation arises in many contexts. A classical example is Rayleigh-Bénard convection: when the temperature between a heated bottom plate and a cooler top plate grows beyond a certain threshold, convection cells form. Busse balloons are a (graphical) representation of these patterns. A prominent example in ecology is dryland vegetation. If yearly precipitation falls below some critical value, vegetation patterns emerge with a wavelength of tens of meters. These patterns have paradoxically been interpreted as both 1) early-warning signals of complete desertification and 2) a way of the ecosystem to adapt to drought. In this talk, we will include grazing in a Klausmeier-type reaction-diffusion model and see how the shape of the corresponding Busse balloon changes. The shape of the Busse balloon is then used to infer ecosystem response to increased drought.

Speaker: Eric Siero (Mathematical and Statistical Methods -- Biometris, Wageningen University & Research, NL)

11:40 AM Understanding the Biomechanics of Plant Tissues: the consequences of cell division, shape and arrangement

How would you build a plant? Where to place the cell walls? Does this even matter? Due to turgor pressure, plant cell walls must resist substantial tensile stresses, and if not managed properly, they can lead to structural damage or an ineffective use of resources. Since plant cells are rigidly connected to one another, to resist this mechanical stress, precise control over the placement of new cell walls is vital for developing effective and efficient tissues. To explore how plants manage these stresses, we use interdisciplinary methods, such as mechanical perturbations on live tissues using an extensometer and performing finite element inflation simulations of different deformations. For this purpose, we have built up and improved existing modelling software to simulate plant tissues in 3D efficiently and with multiple layers. Through such methods, we have investigated the consequences of cell shapes and tissue structure across multiple scales. Our findings offer new insights into the role of cell division patterns, the prevalence of 3-way junctions (staggered like bricks in a wall), and why plant cells take certain shapes like rectangles. This research advances our understanding of how plants sense and respond to mechanical forces in their environment.

Speaker: Euan Smithers (Sainsbury Laboratory, University of Cambridge, UK)

10:40 AM → 12:00 PM Computational Modeling of Cerebrovascular Dynamics

10:40 AM Eye2Heart: A reduced mathematical model bridging cardiovascular and ocular hemodynamics

The cardiovascular and ocular systems are intricately connected, with hemodynamic interactions playing a crucial role in both physiological regulation and pathological conditions. However, existing models often treat these systems separately, thus limiting the understanding of their interdependence.

This talk presents the Eye2Heart model, which is a novel closed-loop mathematical framework that integrates cardiovascular and ocular dynamics \cite{eye2heart}. Using an electrical-hydraulic analogy, the model describes the interactions between the heart and retinal circulation through a nonlinear system of ordinary differential equations. The model is tested against clinical and experimental data, thus demonstrating its ability to reproduce key cardiovascular parameters (e.g., stroke volume, cardiac output) and ocular hemodynamics (e.g., retinal blood flow). Additionally, we explore in silico the effects of intraocular pressure and left ventricular compliance on both local ocular and global systemic circulation, thus revealing critical dependencies between cardiovascular and ocular health. The results highlight the model’s potential for studying cardiovascular diseases with ocular manifestations and support emerging research in oculomics by providing a mechanistic basis to interpret ocular biomarkers within a systemic context.

Speakers: Alon Harris (Icahn School of Medicine at Mount Sinai), Faith Hughes (University of Maine), Giovanna Guidoboni (University of Maine), Lorenzo Sala (Universite Paris-Saclay), Marcela Szopos (Université Paris Cité), Mohamed Zaid (Foresite Healthcare LLC), Sergey Lapin (Washington State University), Virginia Huxley (University of Missouri School of Medicine)

11:00 AM Quantifying haemodynamic forces across autoregulated cerebral micro- networks using a computational modelling approach

The brain is a highly energy-demanding organ that requires an adequate supply of oxygen and nutrients, which is maintained through cerebral blood flow autoregulation. The vascular myogenic tone is an intrinsic regulatory mechanism that enables the vascular wall to respond to mechanical forces induced by changes in luminal blood pressure, limiting blood flow fluctuations [1, 2]. In the current work, we introduce a computational framework to simulate myogenically autoregulated blood flow in cerebral microcirculation. This framework comprises integrated multi-physics components to characterise the underline mechanisms, including cellular signalling, vascular wall contractility, blood flow dynamics, and biphasic
blood rheology. Furthermore, this framework accounts for the heterogeneity of myogenic tone across different vessel types. Besides, a pipeline was developed that employs an optimisation approach to generate optimal boundary conditions based on available experimental data of blood flow and pressure. Results show that the proposed framework's prediction of blood flow distribution and red blood cell velocity in cerebral micro-networks
lies within the in vivo measurements range. The proposed computational framework complements the clinical investigation and, together, can be adapted to provide insights into the haemodynamics of cerebral microcirculation.

Speakers: Alberto Coccarelli (Swansea University), Ammar Al-Areqi (Swansea University)

11:20 AM Modelling Cerebral Autoregulation at the Microvascular Scale: From Health to Post-Stroke Dysfunction

Cerebral autoregulation stabilizes cerebral blood flow despite changes in blood pressure through adjustments in arterial diameter. However, the precise roles of individual vessels and impaired autoregulation in outcomes after ischemic stroke remain poorly understood. We present a computational framework incorporating static myogenic and endothelial regulation in large semi-realistic microvascular networks derived from mouse cortical vasculature (~200,000 vessels). Arteries actively regulate their diameter, whereas capillaries and veins behave passively according to a pressure–area relationship. Changes in transmural pressure and shear stress modulate vascular wall stiffness and compliance, enabling active arterial diameter adaptation and linking local haemodynamic stimuli to vessel-level flow regulation. Autoregulatory responses were evaluated under three conditions: healthy regulation, post-occlusion reperfusion with altered vascular reactivity, and chronic autoregulatory dysfunction. Under healthy conditions, the simulations reveal the dominant role of surface arteries in buffering pressure changes. During reperfusion, impaired myogenic reactivity emerges as a key driver of post-stroke hyperperfusion. Progressive loss of autoregulation in arteries within the previously ischemic territory disrupts capillary perfusion. These results provide mechanistic insight into how microvascular structure and vessel-level regulation shape cerebral perfusion in health and after stroke.

Speakers: Chryso Lambride (University of Bern), Mohamed El Amki (University of Zurich), Susanne Wegener (University of Bern)

11:40 AM Mechanistic modeling of closed-loop cerebrovascular reactivity

Impaired cerebrovascular reactivity (CVR), the ability of cerebral blood vessel tone to respond to stimuli for regulating blood flow and metabolism in the brain, has been linked to many acute and chronic cardiovascular and neurological diseases. In one mechanism of cerebrovascular reactivity, the cerebral blood vessels dilate to lower resistance in response to increased arterial carbon dioxide (CO2), thereby increasing blood flow to wash out the CO2. However, the integration of this with other regulatory processes and the implications for the systemic circulation are still not fully understood. Since the ability to measure the cerebral vasculature is inherently limited, a computational model that incorporates multiple possible factors underlying cerebrovascular blood flow regulation with patient-specific noninvasive data can help determine what most influences dynamics and regulation at the individual level. We present a mechanistic representation of cerebrovascular resistance as a function of partial pressure of CO2 together with a first-order control equation within a closed-loop whole-body circulation framework. We also incorporate functional representations of additional systemic and cerebral responses to CO2 and pressure. The current model is calibrated against experimental blood flow, pressure, and end-tidal CO2 from a cohort of control subjects and patients during a CO2 rebreathing protocol. These model adaptations will improve understanding of the system-level integration of mechanisms underlying CVR.

Speakers: Helen Harris (Virginia Commonwealth University), Laura Ellwein Fix (Virginia Commonwealth University)

10:40 AM → 12:00 PM Stochastic Dynamics and the Realities of Experimental Observation

10:40 AM Parameter Estimation for ODEs, Curve Registration, and Particle Filtering.

A common challenge in mathematical biology arises from data collected from a biological system for which we have a mechanistic model, such as an ODE model. Identifying the parameters of the model is often done through estimation schemes such as non-linear least squares, which presume errors in the amplitude of the data. Such estimation can be challenging, and other sources of error, such as deviations in phase, might also be considered. Relatedly, curve registration is a set of techniques in the statistical analysis of functions to address variations in phase across a collection of observed curves. In this talk, we will present techniques to apply methods of curve registration to estimation of parameters from ordinary differential equations models. We will show how particle filtering methods can facilitate such inference in a computationally tractable way and allow us to quantify the phase variability in such data. A brief discussion of vaccine trials will be included to illustrate how characterizing such phase variability can give new insights into inter-subject biological variation.

Speaker: John Fricks (Arizona State University)

11:20 AM Inferring Regime Changes in Noisy Trajectories via Dendrogram Pruning and Merging

Changepoint detection seeks to identify structural breaks in sequential data, often arising as noisy observations of underlying stochastic dynamical systems. However, exact likelihood-based methods can be computationally expensive, particularly in large-scale settings. We study maximum likelihood estimation for multiple changepoint models under possible overfitting and show that, even when the number of segments is misspecified, the resulting estimator converges to the true signal at a fast parametric $N^{-1/2}$ rate. This observation motivates a bottom–up correction strategy for over-segmented solutions.

We propose Dendrogram Pruning and Merging (DPM), an agglomerative algorithm that starts from an overfitted segmentation and iteratively merges adjacent segments using likelihood-based distances, producing a hierarchical dendrogram of candidate changepoints. We further introduce DsSIC, a dendrogram-based model selection criterion combining DPM with a strengthened Schwarz Information Criterion, and establish consistency of the resulting changepoint estimates.

Simulation studies and a single-molecule tracking application demonstrate that DsSIC achieves accuracy comparable to exact methods while substantially reducing computational cost.

Speaker: Linh Do (Tulane University)

11:40 AM Stochastic fountain dynamics and associated challenges for inference

In the last couple of years, I have noticed an emerging theme in my work. Across multiple biological systems, colleagues and I have articulated models that involve particles that (1) emerge at random times from a fixed source-location distribution; (2) move throughout a local environment randomly (either diffusing, or switching between deterministic states); and (3) are removed from the system due to state-switching or escape from some predefined region.

We have been tentatively calling these systems “stochastic fountains” (in the classic Markov chain literature these are called “open systems”) and have been studying what these systems look like when you only have access to partial information. For example, what if you only have a snapshot of particles at one instant in time? Or, what happens if you can only observe particles at the moment they leave the domain? The associated inference problems arise naturally in mathematical biology applications, and I will give an overview of how they sit at an interesting intersection of stochastic processes, PDE-inverse theory, spatial point processes, and asymptotic statistics.

Speaker: Scott McKinley (Tulane University)

10:40 AM → 12:00 PM Dynamics of Vector Populations and Pathogen Transmission

10:40 AM → 12:00 PM Mathematical Modeling of Infectious Diseases: Classical Foundations to Contemporary Approaches

10:40 AM Optimal release of sterile males in the sterile insect technique for Anopheles mosquitoes

The sterile insect technique (SIT) is a promising strategy for controlling malaria-transmitting Anopheles mosquitoes, but its practical implementation hinges on identifying release protocols that are both effective and resource-efficient. In this talk, I present a mathematical framework for optimizing time-dependent releases of sterile male mosquitoes within a biologically structured population model incorporating nonlinear mating dynamics and life-cycle stages. A key feature of the model is the emergence of an Allee effect induced by mate-finding limitations, creating a threshold below which the wild population collapses naturally. Building on this, I formulate a free-horizon optimal control problem that minimizes the total number of sterile males released while ensuring the population is driven below this threshold. Unlike classical approaches with a fixed terminal time, our formulation uses a state-dependent stopping time corresponding to threshold crossing. I discuss analytical and numerical challenges arising from the geometry of the threshold manifold and the coupling between control intensity and time to elimination. Preliminary results suggest adaptive release strategies can substantially reduce total releases compared to standard protocols, and I explore how mechanisms such as introducing a competing species may further improve SIT efficiency.

Speaker: Alex Safsten (University of Maryland)

11:00 AM Incorporating thermal performance curves into population dynamic models for the West Nile vector, Culex pipiens

Culex mosquitoes are a growing concern in North America given their ability to transmit diseases such as West Nile Virus and adapt their thermal tolerances. Culex pipiens, one species found in temperate environments, is predicted to continue to spread north and south of the equator as environmental conditions become more favorable. As climate change persists, it is of high importance to understand how temperature influences Culex pipiens life-history traits and what impacts this might have on transmission of West Nile and other pathogens. In this work, we explore potential functional forms of thermal performance curves (TPCs) for key traits of Culex pipiens by fitting TPCs to temperature-dependent trait data. We found the best-fitting TPCs for the following traits: age-specific mortality, fecundity, juvenile development, and survival to adulthood.
We then incorporated TPCs for each trait as a parameter function in a system of stage-structured differential equations of Culex pipiens population dynamics and we explored potential impacts on population dynamics of different TPC curves. Separately toggling both rates yielded notable differences in projected population counts and predicted peaks. We also compared the adult population projections from our model to surveillance data to find the best fitting model and see which fits were strongly supported by the data. Mathematical models such as ours are useful for predicting the potential population dynamics of Culex pipiens in specific geographic regions and for informing public health interventions. Further investigation is needed from additional data collection to explore other potential TPCs which may help to further improve these mathematical models.

Speaker: Ben Bruncati (Virginia Tech, USA)

11:20 AM The Prospective & Retrospective Outlook of COVID-19 via Mathematical Modeling

In this talk, we shall emphasize on the mathematical modeling of COVID-19 including multiple features of the disease such as vaccination, limited medical resources and contact tracing or screening. We would also model the effect of non-pharmaceutical interventions such as quarantine, isolation and information induced behavior changes. Further, via a multi-patch model we shall explore the dynamics of COVID-19 disease in 3 states in India. The conclusions will be drawn from both models via mathematical analysis and data fitting. We also provide a cost effective analysis of the applied control interventions on our model and provide the best strategy to be implemented so that not only the infective population is reduced but also the cost of implementation of interventions is minimal.

Speaker: Prashant Kumar Srivastava (Indian Institute of Technology Patna)

11:40 AM The effect of co-infection on disease transmission in plants with multiple transmission pathways

Co-infection of hosts by multiple pathogens can significantly increase disease prevalence and severity. In plant hosts, virus infection typically occurs via multiple transmission pathways. Here, we consider vertical transmission (via seeds, typically between growing seasons) and horizontal transmission (via insect vectors, typically within growing seasons). An open question is whether and how co-infection affects virus transmission, particularly seed transmission. We therefore investigate how the virus spread is affected by increased or decreased seed transmission of co-infected plants, compared to singly infected ones, in a semi-discrete model. A bifurcation analysis reveals that there can be two different types of bistability: (1) between a disease-free and a co-infection equilibrium, and (2) between the two boundary equilibria corresponding to singly infected plants. We interpret these results biologically and discuss their implications for plant disease management.

Speaker: Hannah Hirsch (Osnabrück University, Germany)

10:40 AM → 12:00 PM Mechanochemical modelling of patterning in developmental systems

10:40 AM Cellular nematic order and topological defects shape morphogen patterns

Tissue morphogenesis is the result of a complex interplay of mechanics, geometry and chemical signals. Yet, how heterogeneous and anisotropic tissue structure affects the spread and resulting pattern of signalling molecules remains poorly understood. Here, by homogenising a cell-based model we link cellular shape alignment to locally anisotropic effective diffusion. We then investigate the feedback between cellular nematic order and morphogen pattern formation in a 2D continuum model, where a nematic order parameter is coupled to a reaction-diffusion system with one and with two morphogens. Simulations show that topological defects in the nematic can strongly reshape the morphogen field in their vicinity, leading to novel nemato-chemical patterns. Our results propose the interplay between morphogen transport, nematic order, and defects as way of guiding cell fate patterning.

Speaker: Diana Khoromskaia (University of Münster)

11:00 AM Oscillator coupling separates morphogenesis and patterning into two developmental modules

In the early embryo an intracellular oscillator known as the segmentation clock patterns the somites, blocks of mesoderm that give rise to vertebrae and skeletal muscle. Clock oscillations are coupled between cells of the pre-somitic mesoderm (PSM) via notch-delta signalling, synchronising differentiation of PSM cells into somites. While this is happening, PSM cells are rearranging and dividing, and are being replaced by new cells that ingress from surrounding tissues. The relative contribution of each of these processes to elongation of the PSM varies across species, facilitating the evolution of diverse body plans and ecological niches.
However, processes like cell ingression and division disrupt synchrony of the clock and could affect somite patterning if these events occur too often. How then does the diversity of morphogenetic dynamics evolve without disrupting the clock, and how does this ‘evolvability’ depend on the clock itself? Using a phase oscillator model to describe clock coupling, and a point-based model to describe cell movement, we studied how clock dynamics react to varying morphogenesis of the PSM. We find that clock dynamics are robust to changing morphogenesis when oscillator coupling is of the correct magnitude and timescale. By experimentally quantifying coupling in Lake Malawi cichlids, we show that these conditions are satisfied across 34% of extant vertebrate species. This suggests that clock coupling has permitted the evolution of diverse body plans.

Speaker: James Hammond (University of Cambridge)

11:20 AM Image-based modelling explains variability in morphogen diffusion measurements

Morphogens are intercellular signalling molecules that provide spatial information to cells in developing tissues by establishing long-range concentration gradients. Measurements of morphogen diffusivity vary considerably depending on the experimental approach, and these discrepancies have been used to question diffusion as a viable mechanism for morphogen gradient formation. Using particle-based modelling on realistic zebrafish brain images, we demonstrate that incorporating local tissue architecture together with receptor binding is sufficient to reproduce experimentally observed morphogen dynamics measured by FRAP and FCS. Our model recapitulates a range of biological observations such as generating two distinct particle populations with slow and fast diffusion coefficients, as reported in vivo. We further show how interactions between these populations contribute to setting the length scale of the concentration gradient, and how differences in experimental measurements can arise from the complex dynamics of hindered diffusion-driven transport.

Speaker: Yi Ting Loo (The Francis Crick Institute)

11:40 AM Collisions, Shape and Stigmergy: Modelling the Collective Organisation of ECM

Radial dysplasia (RD) is a musculoskeletal disorder in which the anatomical structure of the forelimb is fundamentally altered - in extreme cases the radius bone is missing, along with a number of muscles. RD is a disorder of later development, that manifests through changes in the extracellular matrix (ECM) deposition behaviour of a population of fibroblast precursors. As muscle cells follow patterning cues in the ECM, this change in fibroblast behaviour and ECM organisation propagates in multiple complex ways to alterations in muscle cell alignment. In my project I am using predictive computational modelling to understand how these emergent changes at the tissue-level derive from collective cell interactions. To do this, I have acquired a rich dataset of collective cell motion timelapse data, designed a model of cellular collective motion incorporating fine-grained simulation of cell motion, and have implemented a novel analysis inspired by methods from information geometry and simulation-based inference to both fit this data and pursue global model reduction. Unexpectedly, I have found that greater collective organisation of cells due to nematic alignment and flocking behaviours can, when ECM feedback is allowed, derange the process of depositing globally organised ECM.

Speaker: Omar El Oakley (The Francis Crick Institute)

10:40 AM → 12:00 PM Discrete frameworks for modeling biological systems

10:40 AM Reproducible Boolean model analyses and simulations with the CoLoMoTo software suite

In order to address the pervasive reproducibility crisis, we combine Docker containers (or Conda packages) with Jupyter electronic notebooks, in order to develop and document dynamical analyses of logical models of complex biological molecular networks. The resulting Common Logical Modelling Tools (CoLoMoTo) environment currently encompasses over 20 tools, written in multiple languages, making them accessible with a single popular language, python.
To illustrate how complementary tools can generate novel insights, we have revisited the analysis of a model of the regulatory network controlling mammalian cell proliferation, published by Sizek et al in PLoS Computational Biology in 2019. Using the CoLoMoTo environment, we could reproduce the main results and figures published in the original article, and further extend these results with the help of a selection of tools included in the CoLoMoTo suite.
More precisely, we developped a notebook encompassing the visualisation of the network with the tool GINsim, an attractor analysis with bioLQM, the identification of synchronous attractors with BNS, the extraction of modules from the full model, stochastic simulations for the wild-type and selected mutant background with MaBoSS, and finally the computation of compressed probabilistic state transition graphs.
The integration of all these analyses in an executable Jupyter notebook greatly eases their reproducibility, as well as novel extensions. This notebook can further be used as a template and enriched with other ColoMoTo tools to enable comprehensive dynamical analyses of biological network models.

Speaker: Denis Thieffry (Ecole Normale Superiore)

11:20 AM Using Canalizing Boolean Functions to Model Regulation in Mammalian Cell Division

Discrete models are a natural framework for biological systems whose regulation is governed by switch-like interactions. In this talk, we will present a reverse-engineering approach to Boolean modeling of mammalian cell division through the regulation of the transcription factor E2F. Starting from partial biological knowledge about the roles of CycB, Rb, p27, and CycA, we will show how a prescribed canalizing-layer structure can be used to recover a family of nested canalizing Boolean functions consistent with the known regulatory logic. This framework makes it possible to encode dominant regulatory effects, distinguish variables acting at different hierarchical levels, and systematically infer admissible update rules from incomplete mechanistic information.

Speaker: Elena Dimitrova (Cal Poly)

11:40 AM Structural Coherence Drives Cooperative Dynamics in Gene Networks

A central challenge in systems biology is understanding how gene regulatory networks (GRNs) coordinate cellular decision-making within complex topological structures. This study introduces a framework to quantify the alignment of regulatory logic among interacting genes, a property defined here as structural coherence. By applying this metric, we identify "teams”, functionally coupled gene sets that exhibit cooperative activation. We investigate the topological implications of structural coherence by characterizing how team size and composition scale with key network features. To link architecture with dynamical behavior, we employ a threshold Boolean model, specifically a probabilistic Ising model, to evaluate the relationship between structural coherence and gene expression coordination. Our results demonstrate that structurally coherent groups significantly influence the configuration and stability of network attractors. Furthermore, analysis of biological GRNs shows how hierarchical organization enables coherent decision-making to scale across large gene assemblies, even in the presence of localized incoherence. The structural coherence framework provides a robust, generalizable tool that integrates local interactions and global network architecture to explain the emergent regulatory coordination.

Speaker: Pradyumna Harlapur (Indian Institute of Science)

10:40 AM → 12:00 PM Recent Development on Digital Twins for Biology and Biomedical Sciences

10:40 AM Developing a Digital Twin of the Maternal Brain

The maternal brain undergoes significant anatomical change during pregnancy, yet the geometric principles governing these transformations remain poorly understood. Studying brain shape change is critical for identifying markers of maternal health, but prior work focuses on scalar volumes, masking subtle deformation. We develop a digital twin that integrates precision imaging with large datasets to map pregnancy trajectories of brain structures. For preprocessing, we conduct a quality control analysis to identify which segmentation and meshing tools provide the most accurate surface representations for the brain structures. Utilizing varifold geometry and multidimensional scaling (MDS), we create a shared latent space representing brain deformations. This merges a densely sampled longitudinal dataset including hormone metrics with a larger population study on postpartum health. Traditional linear statistical models (e.g., PCA) often fail in these paradigms because subcortical shapes exist on very high dimensional nonlinear manifolds, negating impact of Euclidean methods. To manage this, we train a multilayer perceptron to map latent MDS coordinates back to vertex positions, achieving a compact, expressive representation of 3D anatomy. Using regression models, our framework is able to predict 3D shape based on time and hormones. Our digital twin provides a foundational dynamic atlas, enabling personalized modeling to inform our current understanding of maternal brain health.

Speaker: Sarah Kushne (University of California, Santa Barbara)

11:00 AM The mechanobiology of blood vessel formation: Towards a Digital Twin of Zebrafish intersegmental vessel formation

To form new sprouts during angiogenesis, endothelial cells must coordinate their migration through biophysical and biomechanical signaling between each other and the micro-environment. A relatively simple model of angiogenesis is intersegmental vessel (ISV) formation in zebrafish. While various molecular, cellular, and mechanical factors coordinate ISV pathfinding between the somites, the specific contributions of ECM components remain incompletely understood. Here we hypothesize that guidance through ECM molecules laid down in the intersomitic space steers a process of self-organized pattern formation to reproducibly form blood vessels at stereotypic locations. We combine theoretical and experimental approaches in the zebrafish to investigate this hypothesis. Firstly, we developed a hybrid mathematical model to study the effect of ECM mechanics on a self-organized mechanism of endothelial network formation. We combined a previous, experimentally validated [1] model of endothelial network formation based upon the Cellular Potts Model (CPM) with a molecular dynamics-based bead-spring model of the intersegmental ECM [2,3] and gradients of signaling molecules secreted by the somites. While in absence of the ECM, our model predicts that the endothelial cells form network-like patterns as they do in vitro [1], in presence of the ECM, the model predicts the formation of intersomitic sprouts, consisting of endothelial cells that migrate along high concentrations of the ECM [4]. The model predicts that if the concentration of ECM were reduced in the intersomitic space, the endothelial cells should again organize into network-like structures. To investigate the contributions of the ECM to ISV formation in the zebrafish, we employed morpholino-mediated gene knockdown of ECM components in endothelial cell- and ECM-tagged zebrafish lines, coupled with high-resolution laser scanning confocal microscopy [4]. Although knock-down of Fibronectin-a and b or Laminin-a1 and a4 delays ISV sprouting during the first six hours, simultaneous knockdown of both ECM proteins resulted in aberrant vessel pathfinding, leading to disorganized, incomplete ISV development, resembling endothelial network patterns formed through self-organization by endothelial cells in silico and in vitro. Furthermore, we observed that endothelial cells interact with and migrate along laminin- and fibronectin-rich pathways, as revealed by zebrafish reporter lines, further underscoring the role of these ECM components in guiding vessel formation. Our simulations suggest that ECM stiffness may significantly influence endothelial cell migration, with cells potentially traveling further along VEGF gradients on stiff ECM compared to soft ECM under moderate VEGF sensitivity, providing a potential explanation for the observation in ECM component knockdowns. Our results highlight that ECM-regulated tip cell migration could be a key determinant of ISV growth speed and patterning. More generally, our study suggests an integrated, ‘mathematics-driven’ experimental approach, in which a digital twin is developed hand in hand with each next insight into the experimental system.

Speaker: Roeland Merks (Leiden University)

11:20 AM The impact of ephaptic coupling and ionic electrodiffusion on arrhythmogenesis in the heart

Cardiac action potential (AP) propagation occurs through gap junction (GJ)-rich intercalated discs (IDs). However, recent experimental studies show that GJ knockout mice can still maintain heart structure and function, even when GJs are undetectable at IDs. Ephaptic coupling (EpC), an electric field effect across the narrow, tortuous IDs, provides an alternative mechanism for cell-to-cell communication when GJs are impaired. Given the current lack of direct experimental evidence for EpC, modeling studies are essential for understanding its physiological and pathological roles in the heart.
Our research investigates how EpC and ionic electrodiffusion influence arrhythmogenesis in the hearts. We developed the first two-dimensional multidomain electrodiffusion model incorporating EpC. Our findings demonstrate that strong EpC suppresses the initiation of reentry, resulting in absent or nonsustained reentrant activity with a reduced maximum dominant frequency (DF), although it can also introduce transient instability and heterogeneity in cardiac dynamics. In contrast, weak EpC supports the initiation of sustained reentry, characterized by a stable rotor and high DF. Strong EpC terminates reentry through self-attenuation, while moderate EpC does so through self-collision. Additionally, we applied spectrum theory to analyze the impact of EpC on one-dimensional wave trains. Our results show that EpC reduces both the frequency and amplitude of wave trains.

Speaker: Ning Wei (Purdue University)

11:40 AM Virtual dynamics of spatiotemporal single-cell interactions

Building virtual cells and virtual tissues that capture how interacting cell populations evolve in space and time is a central goal of modern biology, yet spatial omics experiments can only provide sparse snapshots of this process. Here, we introduce CytoBridge, a computational method that reconstructs continuous virtual cell dynamics from discrete spatial transcriptomic data. Starting from a joint expression–space manifold, CytoBridge learns stochastic trajectories of cell states, positions, and population sizes through an unbalanced mean-field Schrödinger bridge formulation that explicitly incorporates cell–cell interaction as a dynamical driver. A time-varying interaction graph built from spatial proximity and ligand–receptor priors allows the transition velocity to be decomposed into an interaction program, learned from within-
system observables, and an intrinsic-context program that captures intrinsic regulatory processes. Applied to five datasets across three spatial transcriptomics platforms and spanning development, regeneration, and neurodegeneration, CytoBridge accurately generates tissue dynamics at unmeasurable time points, recovers known lineage trajectories and growth patterns, and reveals spatiotemporal ligand–receptor signalling axes not accessible from static analyses. CytoBridge provides a general method for turning heterogeneous spatiotemporal transcriptomic measurements into continuously evolving virtual tissues.

Speaker: Qing Nie (University of California, Irvine)

10:40 AM → 12:00 PM Deterministic Models to Describe and Analyse Tumour-Immune Interactions and Immunotherapy

10:40 AM Tumor growth and immune response: on the impact of the space-structuration of the tumor microenvironment

Understanding how the tumor microenvironment influences interactions between tumor cells and the immune system is a major question in mathematical oncology. In particular, the spatial organization of nutrient sources and immune cell recruitment may strongly affect tumor progression and immune control.
In this work, we study this question using a continuum mixture model describing nutrient-dependent tumor growth, mechanical interactions within the tissue and the extracellular matrix, and the dynamics of anti- and pro-tumoral immune cell populations. External sources of nutrients and immune cells are included in the model, and their spatial location is treated as a key parameter.
Using numerical simulations, we analyze how different spatial configurations of these sources affect tumor–immune dynamics. The results show a strong sensitivity of the system to the relative position of nutrient and immune sources. In particular, small changes in distance can significantly delay tumor growth, while some configurations lead to stable states where tumor mass and immune activity coexist.
These results highlight the important role of spatial heterogeneity in the tumor microenvironment and show that its geometric organization can strongly influence the balance between tumor progression and immune control.

Speaker: Christian Tayou-Fotso (Université Côte d’Azur)

11:00 AM Modelling the efficacy of CIK cell immunotherapy targeting MET-expressing mesothelioma cells

Malignant pleural mesothelioma (MPM) is an aggressive tumour associated with poor prognosis and limited treatment options, motivating the investigation of novel therapeutic approaches. Among these, chimeric antigen receptor (CAR)–based adoptive cell immunotherapy has attracted considerable interest due to its potential to achieve durable clinical responses

We combine experimental and mathematical approaches to investigate the efficacy of a CAR-based immunotherapy using cytokine-induced killer (CIK) cells engineered with a MET-specific receptor targeting MET-overexpressing tumour cells. \textit{In vitro} data from diverse MPM cell lines and CIK preparations are used to develop and calibrate a mathematical model describing the interaction dynamics between tumour cells, structured by their MET expression level, and CIK cells. The model successfully reproduces experimental observations and is used to predict treatment efficacy under previously untested conditions, which are validated with new data from MPM primary cell lines.

Our results elucidate the interplay between three key factors positively impacting treatment efficacy: the initial immune-to-tumour cell ratio, the percentage of CAR-MET-expressing CIK cells generated upon engineering, and the MET expression level of tumour cells. Together, these findings provide a quantitative basis for assessing CAR-CIK therapy effectiveness and initiate the development of a predictive framework that could support clinical decision making.

Speaker: Federica Padovano (LJLL)

11:20 AM Tumour–Immune Dynamics: Patterns, Trade-offs, and Evasion in a Continuous Modelling Framework

We present a continuous model describing the interplay between tumour mass and the immune system. Building on \cite{carrillo2019population}, we incorporate a nonlocal formulation that captures adhesion and chemoattraction forces at the microscopic level.

We investigate how the proliferation–immune susceptibility trade-off can be calibrated, identifying which balance between rapid growth and immune evasion/resistance leads to more favorable tumour outcomes under immune pressure. The model is designed to explore how the emergence of spatial patterns, arising from the interplay between nonlocal interactions and reaction terms, affects tumour evolution and its response to immune pressure. This perspective is connected to the classification of tumours based on T-cell infiltration (hot vs. cold tumours, see \cite{o2019cancer}), which reflects their inflammatory and immunological state.

We first analyse homogeneous tumour populations, assessing how intrinsic proliferation–evasion properties affect both pattern formation and immune control. We then consider heterogeneous tumours characterised by a different phenotypic traits, examining the role of both quantitative composition (relative abundance) and spatial arrangement.

Overall, this framework highlights how spatial patterns and reaction dynamics jointly determine tumour behavior, providing insight into the emergence of resistant configurations and offering a theoretical basis for identifying optimal strategies in an immunotherapy context.

Speaker: Giulia Chiari (University of Oxford / BCAM (Basque Center for Applied Mathematics))

11:40 AM Mechanistic modeling of the combined dynamics of CAR T-cell therapy and standard care in malignant gliomas

Malignant gliomas (MGs) remain highly resistant to conventional treatments. We propose an ordinary differential equation model to investigate the potential synergistic dynamics between standard therapy (radiotherapy (RT) and temozolomide (TMZ)) \cite{Stupp} and chimeric antigen receptor (CAR) T-cell therapy \cite{Brown}. While both TMZ and RT can be lymphotoxic, TMZ may also enhance CAR T efficacy by upregulating tumor antigens and inducing lymphodepletion, and RT can promote T-cell infiltration.
Our model extends and combines our previous works \cite{Sinelshchikov,Perales}, consisting of a nine-dimensional dynamical system describing MG subpopulations and treatment dynamics and incorporating impulsive inputs to simulate clinical administration. Mathematical analysis reveals parameter regimes under which constant treatment administration achieves tumor eradication.
To bridge theory and clinical application, the model was validated using published trial data \cite{Stupp, Brown, Laigle}. We generated cohorts of virtual patients through random sampling within biologically and clinically relevant ranges to conduct in silico trials. Numerical simulations evaluate various treatment combinations to identify optimal protocols and parameter-derived biomarkers at the population level. Our results provide new theoretical insights into treatment scheduling and offer a mechanistic tool to optimize and personalize MG therapy.

Speaker: Matteo Italia (University of Castilla-La Mancha)

10:40 AM → 12:00 PM Models and Methods for the Analysis of Cancer Treatment

10:40 AM From Image to Simulations: Integrating Imaging Biopsy Data into Agent-Based Models to Understand the Impact of Tumour-Microenvironment Spatial Heterogeneity on Cancer Treatment

Glioblastoma is the most common and deadliest primary brain tumour in adults, with a median survival of 15 months under the current standard of care \cite{Trager2020}. Its tumour microenvironment has been shown to be highly heterogeneous \cite{Karimi2023}, meaning the magnitude of cell-cell interactions might differ due to spatial differences. While ordinary differential equation models can be useful to analyze novel treatment strategies and run preliminary virtual clinical trials \cite{Mongeon_Craig_2025}, they do not easily allow for describing this spatial cell heterogeneity and its impact on treatment outcomes. To that end, new single-cell imaging modalities like imaging mass cytometry can be leveraged and integrated to computational agent-based models \cite{Surendran2023}. However, to effectively capture intra-tumoral dynamics, we have shown that care must be put into this integration and that model initialization must be done with a sufficient number of cells to provide biologically relevant predictions \cite{Mongeon2024}. Here, we propose a mechanistic reconstruction of homogeneous and heterogenous imaging mass cytometry data that captures first- and second-order spatial summary statistics. We then generate larger synthetic datasets from patient-specific glioblastoma biopsy samples using our algorithm and integrate them into an agent-based model to study the effect of tumour micro-environment spatial heterogeneity on glioblastoma treatment outcomes. Though our focus is on the incorporation of imaging mass cytometry data into an ABM, our technique has applications beyond this case study to other multi-type homogeneous and heterogeneous and point patterns.

Speaker: Blanche Mongeon (Sainte-Justine University Hospital Research Centre, Université de Montréal)

11:00 AM Spatial Mechanistic Modelling of T‑Cell Engagers: Insights into Trimer Formation and its effect on Cancer Killing

The rapid expansion of immunotherapies in Oncology has increased the need for quantitative models that can understand their mechanisms and limitations. T cell engagers (TCEs) are an emerging therapeutic class that bind both T cell receptors and tumour associated antigens to promote immunological synapse formation and targeted cytotoxicity. Despite growing clinical success, their efficacy is constrained by challenges such as treatment limiting toxicities, T cell exhaustion, and the hook effect. Mathematical and computational modelling offers a powerful means to understand these processes and support the rational optimisation of TCE design. We present an agent-based multiscale modelling framework using PhysiCell to investigate how binding kinetics, receptor expression, and spatial heterogeneity within the tumour microenvironment influence TCE function. By integrating mechanistic binding rules with spatially explicit cell–cell interactions, the model enables systematic exploration of trimer formation dynamics, the emergence of the hook effect, and their combined impact on tumour cell killing.

Speaker: Gibin Powathil (University of Swansea)

11:20 AM Mechanistic Modeling of Heterogeneous Tumor Response to Anti-NUPR1 Therapy in Docetaxel-Resistant Prostate and Pancreatic Cancers

Resistance to the anti-mitotic drug docetaxel is a major challenge in the treatment of solid tumors, including prostate and pancreatic cancers. The stress-response protein NUPR1 has been identified as a key molecular driver of docetaxel resistance, suggesting that inhibition of NUPR1 may restore treatment sensitivity and enable effective combination therapy. In this talk, I develop mathematical models that incorporate the mechanisms of action of docetaxel and relevant NUPR1 pathways to study tumor response to combined docetaxel and NUPR1-targeted therapy. The models are informed by preclinical data, including in vitro prostate cancer cell-line experiments and in vivo pancreatic cancer xenografts, and capture tumor growth dynamics and treatment-induced cell death. Using these calibrated models, we quantify potential synergy between therapies and extend the analysis to heterogeneous virtual populations that represent variability in tumor growth and drug response. This framework enables systematic exploration of treatment schedules and patient heterogeneity, allowing us to assess when NUPR1-targeted combination therapy is likely to be successful and to identify subpopulations that may benefit most. These results illustrate how mechanistic modeling and virtual populations can support the evaluation and design of combination therapies aimed at overcoming chemotherapy resistance.

Speaker: Harsh Jain (University of Minnesota Duluth)

11:40 AM Model-supported patient stratification using multi-objective synergy optimization in combination therapy

The challenge of stratifying patients for combination therapy is both technically demanding and clinically crucial. We build upon our previous framework for identifying Pareto optimal doses, reconciling competing definitions of synergy through multi-objective optimization to balance synergy of efficacy and potency (a measure of toxicity) such that no further improvement is possible in one without detriment to the other, and extend it to address interpatient heterogeneity. We apply the methodology to our previously developed model of a combination of an immune checkpoint inhibitor and an antiangiogenic agent and extend it to address interpatient heterogeneity. We demonstrate that depending on patient-specific drug sensitivities, different regimens may be Pareto optimal for different subgroups. We also highlight that there exist subpopulations for whom no meaningfully efficacious combination exist, suggesting that these individuals are not good candidates for this drug combination. In situations where measurable biomarkers are unavailable, we propose an initiation protocol with explicit, practical criteria that permit the estimation of patient-specific sensitivities to both monotherapies and to the combination therapy. Taken together, the proposed approach provides a potential way to find the right combination therapy for a patient, and to find the right patient for existing therapy.

Speaker: Irina Kareva (Quercus Insights)

10:40 AM → 12:00 PM Multi-scale dynamical modeling of immune and cancer cell behaviour

10:40 AM Characterization of macrophage phenotypes using mathematical modelling

Macrophages are innate immune cells with a wide range of functional capacities(Wu et al., 2021). They have been broadly classified into M1 or M2 phenotypes based on environmental signals. Due to variation in such regulatory cues, these macrophages are thought to also show states that are intermediate within a spectrum that has M1 and M2 at its two extremes(Karnevi et al., 2014). However, across all these studies, characterization for hybrid macrophages is not consistent due to overlapping macrophage markers. How hybrid macrophages arise, how stable these states are, how easy is it for them to transition from, or to M0, M1, or M2 states, and how is their stability reinforced or attenuated by the distinct secretory states remains poorly understood. To address these set of problems, we define the hybrid macrophage phenotype based on gene regulatory network (GRN) information at intracellular scale. Our findings reveal a 'teams' structure as an emergent property of the macrophage GRN. Perturbation analysis was done with M1 and M2 as initial states and as two different cases. In one node perturbation, the system is unable to switch its phenotype in either case, but in some two and three-node combinations, the system can switch to hybrid phenotype. Furthermore, overexpression analysis was done, where STAT3 and STAT1 combination was specifically observed to give rise to the most hybrid populations. The phenotypic distribution obtained from the Boolean framework was then validated using RAndom CIrcuit PErturbation (RACIPE). The distribution of steady state in overexpression analysis using RACIPE was consistent with the Boolean framework, making the distribution of steady states a robust dynamical property of the network.

Speaker: Soujanya Barik (PhD, IISc Banglore, India)

11:00 AM Dissecting immune-cell communication networks in chronic inflammation and cancer

Immune responses are tightly regulated by a diverse set of interacting immune-cell populations, and immune-cell communication pathways are routinely targeted by immunotherapy in autoimmune diseases and cancer. However, a quantitative understanding of immune-cell regulation in vivo is only beginning to emerge [1]. We assessed cytokine reaction-diffusion dynamics using a 4D finite-element based modeling framework [2]. We found that spatial cytokine gradients robustly arise in physiological parameter regimes and are critical for effective paracrine signaling, and they do not arise by diffusion and uptake alone, but rather depend on properties of the cell population such as an all-or-none behavior of cytokine secreting cells. Next, we explored the effect of cytokine gradients in the context of motile cell populations in the lymph node and the tumor microenvironment, employing both cellular Potts models and a numerically efficient formulation of cytokine gradients based on a homogenization approach. Further, we developed a general mathematical framework for analysis of interactive immune-cell population dynamics, accounting for cell-cell interactions, cell-proliferation, and cell-differentiation by means of measurable response-time distributions [3]. We employed that framework to describe the onset of lupus nephritis, the renal manifestation of systemic lupus erythematosus (SLE) [4]. Starting from analysis of single-cell RNA-sequencing data on innate lymphoid cells, our mathematical model reconciles that experimental data with long-standing clinical observations such as elevated autoantibodies and interferons in individuals with genetic predisposition for SLE. Overall, our results from model simulations and data analysis highlight the complex dynamics imposed by cell-cell signaling networks in the immune system, with implications for therapeutic intervention.

Speaker: Kevin Thurley (University of Bonn)

11:20 AM When data tells the story: Uncovering transcriptional control landscapes in cancer systems using data-driven model inference

A central challenge in systems oncology is understanding how the tumour microenvironment (TME) reconfigures the internal regulatory circuitry of cancer cells. While the reprogramming of immune cells within the TME is well-documented, the longitudinal regulatory dynamics of the cancer cells themselves, especially in response to immune interactions, remain elusive. In this work, we present a data-driven framework that bridges time-series transcriptomics and gene regulatory network (GRN) inference to map these temporal landscapes.

Using Chronic Lymphocytic Leukaemia (CLL) as a model, we integrate longitudinal expression data from patient-derived cells within a reconstituted in vitro TME [1]. By inferring GRNs based on transcription factor activity across multiple time points [2] [3], we uncover a complex orchestration of cytokine signalling, metabolic shifts, and differentiation. Our analysis reveals that while immune-cell interactions significantly drive CLL activation and phenotypic plasticity, the long-term survival trajectories of these cells are governed by deeply ingrained intrinsic features [4]. This underscores a dual regulatory architecture where the environment sets the pace, but the internal network determines the destination. These insights provide a roadmap for identifying patient-specific regulatory nodes that could be targeted to disrupt cancer-immune co-evolution, which can then be used to study the long-term behaviour of the CLL cells through dynamical modelling.

Speaker: Malvina Marku (Toulouse Cancer Research Center)

11:40 AM From Cells to Tissues: Multiscale Systems Biology on the Road to Digital Twins

This talk explores how we move from models toward clinically useful digital twins in biomedicine. It focuses on three pillars: multiscale integration of intracellular signalling with agent-based cell simulations(Estragues-Muñoz et al., 2026) , personalisation using patient-specific omics (Montagud et al., 2022), and community standards for model validation(Ntiniakou et al., 2025).  
We present PhysiBoSS1, a tool that couples stochastic Boolean network simulations with agent-based multicellular dynamics, demonstrating applications in drug screening and in predicting synergies in cancer treatments2. Crucially, this modular architecture enables independent evolution of biological components, such as signalling logic and cell properties, supporting long-term maintainability and scalability. We will highlight that realistic tumour simulations will require better-curated data, novel algorithms and computer architectures, and, more importantly, careful methods to bridge very different temporal and spatial scales(Ponce-de-Leon et al., 2023).
A community benchmarking effort across several major agent-based tools shows that, despite similar core features, differences in underlying mathematics and numerics affect results, underscoring the need for shared interfaces, metrics, and open dissemination(Ntiniakou et al., 2025). Finally, we show that patient-specific Boolean models, parameterised with genomic and transcriptomic data in breast and prostate cancer, can suggest actionable drug targets and are experimentally validated in cell lines, illustrating the potential of predictive, personalised digital twins(Montagud et al., 2022).

Speaker: Arnau Montagud (Institute for Integrative Systems Biology, CSIC)

10:40 AM → 12:00 PM Biology at the Interfaces: Data-Informed Multiscale Modelling

10:40 AM Integrating multiscale multimodal imaging-based and PK/PD-informed models to predict triple negative breast cancer response to neoadjuvant therapy

Neoadjuvant therapy (NAT) is a standard initial treatment for triple-negative breast cancer (TNBC), yet early prediction of treatment response remains challenging. This capability would enable adjustment of therapeutic plans to optimize outcomes and minimize toxicities. To this end, I will present a mechanistic, multiscale mathematical model of TNBC response to NAT that integrates in vivo longitudinal MRI with time-resolved in vitro drug-response data to identify key mechanisms driving tumor dynamics. The model describes tumor cell density evolution through mechanically-constrained mobility and net proliferation, coupled to a pharmacokinetic/pharmacodynamic (PK/PD) representation of NAT drug regimens. To facilitate clinical applicability, a global sensitivity analysis (GSA) is carried out by using Sobol’s method on 3D MRI-based tissue domains from well and poorly-perfused tumors. The parameter space combines prior in silico estimates informed by in vivo imaging with in vitro measurements capturing drug-induced proliferation changes across TNBC cell lines. The GSA reveals a small subset of dominant parameters governing treatment response, enabling construction of a parsimonious surrogate model that preserves the dynamics of the full formulation. Building on these results, I will briefly outline a personalized tumor forecasting pipeline in which the reduced model is calibrated to early-treatment MRI data and used to obtain patient-specific forecasts of tumor response to NAT.

Speaker: Guillermo Lorenzo (University of A Coruña)

11:00 AM Linking Primary and Metastatic Growth: Testable Predictions from a Shared-Carrying-Capacity Model

To inform decisions rather than replicating noise, low-dimensional and identifiable models calibrated with multiscale data can serve as reliable tools through separating host-level constraints from lesion-level properties.

As an example for a simple, yet structured approach, we present a mechanistic model formulating systemic cancer dynamics that links primary and metastatic growth through a shared carrying capacity. Building on Gompertzian growth, lesions are coupled via a host-level constraint on total tumor burden and extend the same idea to a metastatic size-distribution framework, enabling joint calibration to longitudinal primary-tumor measurements and metastatic nodule data. Model selection identifies the most parsimonious formulation that captures cross-lesion interdependence from more classic alternatives. Identifiability analysis shows that key drivers can be practically constrained from limited datasets, supporting robust inference with few parameters. Counterfactual simulations result in competitive metastatic release after primary tumor resection, generating testable hypotheses for prospective experiments. Beyond oncology, the work illustrates a general theoretical-biology principle: simple, yet structured models can denoise multiscale data by separating host- from lesion-level traits, yielding computational biomarkers and efficiently informing experimental designs across interacting population systems.

Speaker: Pirmin Schlicke (University of Salzburg)

11:20 AM Data-driven reconstruction of phenotypic transition networks in colorectal cancer

Cancer cells exhibit a remarkable ability to adopt different phenotypic states in response to cell-intrinsic programs and environmental cues, a phenomenon known as cancer cell plasticity. Plasticity underlies tumour heterogeneity, treatment resistance, and metastasis. To move therapeutic approaches beyond pathway and enrichment analyses comparing early and late disease, we need to understand the principles governing the evolution of phenotypic composition and spatial organisation in cancerous tissue. Mechanistic modelling may be a great asset in this direction, allowing analysis of in vitro studies and in vivo spatial omics data from a complex systems perspective, linking local rules of cell division and state transition to emergent tissue-level patterns.
Here, I will present our work dissecting cell-intrinsic plasticity in colorectal cancer organoids. Perturbation experiments reveal ATRX, a chromatin remodelling enzyme, as a key regulator of plasticity. Using Markov-chain models, we leverage time-course cell sorting experiments to infer phenotypic transition networks following ATRX deletion and identify key transitions driving heterogeneity. I will discuss how to integrate these observations with in vivo spatial transcriptomics measurements, where plasticity is driven by environmental cues, and how analysing the spatial structure with complex systems methods further reveals tissue dynamics.

Speaker: Rodrigo Garcia-Tejera (Institute of Genetics and Cancer)

11:40 AM A data-integrative approach to building ABMs for TNBC metastasis initiation and growth in the lungs

We developed a data-integrative framework to parametrize and validate an agent-based model (ABM) of triple-negative breast cancer (TNBC) metastasis in the lung, focusing on the emergent dynamics of tumor-microenvironment interactions. The model represents tumor cells, fibroblasts, macrophages, and endothelial cells as interacting agents, governed by probabilistic rules for proliferation, death, migration, and phenotypic transitions. Parameterization leverages complementary datasets across scales. Quantitative histology (IHC/IF) provides information on cell type, spatial distribution, and temporal growth dynamics with further constraints on phenotypic composition from flow cytometry. In vitro/vivo assays quantify activation rates underlying tumor–stroma cross-talk, while bulk growth curves constrain system-level dynamics.
These heterogeneous datasets are integrated using Approximate Bayesian Computation to infer parameter distributions consistent with observed multiscale behaviors. We calibrate the model against joint observables, including population growth, phenotypic proportions, and temporal evolution. Validation is performed using chemotherapy and pathway inhibition experiments to assess predictive capacity under intervention. This approach enables identification of constrained interaction rules that reproduce observed metastatic dynamics and provides a principled framework for linking experimental measurements to mechanistic models of metastatic progression.

Speaker: Tatiana Miti (Moffitt Cancer Center)

10:40 AM → 12:00 PM Mechanistic Model Inference for Stochastic Single-Cell Dynamics

10:40 AM Neural approximations for models of transcriptional dynamics enable genome-wide parameter inference

The advent of high-throughput transcriptomics provides an opportunity to advance mechanistic understanding of transcriptional processes and their connections to cellular function at an unprecedented, genome-wide scale. These transcriptional systems, which involve discrete stochastic events, are naturally modeled using chemical master equations (CMEs), which can be solved for probability distributions to fit biophysical rates that govern system dynamics. While CME models have been used as standards in fluorescence transcriptomics for decades to analyze single-species RNA distributions, there are often no closed-form solutions to CMEs that model multiple species, such as nascent and mature RNA transcript counts. This has prevented the application of standard likelihood-based statistical methods for analyzing high-throughput, multi-species transcriptomic datasets using biophysical models. We show how neural networks and statistical understanding of system distributions can produce accurate approximations to a steady-state bivariate distribution of the bursty model of transcription, bypasses intensive numerical solving techniques and reducing likelihood evaluation time by several orders of magnitude. This method can be incorporated into existing machine learning architectures to enable broad exploration of parameter space of transcriptional burst sizes, RNA splicing rates, and mRNA degradation rates from experimental transcriptomic data.

Speaker: Maria Carilli (Caltech)

11:00 AM On (iterated) Schrödinger bridges for inference with prior dynamics

We consider the Schrödinger bridge problem (SBP) which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the “most likely” evolution of the system compatible with the data. Notably, this point of view has spurred a lot of activity in the single cell analysis community over the past few years.
Most existing literature assume Brownian reference dynamics, and are implicitly limited to modelling systems driven by the gradient of a potential energy.
We depart from this regime and consider reference processes described by a multivariate Ornstein-Uhlenbeck process with generic drift matrix $\mathbf{A}$.
When $\mathbf{A}$ is asymmetric, this corresponds to a system in which non-gradient forces are at play: this is important for applications to biological systems such as transcriptional dynamics in cells, which naturally exist out-of-equilibrium.
In the case of Gaussian marginals, we derive explicit expressions that characterise exactly the solution of both the static and dynamic Schrödinger bridge.
For general non-Gaussian marginals, we propose a simulation-free algorithm based on flow and score matching for learning a neural approximation to the Schrödinger bridge.
We demonstrate applications to a range of problems based on synthetic benchmarks and real single cell data. In particular, we highlight an iterative scheme for joint inference in the setting where both the SBP solution and $\mathbf{A}$ are unknown, and its potential applications to joint inference of dynamics and the underlying gene interaction networks.

Speaker: Stephen Zhang (The University of Melbourne)

11:20 AM Biophysical generative modeling of cell fate decision-making with single-cell omics data

Inferring biophysical models of gene regulation from single-cell omics data remains a significant challenge because of the high dimensionality, stochasticity, and cross-sectional nature of the measurements. We aim to bridge this gap by combining flow-based generative modeling with the biophysics of transcriptional regulation to infer interpretable models of cell fate decision-making from single-cell omics data. Existing inference approaches often simplify or ignore the biophysics of gene regulation, compromising accuracy and interpretability for the sake of optimization ease. To address this issue, we recently developed Probability Flow Inference (PFI), a computational approach to infer the phase-space probability flow associated with arbitrary stochastic differential equations. This approach enables inference of detailed models of transcriptional regulation that naturally disentangle molecular noise and cellular proliferation from gene regulation, improving gene regulatory network inference and outperforming purely data-driven approaches in cell fate prediction. Overall, our results demonstrate that flow-based generative modeling offers an opportunity to test, at genome-wide scale, biophysical hypotheses about cell fate decision-making.

Speaker: Victor Chardes (Harvard University)

11:40 AM Simulation-free approximate Bayesian computation for stochastic reaction networks and its applications on scRNA-seq data

In single-cell biology, stochastic reaction networks (SRNs) model molecular production, degradation, and interactions, and inferring their structure and parameters from data is central to understanding underlying biological mechanisms. Approximate Bayesian computation (ABC) offers a flexible Bayesian approach with posterior uncertainty quantification, but its reliance on extensive stochastic simulations results in high computational cost even for small systems, despite advances in sampling schemes. In this work, we propose a simulation-free approximate Bayesian computation (SFABC) framework that avoids explicit simulation of system dynamics. The method instead exploits theoretical constraints derived from the governing equations and uses convex optimization to evaluate whether a candidate parameter set is consistent with the observed data. Using synthetic benchmarks, we show that SFABC is compatible with different sampling schemes and achieves performance comparable to standard ABC algorithms, while substantially reducing computational cost that does not scale with sample size. Applied to steady-state scRNA-seq datasets, SFABC unravels transcriptional bursting kinetics through full posterior inference beyond point estimates. Using metabolic labelling data, we compare snapshot and time resolved models. Extending SFABC to model selection, we distinguish competing models of cell cycle–dependent transcriptional regulation using scRNA-seq data with cell cycle reporters.

Speaker: Zekai Li (Imperial College London)