Three-dimensional (3D) tumor spheroids, reflecting avascular microregions within a tumor, are preclinical cell culture systems for assessing the impact of radio(chemo)therapy. However, spheroid experiments remain laborious, and determining long-term radio(chemo)therapy outcomes is challenging. Mathematical models of spheroid dynamics have the potential to enhance the informative value of...
Detecting extremely rare DNA variants is key in multiple clinical applications, such as circulating tumour DNA detection or transplant monitoring. A serious limitation of detection ability comes from polymeraseโinduced sequencing errors. Unique molecular identifiers (UMIs) help suppress these errors, but their efficiency depends on how many amplified copies each barcoded molecule yields - an...
Physics-Informed Neural Networks (PINNs) are increasingly used in mathematical epidemiology to bridge the gap between noisy clinical data and compartmental models. However, training these hybrid networks is often unstable due to competing optimization objectives. As established in recent literature on โGradient Pathology,โ the gradient vectors derived from the data loss and the physical...
Inspired by empirical observations in animal swarming -- particularly in schooling fish -- we propose an opinion-swarming model for self-propelled particles in order to understand the effect of uninformed individuals in consensus formation \cite{z}. Building on classical bounded-confidence opinion models \cite{k} and self-propelled swarming models \cite{d}, we introduce a three-population...
RNA sequencing is a vital technology for immune repertoire profiling, allowing us to understand how the human adaptive immune system is structured. This technique enables clonal lineages to be tracked spatially and longitudinally: important for quantifying immune responses and the impact of immunotherapies \cite{oakesQuantitativeCharacterizationCell2017}. However, non-Poissonian sources of...
Estimating whole-brain directed connectivity from resting-state fMRI remains an open challenge. Dynamic Causal Modeling (DCM) is prohibitive at whole-brain scale, while lagged correlations conflate direct and indirect propagation with common-input artifacts. We recover directed connectivity by fitting a Network Diffusion Model (NDM) to temporal dynamics. The NDM \cite{Abdelnour2014} describes...
School closures were among the most contentious non-pharmaceutical interventions during the pandemic due to their socio-economic costs and uncertainty surrounding their population-level epidemiological impact. Given the role of schools as key transmission settings, we retrospectively assessed their effect on SARS-CoV-2 dynamics in Portugal prior to mass vaccination.
We used an...
Vascular stenosis, the pathological narrowing of blood vessels due to atherosclerotic plaque, remains a primary driver of cardiovascular disease. Traditional computational fluid dynamics (CFD) models provide detailed hemodynamics but are computationally expensive, limiting their utility for long-term disease forecasting. To address this, we propose a highly efficient stochastic modeling...
Patients with the same cancer diagnosis often respond very differently to therapy, motivating efforts to identify molecular subgroups explaining this heterogeneity. High-dimensional molecular datasets are often analysed using correlation-based similarity among features\cite{1,2}; however, correlation captures global expression patterns and often fails to reveal how signals split patients into...
Many biological, geophysical and industrial systems rely on the transport of material through fluid flow across complex networks. Suspensions in these systems are prone to clogging, particularly in confined geometries, with potentially severe consequences on system function. However, predictive frameworks that couple suspension rheology with network-scale flow redistribution remain limited....
Plant diseases have a major impact on crop production worldwide. However, the success of plant disease control methods depends on their adoption by growers (\cite{MW22}). In the present work, we propose a behavioral epidemiology model, in which a classical SI-model is intertwined with growersโ behavior in terms of roguing (removal of) infected plants or not. This ODE model is built on...
For a biochemical reaction network, the sparsest steady-state relations (that is, steady-state relations involving fewest chemical complexes) reveal the most direct dependencies in the system, and are closely connected to robustness properties. We may ask, what are the sparsest steady-state relations obtainable from all possible linear combinations of the rate equations, and what features of...
The emergence of developmentally regulated life cycles, coordinating cellular growth with multicellular reproduction, was a key step in the evolution of complex multicellularity. Yet how cells use local information to regulate fragmentation in growing multicellular groups, and how these processes depend on spatial structure, remains unclear.
Here, we introduce a computational...
Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection and those responsible from transition from acute to chronic disease, we developed a deterministic mathematical model of hepatitis B infection that...
Neurons receive information through their dendrites. During development, dendrites grow, retract, and branch as they search for connections, and the resulting dendritic arbor shapes the structure of the broader neural network. This talk introduces a flexible model describing the full spatial structure of a single neuron through three processes: a lifetime process that determines whether each...
Dynamic mathematical models of the hypothalamicโpituitaryโthyroid (HPT) axis provide a framework for studying thyroid physiology. A widely used model originally developed in \cite{A, B} has been refined and extended over the past two decades \cite{D}. This model captures the HPT feedback loop, including TSH, T4, T3, and additional regulatory factors \cite{A, D}.
The model was extended to...
Blood clots are deadly. Anticoagulants, which prevent pathological clotting, are therefore vital. Protein S (PS) is an important anticoagulant implicated in pathological bleeding and clotting. PS binds with two other coagulation proteinsโTFPIฮฑ and factor V shortโto form the protein S complex (PSC), which enhances anticoagulant function by incompletely understood means. To investigate, we...
Lipid droplet dynamics during adipogenesis play a central role in adipocyte function and metabolic health, yet the mechanisms governing droplet formation and growth remain poorly quantified. We present a mechanistic ordinary differential equation (ODE) model describing the evolution of lipid droplet size distributions measured in time-resolved imaging experiments of differentiating adipocytes....
The pathways of glioblastoma progression involve a complicated association among tumor cells, immune factors, vascular systems, and metabolite reorganization. Despite the use of mathematical models, which have been used to capture individual aspects, the gap is the approach of having a combined framework. We present a Multi-scale- Multi-processing Combined Glioblastoma Mathematical Model. This...
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour growth. We develop stochastic, on-lattice agent-based models (ABMs) which incorporate volume exclusion, random movement, and multi-stage representations of the...
Strategies to mitigate an infectious disease outbreak can be focused or unfocused. Focused interventions (FI) aim to limit transmission from known or likely infectious individuals (e.g., quarantining contacts). Unfocused interventions (UI) affect all individuals irrespective of infection status by lowering the effective contact rate (e.g., lockdowns or universal masking). The costs of FI...
In many interactions between hosts and pathogens or plants and herbivores, the attacked organism produces a chemical compound to defend itself. The attacker often responds to this by producing a counter defence, e.g. an enzyme that can degrade this defence chemical. Sometimes, the defender responds by producing another chemical, a counter-counter defence, that can inhibit the degrading enzyme....
Protein folding is an NP-hard problem, making accurate prediction of stable three-dimensional structures computationally demanding. Despite advances in classical methods, an efficient general solution remains unresolved. Quantum computing has improved the study of small, simplified folding models, though scaling to realistic proteins is still a challenge. Here, we propose a novel turn-based...
Eastern equine encephalitis virus (EEEV) is a deadly arboviral pathogen with 30% severe case fatality. EEEV exhibits pronounced 2โ3 year cyclical outbreak patterns in the northeastern United States, linked to shifts in mosquito feeding preferences between hatchyear and adult avians. An age-structured vector-host model incorporating differential feeding patterns of Culiseta melanura mosquitoes...
During the COVID-19 pandemic, various social distancing measures were implemented to mitigate epidemic spread. To evaluate the spatial effects of these measures, mobility data were often used as a proxy for disease transmission \cite{schlosser_covid-19_2020, gibbs_detecting_2021}. Here, we analyzed the spatial patterns of 141,881 self-reported transmission pairs that occurred during household...
Live-cell imaging experiments often track mRNA production using fluorescently tagged transcripts. To infer the statistics of initiation events, standard methods assume that transcription has a fixed duration. However, studies of intron splicing and transcriptional pausing show that stochasticity in elongation and termination are often significant and cannot be ignored. In this talk, we...
Many biological systems contain material components that are repaired and replaced over time. One common example is the extra-cellular matrix, an interconnected network of proteins that provides chemical and mechanical protection and support in many systems, for example in tissue basement membranes and bacterial biofilms. The building blocks in these systems can be supplied by accompanying...
Blood vessels are essential components of the mammalian circulatory system, responsible for delivering nutrients and oxygen to tissue cells. Despite recent advances in understanding the biological mechanisms underlying vascular growth, researchers have not yet tackled the generation of synthetic vascular structures using deep learning models that are trained with existing datasets.
This...
Modern single-cell RNA sequencing techniques have transformed molecular biology by enabling genome-wide molecular profiling across thousands to millions of cells. However, these technologies fail to preserve the natural spatial organisation of individual cells, which is vital to understand how cell-to-cell interactions drive the development of multicellular organisms or shape the collective...
African animal trypanosomosis (AAT) is a substantial burden to livestock productivity across sub-Saharan Africa, yet its prevalence is underestimated because the most common diagnostic tests, the haematocrit centrifugation and buffy coat techniques (HCT/BCT), have low sensitivity. The polymerase chain reaction test (PCR) offers a higher sensitivity but is costly and rarely available in field...
This study uses vertex- and Voronoi-based computational models based on Chaste \cite{Cooper2020} to investigate interclonal cooperation within cell populations. We analyze interactions between mutated cell types with distinct hyperproliferative and invasive properties. Modeling the cooperative dynamics among these clones shows how cellular heterogeneity affects tissue growth and invasion,...
High-codimension bifurcations critically contribute to shaping the dynamics of nonlinear models, as their unfoldings establish structured relationships between lower-codimension bifurcations and, ultimately, the attractors they generate. Owing to this unifying and predictive capacity, such bifurcations are attracting growing interest in mathematical biology.
One notable example is the...
The role of phenotypic plasticity in community assembly and promoting and/or hindering coexistence is widely acknowledged but remains poorly understood. The nematode Prisitiounchus pacificus exhibits a case of environmentally-induced phenotypic plasticity in which an adult worm irreversibly develops either a predatory or a non-predatory mouth form. Additionally, the natural lifecycle of *P....
Atherosclerotic plaques are a leading cause of heart attacks and strokes. Macrophage proliferation drives plaque growth, but whether this promotes stability or triggers sudden destabilisation remains unresolved. Using bifurcation analysis of a lipid-structured atherosclerosis model \cite{chambers_lipid-structured_2024}, we uncover the nonlinear dynamics governing this transition.
Our main...
Studying structural brain networks has witnessed significant advancement in recent decades. Findings revealed a geometric principle, the exponential distance rule (EDR) showing that the number of neurons decreases exponentially with the length of their axons. This neuron-level information was used to build a region-level EDR network model that was able to explain various characteristics of...
Anti-VEGF therapy has recently been approved by the FDA to prevent the progression of retinopathy of prematurity (ROP; a leading cause of childhood blindness) and preserve vision in preterm newborns. Following injection, it is known that these drugs leave the eye and enter the systemic circulation; however, from there, the distribution of these drugs to the developing organs is unknown. Whilst...
Tauopathies are a class of neurodegenerative diseases, such as Alzheimer's disease, characterized by a progressive accumulation of toxic misfolded tau proteins in the brain \cite{1}. Model-based approaches have shown that this progression, or โstaging," follows a tau-spread process along the brain's white matter connective network, dubbed the โstructural connectome" (SC). The Network Transport...
Households represent a key unit of interest in infectious disease epidemiology, in both empirical studies and mathematical modelling. The within-household transmission potential of an infectious disease is often summarised in terms of a secondary attack ratio. Despite their widespread use, estimates of secondary attack ratio depend on the distribution of household compositions seen during the...
Microbes adapt their physiology in order to grow in a wide variety of environments. Cellular growth laws quantify the relationship between the levels of essential resources such as ribosomes in a cell and the growth rate under steady-state conditions. However, in nature, the environment inhabited by a cell typically varies with time. A key question is therefore how an individual cell allocates...
Vaccine-related communication can help curb infection, yet it can also depress vaccine uptake and sustain transmission even when effective vaccines exist. We examine how vaccine-information dynamics shape epidemic spread and how they can be steered to support control. We propose a coupled information--infection framework that links a standard SVIRS epidemic model to an...
Glioblastoma Multiforme is an aggressive primary brain tumor with poor prognosis. Understanding the patient-specific phenotype of the disease (e.g., proliferative vs diffusive) can be crucial for treatment planning. However, learning patient-specific parameters in a reaction-diffusion equation of glioma growth is difficult due to the (1) lack of time-series information available for a single...
Female mammals are born with a non-renewable pool of oocytes that underlies the ovarian reserve. The size of the oocyte pool results in great part from a selection process occurring during ovarian development within germ cysts, where clusters of germ cells are surrounded by layers of somatic cells. During selection, oocytes increase in size at the expense of non-selected cells, which are...
Although ordinary and partial differential equation (ODE/PDE) models are widely used in infectious disease inference and public health decision-making, parameter sensitivity and identifiability are often assessed with tools that lack mechanistic interpretability and overlook sensitivity to initial conditions or derived epidemiological quantities. We present a framework for generating...
Macrophages play an important role in the body's innate immune system. They digest smaller external threats, promote healing of internal wounds, and recruit other macrophages using chemokines (chemical signals).
These chemokines bind to specialised receptors on the cell membrane that trigger downstream signals. The receptor CXCR3 in macrophages, for example, is activated by the chemokines...
Astrocytes play an important role in the regulation and support of neural functions in the central nervous system. Neurodegenerative diseases (ND), have been linked to the development of pathological astrocytic phenotypes that result in changes in cellular morphology and mitochondrial dysfunction \cite{r2021, s2024}. Calcium (Ca2+) dysregulation influence key metabolic pathways that can lead...
Traditional thermodynamic views describe organisms as dissipative systems maintaining low internal entropy by exporting disorder, yet this fails to explain how complexity and information increase under the second law. We propose that growth and evolution arise from regulating the rate of explorationโthe import of matter and energy from the environment. When exploration adapts to environmental...
Spatiotemporal variations in hypoxia, cellularity, and vascularity affect the response of glioma to radiotherapy (RT). MRI can quantitatively map these features, identify tumor habitats, and calibrate biology-based models to predict the response to different RT protocols. Our long-term goal is to determine optimal RT strategies through predictive modeling.
Twenty-five female Wistar rats...
Accurate arteryโvein labelling is essential for the analysis of whole-brain vasculature and blood flow simulations to understand cerebrovascular organisation and function. However, most datasets lack arteryโvein annotations~\cite{todorov}, since labeling is generally possible only at acquisition using specific staining protocols~\cite{kirst}.
Despite reported topological differences...
The process of programmed cell death, namely apoptosis, is a natural mechanism that regulates healthy tissue, multicellular structures, and homeostasis [1]. An improved understanding of apoptosis can significantly enhance our knowledge of biological processes and systems. For instance, pathogens can manipulate the apoptotic process to either evade immune detection or to facilitate their...
Mechanistic models based on ordinary differential equations typically involve many parameters that must be estimated from limited experimental data. This process is hindered by multimodal objective landscapes, expensive model simulations, sparse and noisy measurements, plus structural and/or practical identifiability issues, all of which make calibration computationally demanding.
Here, we...
Low-grade gliomas (LGGs) are slow-growing, infiltrative brain tumors for which complete surgical resection is often unfeasible, necessitating the use of adjunctive therapies. In this work \cite{Vela}, we present and analyze a mathematical model for LGG growth and response to chemotherapy, validated against clinical patient data. We prove the existence and uniqueness of a global non-negative...
To control mosquito-borne diseases such as dengue, for which no effective vaccine is available, several strategies focus on targeting mosquito populations. One such approach involves introducing Wolbachia, a symbiotic bacterium that blocks pathogen transmission, into the mosquito population. A mathematical model describing the introduction of Wolbachia and the subsequent population replacement...
Single-cell omics methods promise to revolutionize our understanding of gene regulatory processes, offering genome-wide measurements at single-cell resolution. However, there are three central challenges: they are high-dimensional, noisy, and provide only snapshots.
Together, these challenges obstruct the extraction of accurate time-resolved gene expression dynamics. To still explore these...
Auxin is a hormone that plays key regulatory roles in plant development. Its diverse functions are enabled by its directional (polar) transport through cells and the feedback between this transport and the intracellular localisation of auxin transporters (PINs). These mechanisms are traditionally modelled using discrete compartmental ODEs, where each compartment represents a single...
Waddingtonโs epigenetic landscape (EL) famously represents development as a ball rolling down a branching surface whose valleys correspond to cell fates, while the landscape itself is shaped by pegs and ropes representing gene interactions. Despite its enduring influence, which continues today in fields such as stem cell biology, aging and single-cell omics, the conceptual meaning of this...
When applying Machine Learning (ML) to medical problems, privacy and interpretability are of utmost concern. The inner workings of the model need to be well understood to strengthen user trust, and any patient data used in training should be fully anonymized. These two values can work in opposition to each other, as transparent models like Logistic Regression (LR) can unintentionally leak...
How does spatial structure influence the fate of novel mutations in a population? Fixation dynamics and mutation-selection balance are known to depend sensitively on the interaction network underlying spatial structure \cite{lieberman:nature:2005,sharma:NatComm:2025, sharma:biorxiv:2025}. However, analyzing these processes on large heterogeneous graphs quickly becomes analytically intractable....
High-Grade Serous Ovarian Cancer (HGSOC) is the deadliest gynaecological cancer and the fourth leading cause of cancer deaths in women. Most patients experience treatment failure and recurrence, primarily driven by resistance to chemotherapy, contributing to a 5-year survival rate of 45%. Existing literature lacks immunological models of HGSOC resistance and developing them could provide...
Scissors cut Paper, Paper wraps Rock, and Rock blunts Scissors: the classic game of Rock
Paper-Scissors offers a simple yet compelling model of cyclic dominance. That dynamics is
frequently used to illustrate competition between populations or strategies in evolutionary
game theory and biology and can be observed in a variety of ecological systems.
We consider a Lotka-Volterra model for...
Computed tomography scans remain a common modality for measuring tumor burden in cancer patients. However, diagnostic imaging can be burdensome or invasive for patients due to enclosed environments and clinical discomfort. Tumor volume data is also collected infrequently. Patient-Reported Outcomes (PROs) offer a less intrusive avenue for gauging cancer progression through measurements...
Mathematical models are invaluable for understanding and predicting how biological systems behave. Constructing such models requires specifying the mechanisms and relationships involved, which in practice are not perfectly known. In the presence of multiple competing models, principled approaches to modeling need to account for model uncertainty. Bayesian model averaging (BMA) provides a...
Since Zuckerkandl and Pauling proposed the molecular clock in the 1960s it became common to trace mutations in genomes to infer their evolutionary history \cite{Zuckerkandl1965}.
UPGMA, also known as average linkage, is a hierarchical clustering algorithm, which was one of the first used to infer ultrametric phylogenetic trees \cite{Sokal1958}. Trees can inferred efficiently in $O(n^2)$...
Emerging variants are a key driver of long-term dynamics in pathogens such as SARS-CoV-2 and influenza, yet most transmission models do not consider the dynamic nature of the mutation process.
We introduce a unified framework that couples multi-variant transmission with an explicit mutation process. Transmission is described by a generic compartmental model accounting for multiple variants...
Chemical reaction networks are mathematical tools used to model the dynamics and steady-states of intricate biochemical systems. One major obstacle in analyzing biochemical reaction networks is a lack of precise knowledge of system parameters such as reaction rates. Often, even the structure of the entire network is not accurately known and therefore simulation methods may not be sufficient in...
Mathematical models of prostate cancer progression and treatment response often rely on deterministic dynamics, yet in vivo behaviour reflects stochastic variation across scales. Randomness may arise from clonal heterogeneity, phenotype switching, metabolic plasticity, tumour micro-environment structure, and fluctuating hostโmicrobiome interactions. These factors shape treatment response and...
Tissue engineering scaffolds consist of pores lined with cells through which a nutrient-filled fluid passes. Over time, cells consume the nutrients and proliferate, causing the pores to shrink until they fill with tissue. Existing literature has investigated the effects of nutrient flow rate, nutrient concentration, cell hunger rate, scaffold elasticity, and shear stress on cell proliferation...
Why has maximal human lifespan barely changed in the past two centuries? To understand this we make a mechanistic link between cellular damage, survival curves, and maximum lifespan using a validated stochastic model of damage accumulation and extensive human data. We show that maximal lifespan is set mainly by damage production and clearance rates, as in progeroid syndromes. In contrast,...
Phase Response Curves (PRCs) are useful in studying the existence and stability of various phase-locking modes in networks of oscillators under pulse-coupling assumptions. However, for network oscillations at higher frequencies, the basic assumptions of pulsatile coupling are broken. So, our lab recently introduced a mean field approach to study coupling and phase-locking in a network of...
Invasion into surrounding tissues is a hallmark of cancer \cite{hanahan}. In contrast to individually migrating cells, multicellular clusters exhibit enhanced resistance to radiotherapy and DNA damage \cite{haeger}. In this work we seek to identify the mechanisms that generate the cell-cell contact patterns associated with collective therapy resistance using quantitative and mechanistic...
Melanoma is a type of skin cancer that becomes much more lethal when it spreads or metastasises to other tissues. During tumour initiation, melanoma cells form clusters in the primary tumour that promote metastasis. In the absence of biological tools to visualise cluster formation at primary tumour sites we use in vitro data for two distinct melanoma cell phenotypes, one more proliferative and...
Vector-borne diseases often infect multiple host species, increasing the likelihood of disease persistence due to the presence of multiple reservoirs. Vector biting patterns and feeding preferences can shift in response to selective pressures introduced by disease control interventions, altering the dynamics of transmission. In this talk, we develop a mathematical model that couples host...
Subaerial biofilms (SABs) are microbial communities colonizing air-exposed mineral surfaces, where water availability is crucial for their metabolic activity. Located at the interface between the mineral substrate and the air atmosphere, SABs interact directly with both environments. Although precipitation and dew contribute to SAB hydration, water availability is largely controlled by...
Species interactions take many forms, including antagonism and mutualism, yet the evolutionary conditions under which interactions change character remain poorly understood. Here we investigate how antagonistic interactions can evolve into mutualistic ones using a coevolutionary modeling framework inspired by experimental evolution, where a species interaction transitioned from predatorโprey...
We consider an eco-epidemiological model, where an infectious disease circulates within a predator population. If the disease only alters the attack rate of predators (a so-called trait-mediate effect), this reduces the equilibrium predator population size โ no matter whether the disease increases or decreases the attack rate. By contrast, the prey population size at equilibrium can increase...
We investigate a class of autonomous fractional-order nonlinear dynamical systems motivated by an in-host HIV infection model incorporating three structural mechanisms: logistic proliferation of healthy target cells, two transmission pathways--virus-to-cell infection and cell-to-cell transmission through virological...
We consider a mathematical model of differential equations for the epidemic dynamics with heterogeneity in preventive behaviors among individuals. Our focus is on how the distribution of preventive behaviors influences the epidemic consequence in a community. The preventive behavior determines the level of caution to the disease transmission. We assume that the community could be categorized...
Endosymbioses have significantly changed the course of life on Earth, by giving rise to energy-producing organelles such as mitochondria and chloroplasts. While common in eukaryotes, endosymbiosis is extremely rare in bacteria, with only a handful of known instances. This rarity is shocking given the tremendous diversity and abundance of bacteria. While many factors may contribute to their...
Elevated interstitial fluid pressure (IFP) and abnormal tumor vasculature limit the delivery of therapeutic agents to solid tumors. Although anti-angiogenic therapy can transiently normalize tumor vasculature and improve transport, the impact of treatment scheduling on IFP dynamics and drug delivery remains poorly understood. In this study, we develop a spatiotemporal multiphysics model that...
Malaria imposes significant challenges on human health, healthcare systems, and economic growth/productivity in many countries. In this talk, we will propose a model to understand the interplay between malaria dynamics, economic growth, and transient events. The reproduction number (R_0) is calculated. The model exhibits a backward bifurcation. Additionally, there is a parameter regime for...
Endothelial cells forming blood vessels display complex collective behavior. During vascular network rearrangement and regression, new capillaries are formed while others regress through cellular rearrangements without relying on cell death or proliferation \cite{franco_dynamic_2015}. Furthermore, endothelial cells in arterioles and venules are polarized in the opposite direction of blood...
Focused ultrasound (FUS) combined with thermosensitive liposomes (TSLs) offers a strategy for localized drug delivery in solid tumors. To investigate the mechanisms governing this therapy, we develop a spatiotemporal multiphysics model of ultrasound-triggered nano-drug delivery in tumor tissue. The framework consists of a coupled system of partial differential equations describing acoustic...
Inferring nonlinear interaction structures in complex microbial communities remains a central challenge in systems biology. Generalized Lotka-Volterra (GLV) models are a foundational framework for modeling interacting dynamical systems and are widely used in ecology. However, parameter estimation in GLV models is often hindered by the exploration of numerically unstable regions of parameter...
Many ecological management problems involve allocating limited resources across the life stages of populations in order to influence population growth. Such problems arise in both invasive species control and conservation of threatened species, yet these objectives are often studied within separate modeling frameworks. We consider a general stage-structured formulation for univoltine...
Molecular glues are small molecules that enable targeting of previously โundruggableโ proteins by promoting interactions between a protein of interest (POI) and an effector protein, leading either to stabilization or degradation of the target. Despite increasing interest in these systems, the kinetic mechanisms governing their performance remain poorly understood.
We develop a mathematical...
Cellโcell adhesion is crucial for tissue organization and collective migration. Cells also adhere to the extracellular matrix (ECM) that surrounds them. Both cell-cell \cite{manibog_resolving_2014} and cell-ECM adhesions \cite{kong2009demonstration} can be catch-bonds, which strengthen under increasing force. Although recent mathematical studies \cite{rens_cell_2020} have explored how models...
In this research, we are investigating the relationship between a two-dimensional, quadrilateral, vertex model based on the work of (Brown et al, 2025) and a one-dimensional cell centroid model. The aim being to derive a continuum limit PDE approximation for the behaviour of epithelial monolayers. The movement of the vertices in the two-dimensional model is determined by the minimisation of...
The vertebrate inner ear is a conserved sensory organ for balance. Its morphogenesis follows a twoโphase program: (i) expansion of the otic vesicleโa closed epithelial monolayer enclosing a fluidโfilled lumenโand (ii) a topological transition from a closed vesicle to the toroidal structure of the semicircular canals. Although this two-phase process is broadly conserved, previous studies...
Population density greatly affects how microbes survive and grow in an environment. Porphyromonas gingivalis (Pg), a key pathogen in periodontitis disease, shows a type of growth that depends on population density. This growth suggests that there is a minimum density of Pg needed for it to survive. Interestingly, Pg is often found at low density inside the gum environment but still it...
Most infectious disease datasets are dichotomous, typically indicating the presence or absence of infection. However, many contain quantitative measurements, such as cycle threshold (Ct) values from PCR tests or antibody titers from serological assays. Despite this, epidemiological models often rely on dichotomised data to infer key immunological and transmission parameters. This...
During the COVID-19 pandemic early years, infection-prevention measures suppressed influenza transmission and the early onset and moderate severity of the US 2022-2023 influenza season may have resulted from lower population immunity after two years of limited influenza virus circulation. We used an age stratified mathematical model of influenza virus transmission that incorporates...
We explore the evolutionary dynamics of extrachromosomal DNA (ecDNA) in non-growing cell populations in the precancerous state. Unlike chromosomal DNA, ecDNA segregates randomly during mitosis, producing high variability in copy number across cells. While ecDNA has been studied in expanding tumours, its fate in precancerous populations is less understood. Stochastic simulations indicate that...
Recent advances in cell free transcription-translation (TXTL) systems have renewed interest in quantitative cell-free gene expression modelling. Ordinary Differential Equation (ODE) models can describe TXTL dynamics, enabling users to explore a design space difficult to probe experimentally. A common modelling limitation is the unknown effect of variability in inputs with respect to the...
Human papillomavirus (HPV) infection is the causal agent of cervical cancer. While most HPV infections are transient and cleared by immune responses, a small fraction establish persistent infection, enabling cancer development through a multistage process from precancerous lesions to invasive disease. A distinctive feature of cervical cancer is the high rate of spontaneous remission at...
Trait abundance distributions can help identify processes that determine species coexistence in diverse communities. Niche differences enable speciesโ โstableโ coexistence by reducing interspecific competition and competitively excluding non-optimal species. However, species are favored in their persistence and abundance the more similar they are to optimal niche strategies, producing โtrait...
We develop and analyze a nonlinear mathematical model for autoimmune-mediated demyelination in multiple sclerosis that captures interactions between healthy myelin, autoreactive immune cells, regulatory immune cells, and neuronal functional capacity. Immune activation is driven by myelin damage through a saturating response function, while regulatory cells suppress pathogenic activity and...
A non-monotone dose response is a pharmacokinetic response characterised by stimulation at low dose and inhibition at high dose of the therapeutic compound. This paradoxical phenomenon is observed in many contexts from kinase to immune checkpoint inhibitors in cancer treatment. Two examples of models with this property are presented.
The first is a kinetic model for the action of a kinase...
High-grade serous ovarian cancer (HGSC) almost always relapses after first-line treatment, yet how long patients remain progression-free varies enormously. One plausible explanation is that the immune state at the end of chemotherapy โ in particular, how many memory T cells survive treatment โ shapes the pace of tumour regrowth. Whether this differs between patients with and without homologous...
Synthetic microbial consortia offer a controlled setting to study how ecological and evolutionary forces shape community structure. Here we present a mathematical framework for a cross-kingdom autotrophโheterotroph system in which a sucrose-secreting cyanobacterium feeds a heterotrophic community. We model three heterotrophic metabolic strategies- public metabolizing, private metabolizing and...
The understanding of tissue dynamics is critical across various biological contexts, including morphogenesis, regeneration, and tumor proliferation. While traditional models often focus on volume exclusion, this work investigates the emergence of spatial patterns driven by competition for a shared resource, such as oxygen \cite{Gatenby1996}. We present a family of coarse-grained evolution...
Acute myeloid leukemia (AML) is one of the most aggressive forms of leukemia, driven by uncontrolled proliferation of abnormal stem cells in the bone marrow, which disrupts normal blood cell production.
Through mathematical modeling and analysis, we aim to better understand the dynamical behaviors underlying leukemia progression and to derive insights for optimal treatment design. Starting...
The mitotic cell cycle governs DNA replication and cell division. Efficacy of radiotherapy depends on cell-cycle position and so accurate mathematical models of the cell cycle are essential for understanding and predicting treatment response. Mathematical modellers often face a lack of available, sufficiently resolved data for parametrising models. We consider how the ability to collate...
Plant-parasitic nematodes cause major economic losses worldwide by infecting crops, diverting resources and impairing plant growth. While resistance aims to reduce parasite burden, tolerance allows plants to maintain yield despite infection, offering a complementary and potentially more sustainable strategy. Understanding how tolerance arises requires mechanistic insights into host-parasite...
While biological systems estimate and adapt to fluctuating environments by integrating sensory evidence with internal memory, their information processing is constrained by limited resources. Such limitations introduce intrinsic noise and computational costs, which can fundamentally reshape optimal estimation strategies. Indeed, recent experiments indicate that humans rely on simpler...
Tuberculosis remains a major cause of death among infectious diseases despite the availability of multiple antibiotics against the causative agent Mycobacterium Tuberculosis (Mtb). Heterogeneity in Mtb population upon host infection prevents clearance of Mtb under antibiotic exposure. Mtb is known to differ in its redox environment, and the subpopulation with a reduced (oxidised) cytoplasmic...
Mutation provides the raw material for evolution. Mutation rates thus tune evolvability, the ability to undergo adaptive evolution: if mutation rates are too low, evolution is impeded; if mutation rates are too high, adaptive traits cannot be maintained. Empirical studies have demonstrated that mutation rates may change with individual condition, for instance in the case of stress-induced...
Microbiomes, their composition and stability have been a topic of great interest in recent years as they turn out to influence human health much more than previously thought. However, the mechanisms determining microbiome health remain unclear. As microbiomes are complex, consisting of many species, attacking this problem through modelling is a challenge \cite{G18,K19}. Several unknown...
Quorum-sensing is a biochemical signaling mechanism used by different bacterial taxa to communicate with their co-specifics. This communication allows bacteria to jointly respond to environmental conditions by collectively expressing particular traits once a certain population density is achieved. Its complex structure and multiple bureaucratic layers of gene activation make it difficult to...
Background: Identifying an optimal policy for a country that balances infection suppression and socioeconomic burden is critical during a pandemic \cite{c1}. Lacking global quantitative analysis for country-specific cost-optimal interventions \cite{c2, c3}, this study suggests tailored strategies and identifies national indicators to improve pandemic preparedness \cite{c4,c5}.
Methods: We...
Human intestinal epithelium is organised into test-tube-like structures called โcryptsโ or โglandsโ. These crypts are maintained by a small pool of stem cells that undergo a process of selectively-neutral replacement, leading each crypt to inevitably drift towards monoclonality \cite{lopez-garcia2010}. We previously discovered fluctuating CpGs (fCpGs), endogenous CpG sites that undergo...
Glioblastoma is an aggressive brain tumor characterized by infiltrative growth, frequent recurrence after treatment, and intratumoral and microenvironmental heterogeneity. A key driver of this heterogeneity is the tumor microenvironment, particularly oxygen gradients that arise as tumor expansion outpaces vascular development. These gradients can induce phenotypic plasticity in tumor cells,...
Tumor hypoxia drives radiotherapy failure, as reduced oxygenation lowers radiosensitivity and promotes resistant phenotypes. We propose a phenotype-structured partial differential equation model to study fractionation by varying doseโinterval pairs under oxygen-limited conditions, extending \cite{chiari2023}. The framework couples tumor cell density and oxygen dynamics through a continuous...
A challenge in modelling biological phenomena is that the resulting models often involve many interacting variables that exhibit complex nonlinear dynamics, making them difficult to study using dynamical systems theory. The well-established theory behind the Koopman operator helps to address this challenge by representing complex nonlinear models as simpler, linear models evolving in an...
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...
Boolean networks, first introduced by Kauffman as models for gene regulatory networks, have gained widespread popularity for their ability to capture complex biological behaviors through simple logical rules. A systematic investigation of these biological models suggests that they are incredibly robust. In particular, they are resilient to perturbations and tend to reach the same phenotype...
Since its inception as a discipline, infectious disease modelling has also been aware of the importance of and considered the spreading of behaviours relevant to infection. While there have been many epidemiological modelling studies integrating behaviour in general, it is less common to consider specific behaviours. Here, I will present work that models the specific behaviours around TTI โ...
Limb development is regulated by feedback between the tissue-scale mechanics and cellular decisionsโmigration, contraction, division, and deathโimplemented through gene-regulatory networks. The dynamically changing states of these cellular networks reflect the decisions being made. To integrate these interactions across 3 scales: genes, cells, and tissues, we develop a 3D cell-based model in...
Neutrophils are the most abundant circulating leukocytes and first responders to infection and tissue injury. Once viewed as short-lived and homogeneous, they are now recognised as a dynamically reconfigurable immune compartment with connected phenotypic and functional states in homeostasis and disease [1]. In this talk, I will present various modelling and high-dimensional data-driven...
Tracking changes in functional connectivity (FC) between brain regions is essential for understanding transitions between states of consciousness such as wakefulness, sleep, and anesthesia. Whole-brain models provide a framework to investigate these transitions and have predominantly been developed using functional magnetic resonance imaging (fMRI), see \cite{ponce-alvarez_hopf_2024}. However,...
Cell migration and invasion are key processes underlying cancer metastasis. These behaviors are driven by cellโcell adhesion, chemotaxis, and matrix remodeling. CompuCell3D is a platform for agent-based modeling of cell migration; however, a limitation is that it does not natively support systematic parameter estimation for the stochastic simulations. Traditional Monte Carlo sampling-based...
Hybrid dynamical models are increasingly used to describe complex biological systems. Neural differential equations, such as PINNs, UDEs and Neural ODEs, combine mechanistic structure with data-driven components to model complex dynamical systems. However, this flexibility often weakens practical identifiability, leading to overfitting, redundant neural components, poorly constrained...
Hydraulic conductivity (K) is a key transport property governing interstitial fluid movement through the porous tumor microenvironment. Despite its importance, measurement of hydraulic conductivity relies on invasive and technically demanding experiments, mostly performed on non-human tumor tissues. Experimental studies also show substantial intra- and inter-tumoral heterogeneity in K,...
How invasions of ecosystems by novel species or variants unfold and their ripple effects on the community are central questions in ecology and evolution. In this work, we explore how an invader can replace a resident species in different ecological networks and/or models. Through the lens of modern coexistence theory and invasion rates, we analyze feasibility and stability of invaded...
Understanding and predicting how communities assemble is a paramount challenge in ecology. Here we address these questions normatively by comparing the observed species abundance distribution to a game-theoretically fair distribution based on each speciesโ Shapley value. By analyzing in total 56 distinct community outcomes, we assess how fairly biomass is distributed in microbial communities...
Oral squamous cell carcinoma (OSCC) represents the vast majority of oral cancers and is associated with high mortality. Patients with Oral Potentially Malignant Disorders (OPMD) present a risk of developing OSCC, and identifying OPMD with a high risk of malignant transformation remains a critical clinical issue.
Macrophages constitute a major immune population infiltrating the tumor...
A metapopulation model describes local populations of interacting species distributed across discrete habitat patches connected through migration. In this work, the local dynamics within each patch are modeled by May--Leonard Competitive Lotka--Volterra (MLCLV) systems consisting of three species, whose pairwise competitive interactions are encoded by a circulant interaction matrix. Such...
Turtle populations are unique among animals in their extreme life history strategy: they are long-lived, with adult mortality due largely to human intervention. In contrast, juveniles have extremely low survival rates, mainly due to predation. Practically, this has led to difficultly in re-introducing populations of turtles into historically viable ecosystems. We develop a model of freshwater...
Cell competition is a key mechanism by which tissues regulate cellular fitness and maintain homeostasis. In aging tissues, senescent cells show irreversibly arrested proliferation and yet persist and compete with proliferative non-senescent cells for space. How immune surveillance shapes this competition and regulates health and lifespan of such tissues remains poorly understood especially...
Existing established alternative methods for modeling seasonality use sinusoidal forcing functions, flexible splines, etc. In this talk, I outline a novel method for incorporating seasonality into the SIRS model using modular arithmetic. The study proposes a modular arithmetic approach to model seasonal variations in influenza transmission rates, with smooth transitions between them. Unlike...
Microswimmers typically undergo rapid motion to propel themselves through fluid. When considering the long-time swimmer dynamics of interest, the effect of the rapid motion is often assumed to average out without significantly affecting the trajectories. However, recent work has shown that this is not always the case. In this talk, we consider how the interaction between rapid propulsive...
Aminoglycoside antibiotics are widely used in pediatric care due to their strong activity against Gram-negative bacteria. Dosing remains challenging due to large inter-individual variability in exposure and risks of oto- and nephrotoxicity. As aminoglycosides are predominantly eliminated by renal filtration, developmental changes in body size and kidney function affect exposure.
To quantify...
Tumor progression depends not only on the intrinsic characteristics of the cancerous cells but also on the bidirectional complex interactions within the tumor microenvironment. Among these interactions, lymphocytes, immune cells, play an important role \cite{SanchoAraiz2021}.
In this work, we will generalize the mathematical model developed by Sung et al. in \cite{Sung2020} for...
Interactions between actin filaments and myosin molecular motors generate the forces required for muscle contraction, cell division, and cell movement. The mechanism of contraction is well understood in muscle cells, where actin and myosin adopt a regular sarcomeric structure. In contrast, understanding contractility in the disordered networks of the cell cortex remains an open problem....
Histologically homogenous tumours often hide distinct genetic subpopulations called subclones. These often come about due to mutations and structural variations of particular driver genes that seem to lead to a rapid acceleration of growth, but do not become fully clonal, perhaps not sufficiently fit to outcompete the rest of the population. The recent expansion of spatial transcriptomics has...
Microbial communities display striking macroecological regularities in their temporal abundance fluctuations across very different biomes \cite{grilli2020}. In particular, previous studies reported that species abundances follow a gamma-like distribution, often interpreted as evidence of exogenous stochastic drivers such as environmental noise. In this work, we show \cite{arroyo2026} that...
Understanding how dispersal affects the total biomass of fragmented populations is a central problem in ecology. For the simplest metapopulation network, consisting of two patches, the continuous-time case with logistic local growth was completely described in \cite{gao2022}. In contrast, the analogous discrete-time problem has remained largely unresolved, with previous work describing only...
We develop a next-generation matrix (NGM) framework for evaluating venue access policies that restrict or test attendees based on vaccination status. As both vaccination coverage and contact structures are age-dependent, contact structures at venues will change due to access policies \cite{bootsma2024heterogeneity}. To isolate the effect of selectively excluding unvaccinated individuals from...
An essential step of any modelling effort is to decide which parts of a system should be represented. This decision is implicitly influenced by the experimental questions we ask and hypotheses we make, which in turn determine which aspects of a system are relevant to include in a model. Less explored however is how the choice of modelling formalism itself influences what gets to be...
The innate immune system represents the first line of defence against pathogens. In organisms such as Drosophila it represents the only line of defence. Understanding the organization and working of this innate immune system and the way it counteracts a variety of pathogens can provide a basis for a deeper understanding of the immune system function and associated design...
Insomnia is one of the most prevalent sleep disorders, associated with increased risk of conditions ranging from diabetes to heart disease \cite{b23}. Yet, much about its physiological causes and processes is still far from understood.
Mathematical modelling has had an important role to play in understanding the process of sleep itself. Some of the most important of these contributions have...
Advances in multiregion sequencing have revealed extensive intratumor heterogeneity (ITH) - the presence of genetically distinct subclones within a single tumor. ITH profoundly influences tumor behavior, including well-accepted hallmarks of cancer such as sustained proliferation, resistance to apoptosis, and immune evasion, and the emergence of therapeutic resistance. In this work, we...
Multiple myeloma is a hematological malignancy that primarily impacts older individuals. Despite this, preclinical models often use younger animals that do not accurately represent the aged bone microenvironment in which the disease flourishes. Aging in the bone microenvironment is characterized by changes in bone structure, altered remodeling mechanisms, and increased cellular senescence....
Model-based design advances bioprocess development \cite{FBDURL, FBD2025}, yet multi-stage continuous microbial processes remain empirically designed due to poor system-level understanding. Here, we introduce a systems-level, physiology-based framework for analyzing multi-stage continuous bioprocesses, enabling early-stage screening with minimal experimental effort.
Starting from mass...
Pulsed field ablation (PFA) is a novel cardiac ablation technology based on irreversible electroporation that has revolutionized the arrhythmia treatment. Despite its wide use, computational models are still unable to accurately capture the experimentally observed range of width-to-depth anisotropy ratio of the resulting lesions. This work enhances the porcine open-chest computational model we...
Understanding the role of schools in SARS-CoV-2 transmission is essential for designing effective public health policies. We developed a stochastic age-stratified transmission model, fitted to epidemiological and contact survey data, to evaluate how alternative school closure and reopening strategies could have shaped the COVID-19 pandemic in the Netherlands from early 2020 to late 2021. Using...
Ribosome profiling provides codon-resolution snapshots of translation, but quantitative interpretation requires accurate forward models of ribosome traffic. We revisit mRNA translation stalling by comparing the widely used mean-field Ribosome Flow Model (RFM) with a deterministic discrete-particle TASEP formulation. We found that mean-field factorization can produce artifacts, including...
Household-level vaccine uptake patterns are known to have serious impacts on infectious disease dynamics, with clusters of susceptibility in low-uptake households driving global transmission and potentially leading to inequitable burdens of disease\cite{geard_effects_2015}. Anticipating these uptake patterns could improve the design of vaccine rollout campaigns, but they remain poorly...
Artificial insemination (AI) is widely used to improve the genetic quality and productivity of water buffalo in the Philippines through the nationwide program of the Department of AgricultureโPhilippine Carabao Center (DA-PCC). Despite ongoing efforts, calf production remains low and inconsistent across regions. This study analyzes five years of AI service data comprising 278,978 records from...
Despite the widespread availability of effective vaccines, pertussis remains a significant public health concern in many high-income countries, particularly because of its severe impact on infants. In recent decades, several regions have experienced a resurgence of pertussis, with recurrent outbreaks and an overall increase in incidence \cite{yeung2017update}. These patterns highlight the need...
Gene regulatory networks (GRNs) underpin many of the most important processes in cellular biology โ including cell fate, patterning and adaptation. Whilst the biological realism of GRN models has improved in recent years, there has been little consideration of cell cycle effects on the dynamics of these models. For the classic, bistable toggle switch, we find that the inclusion of cell growth...
Atherosclerosis is a disease driven by cholesterol accumulation within the arterial wall and involving coupled interactions between lipid transport and inflammation. Despite being a leading cause of cardiovascular disease, the spatial and stochastic mechanisms underlying plaque formation remain incompletely understood. To address this, we developed a hybrid continuum-discrete model of...
The recent mpox outbreak in the Democratic Republic of the Congo (DRC) has been marked by substantial transmission among childrenโparticularly those under 15 yearsโand adults with elevated occupational risks, including healthcare workers, sex workers, and hunters. Motivated by emerging evidence that vaccination alone may not fully explain the observed decline in mpox transmission in the DRC,...
The Cellular Potts Model (CPM) is a cell-based model that provides a stochastic, energy minimisation based approach for modelling collective cell behaviour and tissue organisation. Currently, the CPM is defined over a fixed 2D lattice, restricting applicability to tissues that evolve on static planar domains. However, many epithelial and endothelial cell populations reside on curved and...
Organoids are experimental model systems of organ development and function. They have recently gained considerable attention, as they provide insight into processes regulating development and regeneration in different tissues, and allow testing of treatment strategies for various pathogenic conditions. Pancreatic and liver-derived organoids in 3D culture display diverse dynamic behaviors. They...
Reward-based learning relies on a systemโs ability to distinguish between environmental signals across space or time. However, biological reinforcement systems do not always operate under such idealized conditions. In particular, dopamine reward signals are often broadly distributed rather than spatially localized, while environmental stimuli frequently overlap in time in realistic settings....
Yaws is a neglected tropical disease that is one of very few infections that are targeted by the WHO. It is a bacterial infection causing lesions in the skin, and can be treated by a single oral dose of azithromycin. However, the presence of an asymptomatic reservoir, cross-reactivity of serological tests with syphilis and low investment all present challenges for eradication. To date, there...
Fluid transport through brain tissue is important for removing harmful metabolic waste. Experiments on rodents indicate the presence of an active waste efflux system that transports harmful solutes by diffusion and advection. In humans, the existence of this system is still debated. The effective diffusivity within human brain tissue has been estimated using contrast-enhanced magnetic...
Quantitative systems pharmacology (QSP) models are increasingly used to inform dose scheduling in oncology. Standard tumour growth inhibition models typically combine empirical growth laws with drug action functions. Recent work suggests that non-uniform dosing regimens may outperform uniform dosing regimens.
Here we present a systematic evaluation of how modelling choices on growth law...
Colorectal cancer (CRC) is the worldโs third most common malignancy, and patients with the microsatellite instabilityโhigh/mismatch repairโdeficient (MSI-H/dMMR) phenotype respond poorly to conventional chemotherapy yet show striking responsiveness to immune checkpoint inhibitors such as pembrolizumab. Mathematical models based on ordinary differential equations (ODEs) provide a powerful...
Endothelial cells organise within developing tissues to form a vascular network which remodels and matures over time. The mechanisms underlying network formation can be studied experimentally through the tube formation assay, and computationally using Cellular Potts Models or Partial Differential Equations. Such models offer a means to investigate proposed mechanisms which may drive...
Vertical transmission of an infectious disease from parent to offspring is a common transmission route in many systems. Here we explore the role of vertical transmission within a host-parasite system, with a particular focus on how spatial structure effects vertical transmission. We introduce a host-parasite lattice model with a pair approximation that includes both local and global...
Cells are embedded in spatial tissues. This context shapes cell-fate decision, global tissue structures, and, ultimately, the development of multi-cellular systems. One of the pivotal questions is the extent to which coherent tissue structures arise from the interplay between intra- and intercellular signalling and regulatory projects. Here we highlight how spatial context can lead to a...
Mitochondrial networks range from fragmented to hyperfused, spatially organised to meet energetic and signalling demands \cite{Chen2023}. Cycles of fission, fusion, biogenesis, mitophagy, and motility (termed mitochondrial dynamics) underpin the capacity for homeostasis and quality control, yet mechanistic frameworks interrogating these emergent properties are scarce...
Closed-loop auditory stimulation (CLAS) is a promising non-invasive technique for modulating brain oscillations by delivering auditory stimuli phase-locked to ongoing neural activity. Recent work applying CLAS to theta (4.5 โ 7.5 Hz) and alpha (7.5 โ 12.5 Hz) oscillations during REM sleep has demonstrated phase-dependent changes in EEG power and frequency \cite{jaramillo_closed-loop_2024}. It...
There are many instances in cell biology, and in cell signalling in particular where non-monotonic dose responses are encountered, and these have important biological and physiological implications. In this presentation we dissect biphasic responses at the basic biochemical level, at the network level and in concrete cell signalling systems. At the basic biochemical level we explore a variety...
The Ebola virus matrix protein VP40 oligomerizes at the plasma membrane inner leaflet to drive virus-like particle (VLP) formation in mammalian cells, a process dependent on the membrane lipid phosphatidylserine (PS). We previously developed an ODE model of VP40 oligomerization that provided evidence for a nucleation-elongation mechanism and explicitly incorporated the VP40โPS relationship...
Differential contributions to transmission across age groups have been reported for many respiratory infections, including SARS-CoV-2. They are crucial for estimating the impact of age-specific interventions, but disentangling these age-dependent contributions remains challenging.
We developed a Bayesian method to jointly estimate age-specific per-contact infectiousness and susceptibility...
Many biological datasets can be represented as point clouds, such as cell centres in spatial proteomics or transcriptomics imaging. These can be analysed using diverse specialised spatial metrics \cite{Bull2025MuSpAn}. One important property of a point cloud is the presence of topological features - connected components, loops, or voids. Topological Data Analysis (TDA), and in particular...
Recovery from acute infectious diseases can establish a hostโs cross-resistance to other infectious diseases or other strains of the same disease. Unlike many other ecological contexts, diseases such as rhinovirus can offer very high diversity (of strains) in the same local community over long periods of time. In addition to high diversity, rhinovirus has complex patterns of temporary...
The spread of infectious diseases is fundamentally shaped by who contacts whom, when, and for how long. Contact networks capture the population-level structure of these interactions, yet explicitly recorded networks are rarely available, forcing outbreak models to rely on simplifying assumptions. Understanding how interpersonal contact patterns vary across contexts could meaningfully improve...
Resource competition within the tumour microenvironment is a key driver of cancer progression. In this talk, we present a non-local mathematical model to investigate how interactions between M1/M2 macrophages and tumour cells influence tissue invasion.
We demonstrate that the existence and stability of tumour-free versus tumour-present steady states are strictly governed by these...
Vector-borne diseases are infections transmitted between two interacting biological populations: a host, such as birds, and a vector, typically mosquitoes. The dynamics of these types of diseases can be linked to seasonal fluctuations, which in turn influence the spatial spread of the infection.
To this end, following Lewis et al.~\cite{Lewis_2006}, we couple an SIS model for the host...
Biological reactionโdiffusion systems are inherently multiscale, with particle copy numbers varying substantially across the spatial domain. In regions of low concentration, discrete stochastic methods capture noise-driven fluctuations that may critically influence dynamics. In regions of high concentration, continuum PDE models provide an efficient description. Simulating such systems...
Over 75% of cancer patients receive chemo- and/or radiation therapy, but treatment schedules are not optimized for the individual patient. Optimized schedules may lead to improved outcomes. We aim to (1) collect confluence time courses for glioma cells treated over a wide range of chemo- and radiation therapy schedules, (2) calibrate a biology-based math model to the data, and (3) apply...
The functional response describes how a predatorโs consumption rate varies with prey density. There are three types of Holling functional responses: Type I (linear), Type II (hyperbolic), and Type III (sigmoidal). Although many predator-prey models adopt a Type II response for analytical convenience, this choice is more appropriate for specialist predators. In contrast, generalist predators...
In this work, an age-stratified SEIR epidemiological model incorporating a saturated treatment function and heterogeneous
contact rates is developed to study infectious disease transmission dynamics among various age groups. The expression for the basic reproduction number R_0 and conditions for the global stability of the system have been derived by a graph-theoretic (GT) approach. Digraph...
Understanding and accurately describing cell proliferation is a crucial step toward realistic modelling of cancer invasion and progression. We propose a framework for parameter estimation and validation of tissue growth models describing the dynamics of proliferating cell colonies \cite{AMC2026}. By confronting model simulations with experimental data, we assess the ability of these models to...
Virulence management, which studies the evolution of pathogen virulence (i.e., pathogen-induced mortality), shows that when vaccination reduces susceptible host density, selection may favor lower virulence. However, most studies assume fixed host behavior: a constant fraction of the population vaccinates throughout an epidemic. In reality, vaccination behavior is dynamic and shaped by social,...
Cellular signaling networks generate dynamic responses that regulate how cells respond to external stimuli, perturbations or drugs. These responses can result in changes of cell fate, for examples, transitions from apoptosis to survival or from quiescence to proliferation. Mathematical modeling combined with targeted experimentation have successfully elucidated the underlying mechanisms and...
Traditional mathematical models for tumour growth are built upon simple assumptions regarding tumour-intrinsic population dynamics, including logistic growth, diffusion volumetric scaling. With progresses in experimental cancer research combined with advanced phenotyping, insights have been gained into how microenvironmental factors shape tumour growth. This motivated the development of more...
ReactionโdiffusionโODE systems arise in models of biological pattern formation, for example in symmetry breaking during regeneration in Hydra. These systems couple diffusive and non-diffusive nonlinear processes. In contrast to classical reactionโdiffusion systems, such models may exhibit patterns with singularities, including jump discontinuities, which complicate the analysis of nonlinear...
When cancer develops, the cells can present unique proteins called neoantigens. A promising immunotherapy technique uses neoantigen cancer vaccines to activate T-cells to attack tumor cells which present these neoantigens. In this project, we model neoantigen cancer vaccine treatment of a primary tumor and the resulting effects on metastatic emission. We use a system of ordinary differential...
The growth rate of a bacterial population is a fundamental quantity in microbiology, but we lack the tools to predict it for realistic mathematical models. Based on an emerging connection between branching processes and statistical physics, I present a new method to compute growth rates numerically in virtual "chemostats". These provide accurate estimates of growth rates and evolutionary...
In metabolomics, a fundamental question is how the potential number of molecular homologues (congeners) increases with their size. Here, we show that the number of unbranched fatty acids and unbranched aliphatic amino acids grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected and adjacent double bonds are excluded \cite{schuster2017,fichtner2017}. This number...
Bright light soon after waking or blue-blocking glasses in the evening are standard therapies for sleep timing problems. These approaches are grounded in circadian principles which have established that the effect of light depends on the time of the biological clock with light in the biological morning speeding up the biological clock, and light in the biological morning slowing down the...
Despite decades of efforts to control mosquito-borne diseases, the global burden of these diseases remains high due to their complex biological and immunological dynamics. While extensive research has focused on vector-host or between-host transmissions, the within-vector mechanisms remain poorly understood. This gap is critical to fill because mosquitoes have relatively short lifespans, and...
In the wake of the SARS-CoV-2 pandemic, there has been increased interest in mathematical tools that can anticipate changes in infectious disease dynamics from surveillance data. Early warning signals based on critical slowing down have been widely proposed as indicators of tipping points such as disease elimination or resurgence. However, many epidemiological systems are non-stationary and...
In seasonal agroecosystems, diseases persist through both horizontal transmission during the growing season and vertical transmission via farmer-saved seeds. To break this cycle, growers can purchase and plant disease-free seeds, so called clean seeds. Their choice is then between getting such seeds or reusing cost-free, potentially infected farmer seeds. We investigate the combined dynamics...
Hematopoiesis is the process by which blood and immune cells are formed. During fetal development, hematopoietic stem cells emerge from intra-embryonic aortic hemogenic endothelium (HE). We hypothesize that fetal hematopoietic stem cells (HSCs) and multipotent progenitors (MPPs) arise separately from HE, and that fetal MPPs contribute independently to postnatal blood production. However, the...
Inadequate nutrition, driven by the unaffordability of a healthy diet in low and middle-income countries, is a major barrier to achieve the WHO's End Tuberculosis (TB) strategy. To address this issue, the authors have developed a compartmental model by incorporating transmission rate ฮฒฬ(M), recovery rate ฮณฬ(N), and TB-related mortality rate ฮผฬtb(N), as functions of income and nutrition levels....
Continuous glucose monitoring is critical for diabetes management. Hydrogel-based microneedle glucose biosensors have recently emerged as a promising approach for minimally invasive, real-time monitoring by sampling interstitial fluid in the upper skin layers. Because microneedles penetrate only shallow tissue depths, the measured signal reflects a spatially dependent proxy of vascular glucose...
Mean first passage time is a fundamental quantity for characterizing search and encounter processes, since it measures the expected time required for a moving agent to first reach a target. In the context of immune cell dynamics, this provides a natural way to connect cell motility to functional outcomes such as target finding and cytotoxic efficiency. For natural killer cells and other immune...
More than 50% of cancer patients undergo radiotherapy. Nowadays, treatment plannings are based on the linear-quadratic model, that predicts the survival fraction of cancer cells but does not include any temporal component. Moreover, it is usually not valide for large doses (that are used in new radiotherapy modalities such as mini-beam). It is therefore of the utmost importance to develop...
Prisons present a unique environment for the spread of infectious diseases such as influenza, tuberculosis, and SARS-CoV-2, as prison residents are generally confined in close proximity of each other, with regulated movements and interaction with staff often physical in nature. Although logistically difficult to manage, non-pharmaceutical interventions have been used during the COVID-19...
The pregnane X receptor (PXR) is a ligand-activated transcription factor that is highly concentrated in the liver. It is considered a crucial sensor in the xenobiotic response. PXR regulates the transcription of genes involved in drug metabolism, including cytochrome P450 (CYP) enzymes such as CYP3A4, CYP2C9, and CYP2B6. For example, CYP3A4 metabolizes approximately half of all clinically used...
Pharmacology and toxicology studies often use compartmental ordinary differential equation (ODE) mathematical models to understand how a chemical compound distributes and exerts its effects throughout the body. Such models require experimental data to inform parameterisation. However, such data is often costly and not always available and thus we need to identify new ways to parameterise such...
Tumors exhibit phenotypic heterogeneity in proliferation rates, affecting growth, therapy response, and relapse risk. Faster-proliferating cells dominate untreated growth but face fitness costs like increased susceptibility to DNA damage or metabolic stress. Proliferation capacity is a core tumor characteristic, and capturing its heterogeneity is key to understanding tumor evolution and...
Human papillomavirus (HPV) is a major cause of cervical cancer and several other malignancies, posing an important public health challenge in Japan. Following the suspension of proactive HPV vaccination recommendations in 2013, vaccination coverage dropped sharply, raising concerns about future increases in HPV-related disease burden. To evaluate effective prevention strategies, we developed...
Microinvasions in ductal carcinoma in situ (DCIS) of breast cancer arise when malignant cells breach the basement membrane (BM) and invade the stroma. Since this is an early step in metastasis, identifying drivers of microinvasion may improve risk prediction and support treatment de-escalation. Mechanical tumorโstroma interactions, including extracellular matrix (ECM) collagen stiffening and...
Epidemiological models are often expressed through systems of differential equations of varying levels of complexity. In multi-strain models, complexity arises from the interaction of different serotypes as a result of cross-reactivity with the host's immune system. This study proposes a novel framework for representing multi-strain disease transmission models, with some mapping of sets and...
Cancer affects a countless number of lives across the world each day, and mathematical oncology offers a tool to simulate cancer and potentially improve its treatment. One of the current challenges is the development of resistant populations in response to treatment. In this talk, we present an agent-based model for treatment-resistant prostate cancer, with the aim of gaining insights into...
Cellular differentiation is the biological process that leads a cell to opt for a particular cellular identity. Recently, single-cell RNA-sequencing has enabled the simultaneous measurement of gene expression levels at specific times for a large number of individual cells and a large number of genes. Repeating such measurements at different time points gives then access to the temporal...
Gonorrhoea is a sexually transmitted infection caused by the bacterium Neisseria gonorrhoeae. Although there is no specific vaccine against N. gonorrhoeae, the 4CMenB vaccine targeted to N. meningitidis, the bacterium (of the same genus) that causes meningitis, has been shown to be 30-40% effective in preventing gonorrhoea infection and since August 2025 is offered in the UK to those at...
The use of antiviral drugs to treat SARS-CoV-2 infection has been widely extended and several antiviral treatments have been tested, involving different modes of action (MOAs). These drugs may be either newly developed treatments or repurposed drugs and, though a positive effect may be observed from the application of these treatments, it may not always be clear what is the driving mechanism...
Severe fever with thrombocytopenia syndrome (SFTS) is a tick-borne viral disease primarily reported in East Asia. In the Republic of Korea, the disease burden is concentrated among older adults, who experience higher incidence and case fatality rates. Meanwhile, Korea is undergoing demographic aging alongside environmental changes associated with climate change. These shifts raise important...
We propose and analyze a model for antibiotic resistance transfer in a bacterial biofilm and examine antibiotic dosing strategies that are effective in bacterial elimination. In particular, we consider a 1-D model of a biofilm with susceptible, persistor and resistant bacteria. Resistance can be transferred to the susceptible bacteria via horizontal gene transfer (HGT), specifically via...
Infectious disease models are common at both the cellular scale to describe invasion probabilities and the tissue scale to describe pathogen replication dynamics once an infection has been established. We develop Bayesian methods that link the infection establishment with mechanistic target cell ODE models of viral replication. First, given longitudinal measurements of hostsโ viral load, we...
Spatial biological networks derived from microscopy are commonly represented as embedded graphs whose topology reflects underlying organisation. Subtle precursor events often precede visible structural reorganisation: for example, branch migration preceding mitochondrial fission, local neurite remodelling in dendritic arbors, or early junction displacement in microvascular networks. Detecting...
Schistosomiasis is driven by complex transmission dynamics influenced by human behaviour and environmental factors. While existing individual-based models (IBMs) have advanced our understanding of the disease, they often lack a spatial component, limiting their ability to inform geographically targeted interventions. In this work, we present a spatially explicit IBM to better simulate the...
Classical mean-field models of cell population dynamics, including cancer progression, often rely on the "well-mixed" assumption and neglect the role of cell death. In this work, we demonstrate how these simplifications lead to a significant overestimation of growth rates and saturation levels, with critical implications for tumor therapy design.
First, we present a stochastic modeling...
Inferring signed and directed interaction structure from multivariate time-series data is a central problem in regulatory network reconstruction and dynamical systems biology. Albeit many biological systems are modeled as $\dot{x}=f(x)$, identifying the structural architecture underlying $f$ from observational data remains challenging: equation fitting requires strong parametric assumptions,...
Quantitative estimates of fitness, particularly of individual genetic mutations, are crucial to predict the evolutionary dynamics of biological systems. Estimating fitness is challenging due to linkage disequilibrium of mutations on the same genome as well as clonal interference between competing genotypes. We estimate the fitness effects of individual mutations that are observed in a...
Understanding the transmission dynamics of infectious diseases within households is crucial for informing and improving public health interventions, but household-level transmission patterns are typically difficult to identify from data. This study presents a likelihood-based inference method which infers epidemiological parameters governing household-level transmission pathways from...
Ordinary differential equation models of biological systems are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a...
Individuals adapt to epidemics, creating a feedback loop between disease spread and human behavior. Incorporating this dynamic into infectious disease models is critical for evaluating interventions against future pandemic threats. We embedded an XGBoost algorithm, trained on real-world survey data (Imperial College London YouGov COVID-19 Behavior Tracker; Netherlands, Jun 2020โJan 2021;...
Chronic Obstructive Pulmonary Disease (COPD) is a highly prevalent lung disease characterized by alveolar wall damage, leading to progressive loss of lung function\cite{1}. Lymphangioleimyostasis (LAM), a rare respiratory disease, is also characterised by lung tissue destruction, but also by the growth of abnormal smooth muscle-like cells\cite{2}. The interactions between injury and abnormal...
The epidemic dynamics of West Nile Virus in Northern Italy (where it has been endemic since 2012) has been analysed in several studies, from modelling studies elucidating the main factors allowing for its persistence \cite{Marini2020,DeNardi2025}, to genetic and epidemiological analysis identifying the most likely transmission routes \cite{Mencattelli2023,Gobbo2025}. Here, we extend the...
The efficacy of CAR-T cell treatment is heavily impacted by low levels of oxygen (hypoxia) in solid tumors. However, CAR-T cells with different affinities show distinct behavior and functionality in hypoxic areas. Thus, we could optimize the composition of CAR-T cells cocktails of different affinities to maximize their efficacy in the heterogeneous microenvironment of melanoma. To do so, we...
Treatment of urinary tract infections (UTIs) and the prevention of their recurrence is a pressing global health problem. In a UTI, pathogenic bacteria not only reside in the bladder lumen but also attach to and invade the bladder tissue. Planktonic, attached, and intracellular bacteria face different selection pressures from physiological processes such as micturition, immune response, and...
Nano-engineered particles are a promising tool for medical diagnostics, biomedical imaging and targeted drug delivery. Fundamental to the assessment of particle performance are in vitro particleโcell interaction experiments. These experiments can be summarized with key parameters that facilitate objective comparisons across various cell and particle pairs, such as the particleโcell association...
Glioblastoma is characterized by spatial heterogeneity and severe hypoxia, which shape the immune response and contribute to poor therapeutic outcomes \cite{Bayona2026}. In this work, we reproduce a multiscale tumorโimmune model \cite{Gong2017} and develop an agent-based model with PhysiCell \cite{Ghaffarizadeh2018} that captures key biological features driving glioblastoma progression.
The...
Fireblight is a bacterial disease of apple and pear trees that can wipe out an entire orchard in a single growing season. We formulate a mathematical model for the spread of this disease during bloom. The resulting model consists of a system of two semilinear PDEs for the pathogen, coupled to three ODEs describing the infection dynamics. Numerical simulations suggest the existence of...
Type 1 diabetes (T1D) is an autoimmune disease in which the immune system attacks pancreatic beta cells, leading to high blood glucose levels and requiring lifelong insulin therapy. There is no cure, and individuals with T1D may face a reduced lifespan of up to 12 years. Defects in regulatory T cells (Tregs) are a key contributor to disease onset and are being explored as a therapeutic avenue....
Drosophila suzukii is a fruit fly species native to South-East Asia that has become a major invasive pest in Europe and North America. Thanks to its serrated ovipositor, which allows it to lay eggs in healthy fruit, it causes significant damage to several soft fruit crops such as strawberries, blueberries, and cherries. As pesticide use alone is environmentally costly and increasingly...
Respiratory syncytial virus (RSV) is a leading cause of hospitalization among infants. An infantโs birth month relative to the RSV season is an important determinant of hospitalization risk, with infants born shortly before peak seasonal activity often experiencing the highest burden. Although existing epidemiological studies largely describe these patterns, mechanistic evaluation of how birth...
Cholera remains a global threat, as highlighted by the 2010 Haiti outbreak, where poor sanitation led to severe exposure. With limited vaccines and treatments, control efforts rely on awareness campaigns and sanitation to promote preventive behavior.
We developed a cholera transmission model incorporating public awareness and behavioral responses. Stability was analyzed using the basic...
Phase-field models provide a fundamental continuum framework for describing phase separation and pattern formation in many physical and biological systems. Their predictive capability depends critically on constitutive quantities such as the bulk free-energy density and interfacial thickness parameter, which are often unknown and must be inferred from limited observations. In this work, we...
We develop and analyze a temperature-driven, stage-structured model for the transmission of Borrelia burgdorferi (Lyme disease) involving the tick vector Ixodes scapularis and multiple host classes. The model is formulated as a system of nonlinear ordinary differential equations incorporating seasonal forcing, life-stage transitions, and host-dependent feeding dynamics.
We compare two...
Understanding glioblastoma resistance and recurrence remains a primary challenge in oncology. PDE models remain critical tools in the study of their underlying biology \cite{A2019}. In this study, we model a glioblastoma cell population, analyzing the distribution of resistance levels across the population under various treatment levels. Specifically, we investigate the "convection factor,"...
Throughout the SARS-CoV-2 pandemic, healthcare workers (HCWs) played a critical role in the response and faced elevated risk of infection. This work investigates the transmission and interaction between the general community and HCWs, aiming to understand how COVID-19 transmission flows between these two populations.
The COVID-19 Infection Survey run by the Office of National Statistics,...
Genetic data sampled from human populations are high-dimensional and complex. Many tools have been developed to analyze such data; however, these methods often require specifying a pre-determined number of ancestral populations, may not scale efficiently to large datasets, or rely on model assumptions about processes such as migration and population bottlenecks. Here, we investigate whether...
Neuroblastomas are solid tumors and represent the most common extracranial tumors in children. The analysis of tumoroid data (artificial organoids capable of reproducing neuroblastoma growth) has revealed a distinctive spatial organization: cancer stem cells tend to cluster at the center of the tumor. A multiscale agent-based neuroblastoma tumoroid model was developed to simulate neuroblastoma...
We study the dynamics of a three-trophic level food web model representing a
wasp-waist marine ecosystem, where a single or multiple intermediate consumers
mediate energy flow between primary producers and apex predators. Using a
system of nonlinear ordinary differential equations with ratio-dependent func-
tional responses, we investigate conditions under which the consumer...
Rising dietary and drinking-water intake of nitrate (NO$_3^-$) and nitrite (NO$_2^-$) poses a significant public health concern. After ingestion, NO$_3^-$ enters the enterosalivary circulation, where oral bacteria reduce it to NO$_2^-$. When swallowed, NO$_2^-$ enters the acidic gastric environment, where it can react to form N-nitroso compounds (NOCs), many of which are suspected carcinogens....
Cells sense and respond to their local environment through an integrated network of subcellular structures that convert mechanical and biochemical cues into coordinated biological responses. Understanding how these components interact to regulate cellular mechanosensing and signalling is central to controlling cell behaviour, with applications in tissue engineering and regenerative medicine....
DNA replication duplicates the genome before cell division, and its faithful completion is essential for genome stability. Failures in this process generate replication stress, a hallmark of cancer, but also a therapeutic opportunity, since drugs that further perturb replication can push tumour cells beyond tolerable limits \cite{jones2025high}. Understanding these effects remains difficult,...
The aim of this work is to introduce a new class of immuno-epidemiological models for infectious diseases and to investigate some of its mathematical properties. The proposed framework couples two dynamical subsystems operating at different biological scales: a within-host model describing viral and immunological kinetics, and a between-host model governing population-level transmission. The...
Cell polarity, specifically apico-basal polarity, is defined by the asymmetry of internal cell proteins and structures between the basolateral region of the cell, the region in contact with the basal membrane and cell neighbours, and the apical region, which faces the lumen. The establishment and robust maintenance of apico-basal polarity in epithelial cells is critical to healthy function of...
Recent advances in experimental biology provide time-resolved datasets that capture key features of complex dynamical systems. Recovering the underlying interactions from such data is a nontrivial inverse problem, especially when one must disentangle deterministic dynamics, intrinsic fluctuations, and measurement noise from limited observations.
We build on the inference framework...
Fractional-order compartmental models have been increasingly adopted in pharmacokinetics to capture anomalous drug diffusion, memory effects, and non-exponential elimination patterns that classical integer-order models cannot adequately describe. However, the numerical treatment of these models remains challenging because of nonlocal operators, memory dependence, and mass-balance...
Ovarian follicle development is commonly described either by compartmental models, in which each developmental stage is represented by a discrete compartment (e.g. \cite{Hendrix2014}), or by physiologically structured population models (PSPMs), formulated as transport PDEs, where each follicle is treated as a cell population distributed along a continuous maturation variable (e.g....
Abstract: 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...
In mammalian fat cells, insulin regulates glucose uptake by controlling the trafficking of the glucose transporter GLUT4 between intracellular compartments and the plasma membrane. Under basal conditions, GLUT4 is largely sequestered in slowly cycling pools, but insulin stimulates its mobilisation, exocytosis, and cycling, with rapid re-sequestration following insulin withdrawal....
Toivonen and Fromhage (2018) proposed a competition model between size-based and age-based populations to study the evolution of periodicity in periodical cicadas. They demonstrated that the effect of predator satiation triggers the replacement of a size-based population by an age-based one, even when the former possesses a higher reproductive number. This suggests that the perfect periodicity...
Evolvabilityโthe capacity of a population to generate heritable phenotypic variationโplays a central role in adaptation, yet its evolutionary dynamics are not fully understood. In this work, we investigate how evolvability, treated as a continuous phenotypic trait, shapes the adaptation of asexual populations. To this end, we develop ad hoc discrete and continuum mathematical models describing...
We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in discrete time extinction and revival events. The dynamics are generated by a random elliptic community matrix with tunable correlation strength. We show...
We study the random times between successive cases in a transmission chain, of infectious diseases with asymptomatic carriers. We derive the probability distribution of this generation time (in days) from a discrete-time epidemic model with variable infectiousness both along elapsed times and across phases. The introduced non-Markovian model is a recursive system featuring random waiting times...
Differences in population growth rates between ancestors and mutants in increasingly stressful environments are often attributed to one group of individuals (ancestor or mutant) being more vulnerable to the stressful environment than the other. However, modelling the behaviour of these groups with the assumption of there being more than one phenotype in a particular group (in this case the...
CD8โบ T cells play a central role in anti-tumour immunity by eliminating cancer cells. However, sustained exposure to tumour antigens can drive them into a differentiation pathway culminating in a dysfunctional exhausted state, limiting immune control of cancer. This process emerges from collective inter- and intracellular interactions within complex immune signalling networks. Revealing the...
Angiogenesis is a hallmark of cancer wherein cancerous cells generate new vasculature to ensure that all cells continue to receive adequate nutrients as the tumour grows. Mathematical models exist for dynamics between tumour cells and vasculature, and a primary assumption in many of these models is that tumour carrying capacity is related to vasculature density \cite{H}. Although this is known...
Combination therapy can be an effective strategy to limit the evolution and spread of antibiotic resistance, a major challenge for patient treatment worldwide. The administration of multiple drugs during treatment increases the genetic barrier to resistance, as (in the absence of cross-resistance) the bacteria would need to evolve resistance against each drug separately. Yet the success of...
In this contribution, mathematical models describing the interaction between leukemic cells and CAR-T cells are developed and analyzed from the perspective of mathematical oncology. As a starting point, we consider the system of nonlinear ordinary differential equations proposed by \cite{PerezGarcia2021CART}, which describes the joint dynamics of CAR-T and tumor cells by incorporating...
Recent studies in political science have revealed a counterintuitive phenomenon: American partisans systemically underestimate the heterogeneity of opinions within each party. Yet, they correctly perceive each partyโs mean opinion. Since these studies were published, political scientists have speculated about the causes and effects of this phenomenon, but their results have remained vague due...
The epithelium is the tissue that separates us from the outside. Healthy epithelia are simultaneously plastic and robust, dynamically responding to changing environments without large or long-lasting deviations from a homeostatic set point. This fine balance is achieved through an exquisitely connected network of regulatory interactions between epithelial barrier function, immune response, and...
Cancer-associated fibroblasts (CAFs) are key components of the tumor microenvironment (TME) and exhibit highly heterogeneous phenotypes that can either promote or suppress tumor growth. Our previous ODE-based mathematical model quantitatively described the interactions among cancer cells, T cells, and CAFs, demonstrating that CAF composition critically determines treatment outcomes. The model...
Stochasticity plays an important role in all biological systems. The standard way to deal with stochasticity involves averaging over an ensemble of independent realizations. However, such mean statistics need not accurately reflect the typical outcomes in any finite sample unless the system satisfies the property of ergodicity, which guarantees that each trajectory will over time experience...
Cell migration is regulated by the ability of cells to sense their surroundings over distances of several cell diameters and adjust both their direction and speed accordingly. We study the stability of a kinetic model for cell migration \cite{loy_kinetic_2020} that incorporates such non-local sensing mechanisms. In the model, cell density is perceived through sensing kernels that may differ...
Defective interfering particles (DIPs) are considered promising antiviral agents because they can strongly inhibit viral infections \cite{1}. OP7, an influenza virus DIP with numerous point mutations, has demonstrated greater efficacy than other DIPs in animal models \cite{2,3}. However, the impact of OP7 on human cells that induce an innate immune response (IIR) has not yet been...
Mutual information is a theoretically grounded metric for quantifying information flow in cellular signaling pathways. However, its measurement requires characterization of the joint distribution of both input and output variables, which is data-intensive and often impractical, particularly when the input is high-dimensional, such as temporal trajectories of signaling molecules.
Here, we...
Evolution during range expansions shapes biological systems from microbial communities and tumours to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference and sweep to fixation. However, most theoretical investigations of range expansions have considered regimes in which selective sweeps are...
Periodic oscillations in Cyclin BโCdk1 activity function as the core timing mechanism that controls the onset of cell division. These oscillations emerge from a complex regulatory network of interacting proteins, creating a self-sustained biochemical oscillator that regulates mitotic progression. In spatially extended systems, such oscillatory behavior can propagate as waves that synchronize...
Background: Neural power spectra contain an aperiodic $\frac{1}{f^\alpha}$ background and superimposed oscillatory peaks, but conventional band-power metrics do not separate these contributions. The FOOOF (Fitting Oscillations & One-Over-F) algorithm \cite{1} provides a parametric decomposition of both components, enabling analysis of spectral features associated with distinct physiological...
Relapse in acute lymphoblastic leukemia (ALL) remains a clinical challenge, affecting ~15\% of pediatric patients despite effective therapies. Understanding the population dynamics underlying treatment response and resistance is central in mathematical oncology.
Within the LEUKODOMICS project, we develop a stochastic population framework to model leukemic cell dynamics under multi-drug...
Background: Real-world evidence on the clinical presentation and severity of mpox infections following vaccination with the MVA-BN vaccine remains limited.
Methods: We conducted a scoping review and meta-analysis of 45 studies published between 2022 and 2025 to epidemiologically characterise mpox breakthrough infections following MVA-BN vaccination.
Results: 17 studies provided suitably...
We construct a mathematical model of cancer dynamics with chemotherapeutic treatment, in the presence of bacteria that are capable of metabolizing the chemotherapeutic drug, hence sabotaging the therapy. We investigate the possibility of complementing the cancer treatment with antibiotic drugs, thus eradicating the bacteria or at least mitigating their negative impact on the prospects of...
Intratumoral heterogeneity in breast cancer is a major challenge for prognosis and treatment, yet the dynamical mechanisms underlying subtype transitions remain poorly understood. Using a gene regulatory network model calibrated with experimental data, we show that stochastic variability in NF-ฮบB can induce irreversible switching from HER2+ to TNBC states, providing a dynamical mechanism for...
Adipocytes serve as an energy reservoir for the body thanks to their capacity to store and release lipids by adapting their size. Under energy surplus conditions, adipocytes store excess calories in the form of triglycerides through lipogenesis \cite{li}. When existing cells reach storage capacity, new cells are recruited via pre-adipocyte differentiation \cite{horwitz}. During periods of...
Microbial communities play key roles in biotechnology, environmental systems, and human health. Understanding and predicting the dynamics of interacting microbial populations is essential for both advancing fundamental knowledge and enabling the rational design and optimization of these systems. Mechanistic models provide a powerful framework for this purpose, enabling hypothesis testing and...
Plant development and adaptation are highly dependent on cell morphology and growth. High turgor pressure in plants causes stress on the cell wall, followed by cell extension. In tip-growing cells, the localization of vesicles and cytoskeleton components has been well studied. However, there has been a lack of attention to the spatial profile of mechanical properties, specifically the cell...
Phagocytosis is a fundamental process of the immune system, yet the physical determinants that govern the engulfment of soft, deformable targets remain poorly understood. Existing theoretical models typically approximate targets as rigid particles, overlooking the fact that both immune cells and many biological targets undergo significant membrane deformation during contact. Here, we develop a...
Eco-epidemic systems offer a fundamental framework for examining the interaction between predatorโprey dynamics and infectious disease transmission. Motivated by the European rabbitโIberian lynx system, we extend the model in \cite{upadhyay2016wave} by incorporating a nonlinear predator-induced fear function that captures immediate behavioral responses and memory-driven carryover effects...
The current cancer treatment paradigm of administering a โmaximum tolerated doseโ to patients fails to account for the eco-evolutionary dynamics that drive disease relapse. Adaptive therapy has shown clinically encouraging results in controlling tumors by modeling patient-specific evolutionary dynamics, based on the premise that resistance comes at a cost and that sensitive cells can suppress...
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...
Biologically, metastatic spread refers to the process by which a primary tumour releases cancer cells into the bloodstream that eventually colonise new organs, thereby often acquiring genetic mutations. Metastases cause about 80\% of cancer-related deaths \cite{F19}, hence, predicting when and where metastases are likely to emerge, and identifying advantageous mutations presents an urgent...
Communication plays a fundamental role in collective behavior among social animals. In honeybees, waggle dances recruit nestmates to profitable food sources, allowing colonies to coordinate foraging effort. However, natural environments often contain multiple colonies competing for the same limited resources, raising the question of how recruitment communication adapts under inter-colony...
Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly heterogeneous. Clinical evidence suggests that the CD4:CD8 T cell ratio in CAR-T cell treatments influences therapeutic outcomes \cite{Galli2023}, but the quantitative roles of these subsets in shaping treatment dynamics are incompletely understood....
Molecular dynamics simulations have been remarkably effective for observing and analyzing structures and dynamics of proteins, with longer trajectories being computed every day. Still, often, relevant time scales are not observed. Adequately analyzing the generated trajectories can highlight the interesting areas within a protein such as mutation sites or allosteric hotspots, which might...
Advances in data collection and simulation-based inference now enable fitting complex individual-based models (IBMs) to rich, fine-grained observations of interacting systems. However, mere data fitting is not understanding: these methods do not clarify which model quantities are truly constrained by the data and which are fundamentally underdetermined. This is the problem of...
Tertiary lymphoid structures (TLSs) are inducible ectopic lymphoid structures that emerge under chronic inflammatory conditions, including in the kidneys of patients with autoimmune diseases, and are closely associated with poor renal outcomes. Recent studies have classified TLS development into three stages correlated with chronic kidney disease severity. However, the mechanisms governing TLS...
Glioblastoma (GBM) is a highly invasive brain tumour with a 5-year survival rate below 5%. The first step of treatment for GBM is surgery with the goal of removing the entire visible tumour. However, even when all the visible tumour is removed, it almost always recurs leading to the cancerโs poor prognosis. Margins between tumour tissue and healthy tissue can appear unclear during surgery. To...
The efficacy of Immune Checkpoint Inhibitors (ICIs) is frequently limited by adaptive immune resistance via the PD-1/PD-L1 pathway. While pairing ICIs with potent immunostimulants (such as NHS-muIL12) offers a strategy to overcome this, foundational mathematical models often struggle to capture complex preclinical behaviors, specifically non-monotonic tumor responses. In this talk, we...
Microfiltration is a widely used technology for water production and wastewater treatment. The major limitation associated with this process is the formation of fouling layers on membrane surfaces, primarily composed of organic matter such as bacteria and extracellular polymeric substances (EPS). The dynamics of these deposits leads to an increase in the hydraulic resistance and a consequent...
Abstract: Lyme disease, the most prevalent vector-borne disease in the United States, has been expanding across Maryland, with rising temperatures accelerating its spread. Transmission of Borrelia burgdorferi by Ixodes scapularis ticks is highly sensitive to climatic variables. This study develops a climate-driven epidemiological model to investigate the spatiotemporal dynamics of Lyme disease...
Functional magnetic resonance imaging (fMRI) provides insights into cognitive processes with significant clinical potential. However, delays in brain region communication and dynamic variations are often over-looked in functional network studies. In our \cite{CellSystems} paper we demonstrated that networks extracted from fMRI cross-correlation matrices considering time lags between signals...
A classic model of a cell fate transition, following on Waddington, treats distinct cell phenotypes as attractors emerging from the nonlinear dynamics of biochemical signaling pathways. Transitions between phenotypes are achieved by external modulation of the system, which produces bifurcations among the stable states and otherwise drives the system from one attractor to another. This talk...
Invasive species are spreading globally, threatening ecosystems, biodiversity, agriculture, and human health. When efforts to prevent the establishment of invasive species fail and eradication is not possible, containment becomes necessary to slow or stop the spread of established invaders. A major question is, therefore, how to allocate treatments across space and time to contain populations...
Breast cancer is a heterogeneous disease and remains as a leading cause of cancer-related deaths among women worldwide \cite{kashyap2022retracted}. Estrogen receptor-positive(ER+) breast cancer accounts for approximately 70\% of all diagnosed cases \cite{hanker2020overcoming}. The tumor microenvironment (TME) plays a pivotal role in modulating cancer progression and mediating therapeutic...
Dynamic positron emission tomography (dPET) enables the estimation of pharmacokinetic parameters from time-activity curves, providing quantitative information relevant to cancer theranostics \cite{T}. However, its clinical adoption remains limited, partly due to the lack of optimized acquisition protocols. Here, we optimize dPET acquisition using the theory of design of experiments applied to...
Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate, or population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete lineages that do not survive until the end of the experiment? In this talk, I will introduce a model-independent theoretical framework to address this issue....
The panzootic high pathogenicity avian influenza H5N1 2.3.4.4b (HPAI) has been circulating globally since 2021, causing wild bird and poultry mortality, alongside spillover into cattle and humans. As of early 2026, Australia remains free of HPAI, although it's arrival is possibly a matter of when, rather than if. The "HASTE project" has been developing decision tools and forecasting models to...
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes mixed-effects models widely applied in fields such as biology, pharmacokinetics, and sociology. In this work \cite{hagg26}, we propose a novel methodology...
Sprouting angiogenesis is the process by which new blood vessels form through the emergence of multicellular sprouts led by endothelial tip cells and followed by stalk cells. Tipโstalk selection is largely regulated by DeltaโNotch signalling, involving Notch receptors and the ligands Delta and Jagged. DeltaโNotch interactions can occur within the same cell (cis), leading to mutual degradation...
Several game-theoretic models such as oligopoly, war of attrition, and international trade, are inherently asymmetric (role dependent). However, in contrast to symmetric games (role independent), relatively limited research has been devoted to the evolutionary analysis of asymmetric games. Systematic attention to these games emerged over the last four to five decades.
For asymmetric games...
Yeast colonies exhibit a wide range of patterns and growth modes, making them a fruitful source of mathematical modelling problems. Our group aims to better understand yeast growth using agent-based, reactionโdiffusion, and continuum mechanical models, and collaborates with experimental yeast biologists based in Australia and the UK. Biofilms are a form of growth characterised by communities...
Robust perfect adaptation (RPA), whereby a consistent output level is maintained even after a disturbance, is a highly desired feature in biological systems. This property can be achieved at the population average level by combining the well-known antithetic integral feedback (AIF) loop into the target network. However, the AIF controller amplifies the noise of the output level, disrupting the...
We consider a previously developed qualitative model for the inflammatory response in atherosclerosis and extend it to account for time-dependent anti-oxidant and anti-inflammatory therapies. The model consists of a five-dimensional system of ordinary differential equations tracking the concentrations of LDL, free radicals, oxidized LDL, macrophages and cytokines. Drug actions are incorporated...
The osteocyte network is a spatial cellular network connected by dendritic cell protrusions whose structure is determined by the embedment of bone forming cells (osteoblasts) at the moving bone-forming surface. Network architecture is important for many bone functions, but little is known about how the network forms during bone growth. It has been suggested that osteoblast embedment may be...
Tuberculosis (TB) is an airborne disease caused by the pathogen Mycobacterium tuberculosis. In 2023, it returned to being the leading cause of death from an infectious agent globally, replacing COVID-19; in the nineteenth century, one in seven of all humans died of tuberculosis. More than 10 million people are diagnosed with TB every year. The majority of cases in adults occur in males...
Mathematical modelling is the primary tool to predict and control the evolution of complex natural and engineered systems. However, sometimes many different models might predict similar behavior. This might typically happen when the microscopic rules governing an observed phenomenon are not known, and one then has to rely on effective, empirical models.
In this talk, I will introduce an...
Proliferation rate is a central life-history trait linking ecological interactions and evolutionary changes. This talk reviews eco-evolutionary models in which reproduction rate explicitly evolves, generating feedback between ecological structure and trait dynamics that shapes community composition and diversity.
A generic interaction and agent-based model with a life-history trade-off is...
Collateral sensitivity, where resistance to one antibiotic induces increased sensitivity to another, has been proposed as a strategy to combat antimicrobial resistance. Predicting the evolutionary outcomes of sequential antibiotic exposure, however, remains a major challenge. In this work we develop a mathematical framework that integrates collateral sensitivity networks with switched...
Inter-cellular signaling through the Notch receptor plays a central role in a wide range of developmental and physiological processes. In many contexts, signalling-dependent feedback can drive cellular decisions contributing to the regulation of proliferation and differentiation and spatial pattern formation.
In addition to mediating inter-cellular signaling by trans-binding, Notch ligands...
Metastatic cells are often assumed to undergo epithelialโmesenchymal transition (EMT). However, recent studies suggest that, in several cases, malignant cells retain adhesive contacts. In addition, highly invasive cells have been observed to migrate superdiffusively. Here, the interplay between cellโcell adhesion and high motility is investigated using a simple cellular automaton model. The...
Olive Quick Decline Syndrome (OQDS), caused by the bacterium Xylella fastidiosa, is a vector-borne disease affecting olive groves across Europe, severely impacting areas of southern Italy. We consider an ODE model for the olive tree canopies, the vector insects, and the weeds. Under the assumption that the insects reproduce significantly faster than the trees and weeds, the model equations...
In this study, we consider a degenerate reaction-diffusion system that models the interactions among the prey, the predator, and the predator's natural enemy. A typical scenario of our model arises from the plant-insect-natural enemy interaction in agriculture, in which the prey is a plant species that lacks diffusion; meanwhile, the natural enemy not only eradicates the predator but also...
We introduce the so-called identical ancestor point axiom, a formalization (under the simplifying assumption that life does not go extinct) of Hennig's non-splitting criterion for species. This axiom states that for any organism in any species, either the species contains at most finitely many descendants of that organism, or else the species contains at most finitely many non-descendants of...
The apicomedial actomyosin network is crucial for generating mechanical forces in cells. Pulsatile, oscillatory behaviour of this contractile network occurs in multiple organisms and contexts, for example during mouse embryo compaction or xenopus neurulation. However, the emergence and control of such pulsed contractions are not fully understood. Here, we study pulsed contractions of larval...
Intraspecific trait variation (ITV) can be important for population performance in a variable and changing environment because individuals with different traits have different fitness consequences in different environments. Furthermore, individuals can potentially improve their fitness by interacting with their environment, for example, by performing niche choice and moving to a different...
Insects have acquired a variety of sensory receptors through coevolution with plants, which transmit floral cues such as scent, colour and shape. Recently discovered among this suite of arthropod senses is electroreception โ the ability to detect electric fields. This raises the question of whether plants also convey biologically relevant information electrically to nearby pollinators, and how...
Quantitative Systems Pharmacology (QSP) models are increasingly employed to generate virtual populations (VPop), particularly in the field of immuno-oncology (IO). These populations can be integrated into existing drug development frameworks to reduce the number of clinical trials, support the selection and validation of novel therapeutic targets, and optimize combination therapies....
Understanding how internal community structure shapes the course of epidemics remains a fundamental challenge in modeling real-world populations \cite{Kiss2017}. Standard metapopulation models often assume uniform mixing within communities, overlooking how internal heterogeneity affects global outcomes \cite{Davis2020}. Here, we develop a general framework for epidemic spreading in...
Cellular metabolism can be viewed as a compartmental reaction network constrained by stoichiometry, transport processes, and enzymatic capacities. Mitochondrial transporters couple mitochondrial and cytosolic metabolism, yet their impact on feasible flux states remains poorly understood. Mutations in succinate dehydrogenase (SDH), observed in several cancers and mitochondrial disorders, lead...
Administration time-of-day may modulate antitumor treatment efficacy both in preclinical and clinical studies, likely due to the circadian regulation of physiological processes (\cite{fey},\cite{levi}). However, appropriate biostatistical methods to analyze such periodic variables in clinical studies are lacking. This project aims to identify robust survival analysis methods integrating...
Oral contraceptive pills remain widely used for both birth control and the management of reproductive disorders. However, side effects such as thrombosis and myocardial infarction continue to raise concerns, even with current formulations. While formulation improvements persist, alignment of drug administration with circadian rhythms -- proven to enhance safety and efficacy in other drug...
Arthropods possess a variety of novel senses to acquire environmental and biotic cues, with recent research reveals the possibility for arthropods to detect and respond to naturally occurring electrical fields. In this talk, I will present a suite experiments and models that show the role that this electrical sense plays in the sensory life and ecology of terrestrial arthropods. Our latest...
Novel variant emergence during viral outbreaks, as in the COVID-19 pandemic, undermines vaccine effectiveness. When a variant emerges, policy advisors must decide whether to recommend continuing booster vaccination with the existing vaccine or delaying until a variant-adapted vaccine is available. We present a mathematical model for evaluating these strategies by quantifying severe outcomes...
Population dynamics are often observed as distributions of individuals with respect to structuring variables such as size or age. The associated inverse problem consists of inferring the underlying vital rates (recruitment/birth, growth, and death), which are typically complex, nonparametric functions due to limited prior knowledge.
Physics-Informed Neural Networks (PINNs) provide a natural...
The rate of de novo mutations varies across species and is predicted to be dependent on parameters such as population size, the average generation time, and how far the population is from the fitness peak. Mutations that modify the mutation rate itself often emerge in bacterial evolution experiments, either increasing or decreasing the mutation rate of ancestral lineages. Previous theoretical...
Inflammation is a physiological process aimed at protecting the organism from various external stimuli. It plays an important role in numerous diseases including viral infection, atherosclerosis, cancer, and neurodegenerative diseases. Although each type of inflammatory disease has its own characteristic stimuli, the inflammatory response mechanism is generic.
In this work, we present...
Epithelial-Mesenchymal Transition (EMT) is a central regulatory program in cancer progression that enables epithelial cells to acquire migratory and invasive capabilities. Rather than functioning as a simple binary switch, EMT often generates a spectrum of phenotypic states, including hybrid epithelial-mesenchymal phenotypes that contribute to tumor heterogeneity, collective migration, and...
The combination of chemoradiotherapy (CRT) and immune checkpoint inhibition (ICI) in unresectable stage III NSCLC yields markedly divergent outcomes depending on treatment sequencing: consolidation ICI following CRT confers significant survival benefits,ยน whereas concurrent administration fails to improve survival.ยฒ This paradox implicates radiation-induced remodeling of the tumor-immune...
Circular, megabase-size, episomal DNA termed extrachromosomal DNA (ecDNA) drive the evolution of about 20% of all tumours, promoting oncogene heterogeneity and therapy resistance \cite{A,B,C}. While recent studies have elucidated its role in driving cell-to-cell phenotypic variation, little remains known about if, or how, the genomic structure of ecDNA itself evolves during tumour evolution....
Studying the correlation between structure and function in brain networks has long been a central and compelling topic in neuroscience. The FlyWire project achieved a major milestone by completing a fully digitized brain map of Drosophila melanogaster \cite{Dorkenwald2024}. In this study, we analyzed a total of 125,330 three-dimensional neuron skeletons from intrinsic, afferent, and efferent...
A hallmark of colorectal cancer is the progressive deterioration of the colonic tissue architecture. Intestinal crypts โ tubular epithelial glands essential for homeostasis โ gradually lose their characteristic morphology and function due to uncontrolled cell proliferation and tissue invasion. Quantifying this disruption in biopsied samples is critical for both patient diagnosis and...
During gastrulation, an early stage of embryonic development, cell migration is crucial for the formation of germ layers that eventually develop into tissues and organs. We develop a continuum mechanical model of dual layer cell migration during gastrulation that includes intercalation of cells between the mesenchymal and epithelial cell layers. Approximate Bayesian computation with sequential...
Hepatitis C virus (HCV) is a blood-borne RNA virus that remains the major cause of liver-related morbidity worldwide. Following acute infection, outcomes vary drastically across individuals: some patients spontaneously clear the virus, while others develop chronic infection progressing to severe liver disease. This variation is known to be driven by the heterogeneities in host immunity, an...
Effective control of livestock diseases often produces a sub-critical phase โ outbreaks occur but die out before becoming epidemic โ in which standard epidemic models are poorly suited to characterising transmission dynamics. Foot-and-Mouth Disease (FMD) in India offers a clear example: national control programs have been in place and intensifying since 2012, yet the disease persists across...
The rapid expansion of remote and technology-mediated assessment during and after the COVID-19 period exposed serious challenges to academic integrity, particularly in contexts where students were left to self-regulate with limited institutional oversight. These challenges have been amplified by increasingly easy access to generative AI tools, through which answers to problem sets and even...
Oncolytic virotherapy uses engineered viruses to selectively infect and destroy tumour cells. Despite some clinical successes, the spatial dynamics governing viral spread in solid tumours remain poorly understood. The integration of agent-based models, continuum models and hybrid approaches has been particularly valuable for capturing the multi-scale and stochastic nature of this biological...
In this talk we discuss the influence of inertial effects on the formation and evolution of vegetation patterns on sloped arid terrains in different dynamical regimes. Analyses are carried out in a hyperbolic extension of the one-dimensional Klausmeier model [1], where autotoxicity effects are also considered. As the system moves away from the wave bifurcation threshold, two classes of...
We propose a novel approach for model reduction in kinetic models of mass-action chemical reaction networks (CRN), based on the Kron reduction of the species-reaction graph associated with the network. This type of reduction comes from the theory of linear electrical networks. Although CRNs are not linear, they are endowed with a linear structure defined by the graph Laplacian, describing how...
Artemisinin-based combination therapies (ACTs) are the most widely used treatment for Plasmodium falciparum malaria. Kelch 13 mutations associated with artemisinin partial resistance (ART-R) have emerged in Sub-Saharan Africa (SSA) and are now reported in an increasing number of countries. ACT treatment failure rates are at risk of unprecedented increase. To summarise existing surveillance...
Prostate cancer is commonly treated with androgen deprivation therapy, yet resistance frequently emerges during long-term treatment. Intermittent androgen deprivation therapy (IADT), in which treatment is periodically suspended and reintroduced, has been proposed to reduce treatment burden while potentially delaying resistance. Determining when resistance is likely to arise remains a central...
Experimental investigation consistently reveals that mechanical signals direct and coordinate cell behaviours across tissue types, with cell adhesion and contractility playing key roles. In individual cells, it is observed that focal adhesions and cytoskeletal contractility are both mechanosensitive, changing in response to environmental stiffness. Within tissues, however, adhesion and...
The interplay between the perceived risk of infection and the host's protective behavior in response to an emerging infection is complex and difficult to abstract. We present a human behavior model here, based on the assumption that the human host exhibits positive adaptive behavior when the disease incidence reaches a certain threshold. Furthermore, we assume that when incidence is low, the...
The outbreak of Mpox in the Democratic Republic of Congo (DRC) in 2024 spread internationally, prompting the WHO to declare a public health emergency and underscoring the need to understand the diseaseโs transmission dynamics and potential control measures. We develop and analyze two different models for Mpox transmission. The first deals with the outbreak of Mpox in a single human population...
A distinguishing feature of eukaryotic cells is their ability to consume other cells. By contrast, prokaryotes are much more likely to engage in competitive and cooperative interactions. However, in the evolutionary transition from prokaryotes to eukaryotes, predation must have emerged from communities with primarily competitive or cooperative interactions. There are clear benefits to...
Yeasts play a key role in fermentation processes widely used in industrial biotechnology. During fermentation, yeasts produce ethanol and a wide range of metabolites, including aroma compounds. Among the factors controlling the process, nitrogen availability strongly influences yeast growth, metabolic activity, and metabolite production. Understanding how nitrogen metabolism affects...
Scientific outreach provides many benefits for researchers, as it helps to acquire and establish (or strengthen) essential skills for an academic career. Yet many barriers prevent interested researchers from participating in outreach programs, such as the lack of time or the lack in experience and information on designing an outreach activity. During my graduate research, I participated in an...
Consumerโresource models provide a framework for describing interacting populations mediated by shared resources and have been widely used to study the dynamics of complex biological systems. In this work, we examine consumerโresource systems from a dynamical perspective. Starting from simple model settings, we extend the analysis to a triangular region and investigate how structural...
In vertebrate retinas, multiple types of cone photoreceptors, each sensitive to different wavelengths, exhibit various two-dimensional arrangements. In zebrafish, each of four cone types (blue, red, green, and UV) appears periodically, forming a nearly square lattice, called โcone mosaicโ. Such regularity seems to realize uniform color resolution across the retina.
Regular mosaic patterns...
Introduction
Schools are a critical setting during respiratory pandemics. While their high-contact environments can amplify community transmission, they remain essential for childrenโs learning and wellbeing. The RE-PASS project develops a multi-scale modeling framework to support school-based interventions that balance infection control with minimizing educational disruption.
Methods
The...
Respiratory syncytial virus (RSV) is one of the leading causes of hospitalisation for bronchiolitis and other lower respiratory tract infections in infants, representing a major cause of pressure on paediatric healthcare systems \cite{manzoni2025prevention}. Recent post-pandemic seasons, for instance in Italy, have highlighted how changes in respiratory virus circulation and heterogeneous...
Predicting T cell receptor (TCR) recognition of peptideโMHC (pMHC) complexes remains a major challenge in immunology. Existing computational approaches are limited by the lack of dense, locally informative binding data. Synthetic co-evolution via yeast display has recently emerged as a powerful technique to probe proteinโprotein interactions at scale. Applying these methods to TCRโpeptide...
This study investigates the impact of information-induced vaccination, behavioural responses, and saturated treatment on infectious diseases via a delay mathematical model. Also, the dynamics of information are quantified via a separate rate equation, which influences healthy individuals to adopt controls. Stability and bifurcation analysis are carried out to understand qualitative changes in...
In this talk, we present our research on using mathematical modeling and machine learning to characterize the evolutionary dynamics of the tumor immune microenvironment (TIME) for personalized cancer therapy. We developed various ODE-based TIME models, integrating genomic and transcriptomic data. These models, enhanced by deep reinforcement learning (DRL), optimize therapy regimens, including...
Understanding which types of contact drive pathogen transmission is critical for outbreak control. Traditionally, high-risk contacts are inferred with contact tracing or network data. Including genetic data may better elucidate the contribution of different types of contact to transmission. Vice versa, contact data may improve transmission inference (who infected whom) of outbreaks.
We...
Foraging is a ubiquitous strategy employed by diverse species and organisms for collecting, accumulating, and consuming vital resources. Examples of this can be observed in various populations, from the intracellular environment where vesicles explore the cytoplasm, carrying resources to the lysosome for consumption, to a bumblebee hive where foragers explore the exterior in search of nectar...
Epigenetic transitions in the tumor microenvironment exhibit history-dependent memory effects and abrupt phenotypic shifts that classical smooth dynamical systems fail to capture from a physical perspective \cite{Esteller2002}. We present a novel mathematical framework grounded in the theory of rate-independent systems to describe the evolution of epigenetic marksโspecifically DNA...
Understanding how germinal center (GC) dynamics generate antibody responses against emerging viral variants is important for vaccine modeling. Here we develop a stochastic GC model formulated in an antigenic space framework to study antibody responses to SARS-CoV-2 vaccination. Naรฏve B cells and antigens are represented as coordinates in antigenic space, and affinity is determined through a...
Spatial relationships in multi-species data can shape biological system behaviors, from cancer progression in pathology to coral reef resilience in ecology. We propose a topological data analysis framework to quantify higher-order spatial relationships in multi-species point cloud data \cite{Natarajan2026}.
Our approach is applicable to the analysis of interactions between three or even more...
This talk describes a junior-level interdisciplinary Math/Biology course that integrates mathematical modeling with community-engaged learning. Students explore complex social and environmental systems through project-based learning, applying modeling approaches from ecology, public health, conservation, and sociology. The course emphasizes modeling as a tool for understanding and addressing...
Evolutionary biology studies populations of reproducing individuals and how their composition changes over time.
An important question is to determine the fixation probability of a single advantageous mutant that attempts to invade a homogeneous population of $N$ residents.
Many real populations experience gradients of chemicals or nutrients that cause mutations to be beneficial in some...
Many mathematical models describing vegetation patterns are based on biomassโwater interactions, due to the impact of this limited resource in arid and semi-arid environments. However, in recent years, a novel biological factor called autotoxicity has proved to play a key role in vegetation spatiotemporal dynamics, particularly by inhibiting biomass growth and increasing its natural mortality...
Background:
Monitoring anesthesia levels via EEG is essential to ensure adequate unconsciousness while minimizing complications such as intraoperative awareness or postoperative delirium. Established metrics like SEF95 and SpEn are robust but computationally demanding due to frequency domain transformation. This study evaluates whether low-complexity time domain EEG parameters can provide...
Household transmission models are widely used in infectious disease
epidemiology, yet transmission ordering is typically ignored because it
does not affect final outbreak size. Consequently, many distinct
transmission histories produce identical epidemiological outcomes,
making it difficult to distinguish internal from external transmission
and limiting parameter...
ALS is a neurodegenerative disease driven by proteotoxic stress. Many ALS-associated mutations affect aggrephagy, a selective autophagy pathway that clears protein aggregates\cite{ling_converging_2013}. The mTOR pathway is a bulk autophagy regulator and a potential therapeutic target.
We identified, through literature analysis, a link between p62, an aggrephagy receptor and an ALS-associated...
Polycythaemia Vera (PV) is a haematological malignancy characterised by an overproduction of blood cells. Recent clinical studies have shown that combination therapy with interferon-ฮฑ-2a (IFN-ฮฑ) and ruxolitinib (RUX) yields substantial reductions in JAK2 V617F variant allele frequency (VAF), a measure of disease burden. Here, we study the mechanisms behind the observed reductions in VAF...
Pandemics are expected to emerge more frequently due to population growth and climate change. Alongside traditional vaccines, broad-spectrum medical countermeasures offer potential to control diverse, unknown pathogens. We developed a hybrid mathematical framework to evaluate these interventions, combining an individual-based network branching process for early stochastic outbreaks with a...
Contact tracing (CT) is a targeted intervention that can reduce transmission during infectious disease outbreaks without requiring population-wide restrictions. Most mathematical models evaluate CT using transmission-tree frameworks that assume independent infection events and donโt explicitly account for the underlying contact network. These approaches ignore that traced susceptible contacts...
Age-structured heterogeneity in contact behavior, susceptibility, and severity makes epidemic dynamics difficult to interpret from aggregate measures alone. The effective reproduction number $R_e(t)$ collapses this heterogeneity into a single quantity, concealing which subgroups drive transmission and how interventions reshape that balance over time.
We extend elasticity analysis, a method...
Deconvolution of bulk RNA-seq data for simultaneous estimation of cell-type-specific gene expression profiles (GEPs) and relative cell abundances can be formulated as a constrained matrix factorization problem, but the widely used nonnegative matrix factorization (NMF) framework is mathematically ill-posed, as multiple factorizations may explain the observed bulk expression matrix equally well...
Non-small cell lung cancer (NSCLC) treated with tyrosine-kinase inhibitors (TKIs) initially responds well but rapidly develops resistance. This happens because in heterogeneous tumour microenvironments, continuous standard-of-care treatment rapidly eliminates drug sensitive cells, enabling resistant populations to dominate and leading to treatment failure. Evolutionary therapies (ET), guided...
In order for epidemiological forecasts to be useful for decision-makers the forecasts need to be properly validated and evaluated \cite{c19}. Although several metrics fore evaluation have been proposed and used none of them account for the potential costs and losses that the decision-maker faces. We have adapted a decision-theoretic framework to an epidemiological context which assigns a Value...
Agroโforestry socio-ecological systems in high-latitude regions are strongly influenced by climate variability, snow dynamics, and land-use change, leading to nonlinear behaviors and regime shifts \cite{Scheffer2001}. We develop a satellite-informed dynamical systems framework to model these systems under environmental forcing.
The objective is to construct a non-autonomous system of...
Defective viral genomes (DVGs) interfere with infectious standard virus (STV) replication and are considered promising antiviral agents. In longitudinal influenza A virus (IAV) infections, DVG accumulation drives oscillatory virus dynamics (von-Magnus effect [1]). Experimental evaluation of individual DVGs is resource-intensive, motivating computational prioritization.
We aim to identify DVGs...
Accumulated evidence suggests that the antitumour efficacy of immune checkpoint inhibitors (ICI) may depend on infusion time-of-day. Although circadian regulation of many immune processes has been documented \cite{l}, the mechanisms of such dosing time dependency remain unclear. To investigate this, we developed models of ICI pharmacokinetic (PK) and pharmacodynamic (PD) accounting for key...
Abstract
This study presents a six-compartment deterministic model for tuberculosis TB) transmission dynamics in populations stratified by comorbidity status. TB caused 1.3 million deaths globally in 2023, while diabetes(a major TB comorbidity), affects 537 million adults and contributes to $15-20\%$ of TB cases worldwide \cite{bi_comments_2025, kumar_prevalence_2024}. The syndemic is...
Candida albicans can cause life-threatening invasive infections, yet in an ex vivo human whole-blood infection model a substantial fraction of fungal cells remains extracellular despite the presence of phagocytes. Previous work suggested that fungal cells acquire host-derived surface markers via binding of neutrophil-derived extracellular vesicles (EV), reducing their uptake by immune...
Gene drives are engineered genetic constructs with biased inheritance that can spread in a population despite deleterious fitness effects, and are a promising tool for suppressing malaria mosquitoes, invasive rodents and other pest species. A key safety requirement for field deployment is the predictability of gene drive dynamics in natural populations. Most existing gene drive models assume a...
The observation that infectious agents (such as viruses and bacteria) limit their ability to persist if they kill their hosts too rapidly underpins a large body of work related to the evolution of virulence. Theory stemming from this explains many phenomena, such as the sustainment of deadly infectious diseases in large, dense populations. However, it is not clear whether the existing theory...
We study the detection of a contagious disease using a stochastic SVIR (susceptibleโvaccinatedโinfectedโremoved) epidemic model. In this framework, vaccination is introduced as a preventive measure. However, the administered vaccine may fail to protect some individuals, and vaccine-induced immunity may wane over time.
The epidemic dynamics of this model are described through a...
Giardiasis is usually treated successfully with short oral courses of nitroimidazoles or related agents, yet refractory infection remains clinically important and mechanistically under-modelled. We present a human within-host model for Giardia duodenalis motivated by a prolonged refractory infection in the presenting author, an epidemiologist. The model links trophozoite and cyst dynamics in...
COVID-19 affects diabetic and non-diabetic individuals differently, requiring models that capture heterogeneous disease dynamics. We propose a nonlinear compartmental model coupled with a Disease-Informed Neural Network (DINN) to study the spread of COVID-19 in these two risk groups. The model divides the population into susceptible, infected diabetic, and infected non-diabetic classes, with...
Neutral birthโdeathโmutation dynamics in finite populations can produce patterns in low-dimensional summaries of trait-distance space (e.g., mean pairwise distance) often interpreted as signatures of selection, making inference of selection from snapshot data fundamentally ambiguous. We introduce a distance-space framework for finite-length, one-parent Moran populations that separates neutral...
Accurately predicting microbial growth across varying environmental conditions and cultivation scales remains a central challenge in mathematical biology. ODE models offer mechanistic interpretability but typically rely on fixed kinetic parameters, restricting their validity to narrow operating ranges. Data-driven approaches such as Response Surface Methodology (RSM) \cite{Breig2021}...
Colorectal cancer progression is strongly influenced by metabolic signals from the gut microbiome, yet the underlying mechanisms remain poorly understood. In particular, the short-chain fatty acid butyrate - produced by fiber-fermenting gut bacteria - has been shown to inhibit cancer cell proliferation while supporting the growth and function of healthy colonocytes and immune cells. We...
Chronic spontaneous urticaria (CSU) is an immune-mediated skin disease characterized by red, itchy eruptions of various shapes, known as wheals. Second-generation H1 antihistamines are a mainstay of treatment, but treatment responses vary widely among patients, with approximately 30% remaining symptomatic despite conventional therapy. On the other hand, the results of our previous studies...
Since their introduction, neural fields have been a popular topic of research. However, most existing studies fix specific parameter choices or make physical approximations. The aim of this presentation is to provide a general and mathematically rigorous framework for traveling wave solutions in neural fields with direction preference, modeled by an asymmetric connectivity kernel, on a...
Reaction-diffusion equations exhibit a wide range of spatial and temporal behaviours and are often used to describe propagating phenomena in biological systems. In this talk, we present two such models. One describes the spread of wildfires, the other the development of resistance in agriculture. We compare how the reaction terms relate to the dynamics of the system, considering similarities...
Synchronization of coupled oscillators is a common phenomenon in biological systems. A closely related phenomenon, anti-synchronization, occurs when neighboring elements adopt opposite phases, as seen in checkerboard-like patterns in cell populations. Such patterns have been observed in the auditory sensory epithelium.
We investigate systems of coupled Kuramoto-type oscillators with...
Metastatic relapse can occur years after diagnosis, highlighting the need to better understand the mechanisms behind cancer cell dormancy and reactivation.
Here we present a mathematical model, \cite{Sf} that integrates cancer-cell dormancy, reactivation, proliferation and death, tested/calibrated with experimental murine metastasis datasets. The model couples population dynamics with...
Parameter estimation for ordinary differential equation (ODE) models of biological systems commonly assumes independent and identically distributed (IID) measurement noise. However, many experimental techniques, such as fluorescence measurements or western blots, yield data proportional to or shifted from true species concentrations, requiring unknown scaling and offset parameters. In...
Genetic mutations can lead to the formation of genetically distinct subpopulations of cells, called clones, which can vary in size over time. Due to the difficulty of obtaining meaningful longitudinal genetic data, one of the main challenges lies in the complexity of inferring the dynamics that govern the emergence and evolution of clones from snapshot data. In this context, DNA methylation...
Inferring causal relationships from ecological time series enables the study of ecosystem dynamics without direct observation. Methods such as Unified Information-Theoretic Causality (UIC) make this possible but assume independent abundance measurements. In many ecological applications, particularly eDNA studies, data are compositional and contain only relative abundances. The common remedy is...
Microsatellite instability (MSI) describes the accumulation of length alterations in microsatellite loci caused by deficiencies in the DNA mismatch repair system. In clinical diagnostics, MSI status is commonly assessed using polymerase chain reaction (PCR) assays targeting a panel of microsatellite markers. This testing plays an important role in the molecular characterization of colorectal...
Lipolysis, also called lipid hydrolysis, is a life-essential biochemical process that releases fatty acids and glycerols stored in the form of water-insoluble triglycerides within lipid droplets of specialised cells known as adipocytes. The enzyme adipose triglyceride lipase (ATGL) is believed to be the rate-limiting and key regulator of lipolysis. However, recent studies show that besides...
Immune checkpoint inhibitors (ICIs) restore antitumour immunity by blocking checkpoint interactions such as PD-1/PD-L1, while oncolytic viruses (OVs) selectively infect and lyse tumour cells, releasing viral progeny, tumour associated antigens, and danger signals that further stimulate immune responses. Motivated by these complementary mechanisms, we study the combination of virotherapy and...
Oncogene amplification on circular extrachromosomal DNA (ecDNA) has been linked to poor prognosis and higher treatment resistance in multiple types of human cancer. ecDNA are mobile genetic elements lacking centromeres that are partitioned unevenly into daughter cells at mitosis. While random segregation of ecDNA contributes to gene-copy-number heterogeneity among tumour cells, how ecDNA...
Primary myelofibrosis (PMF) is a malignant clonal disease of the hematopoietic system. It is characterized by an excess of fiber production in the bone marrow and eventually leads to an impaired blood cell formation and an increased risk of leukemic transformation. Although driver mutations in the genes for JAK2, CALR, and MPL have been identified in most patients, the pathophysiologic...
Microfluidic spheroid-on-chip platforms are widely used for high-throughput drug screening, providing controlled microenvironments for studying tumorโdrug interactions. However, drug delivery to tumor spheroids in these devices is governed by complex fluid flow and mass transport processes, making device design challenging. Consequently, their design has often relied on time- and...
Wildfires disrupt ecosystems, with much evidence to show that climate change is exacerbating vulnerability in regions poorly adapted to such disturbances. These events are driven by complex, multi-scale interactions where small perturbations in environmental factors can trigger large-scale shifts, complicating prediction efforts. We propose a coupled convection-reaction-diffusion system for...
Waddingtonโs epigenetic landscape has become one of biology's cornerstone metaphors, widely used both conceptually and computationally. Cell types are often associated with the stable qualitatively stationary points or valleys of this landscape. In previous work, we showed that the molecular noise dominating sub-cellular dynamics can distort and profoundly reshape this landscape. In...
Traditional computational approaches struggle to capture the complex interactions that occur across multiple molecular layers in disease systems, particularly as the volume of biological data continues to grow. We developed mathematical modelโbased computational tools to identify potential drug targets from large-scale datasets. Focusing on bistability in cell signalling networks, we...
The freshwater polyp Hydra is a classical model organism for studying body axis formation due to its remarkable regenerative capacity. In regenerating tissue spheroids, mechanical cues arising from tissue deformation interact with biochemical signaling pathways and influence pattern formation.
In this talk I will propose a mechanochemical model for body axis formation in regenerating Hydra...
One of the anesthesiologistโs key tasks during target controlled infusion (TCI) in total intravenous anesthesia (TIVA), where agents such as propofol are administered intravenously, is assessing the depth of hypnosis (DoH). As DoH cannot be measured directly, clinicians rely on indirect indicators such as the Bispectral Index (BIS), derived from EEG signals. However,...
The Indian House Crow (Corvus splendens) is an invasive species of growing concern in Oman due to its rapid expansion and ecological impact. This study provides a detailed phenotypic and morphometric assessment of 367 adult crows collected from four governorates: Muscat, Dhofar, North Al Batinah, and South Al Sharqiyah. Plumage coloration was highly conserved, with primary, secondary, tail,...
Determining whether a new species can invade an established microbial community is a central problem in ecology and evolution. We develop a replicator-dynamics framework that links invasion outcomes to microbiome composition through frequency-dependent interactions between species \cite{3,4}.
In this formulation, the initial growth of an invader has two components: interactions between the...
Mice orthotopically implanted with bladder cancer showed improved responses on average to intravesical (inV) T cell therapy (OT1) when preconditioned with inV gemcitabine; however, responses varied among individual mice. We developed a virtual cohort for this combination therapy to expand of the murine population while capturing response variability.
Using parameters identifiable with...
We investigate self-organization in stochastic dynamical systems using rigorous and numerical multiscale analysis. At the mesoscale, the model describes conflict resolution between two types of individuals in interconnected domains. Conflicts occur as a Poisson process governed by the mass-action law. Each conflict in a given domain triggers the transfer of one of the interacting individuals...
Robust parameter inference is central to infectious disease modelling. Traditional Bayesian approaches require an analytical likelihood, which is rarely available for complex models. Classical likelihood-free methods circumvent this limitation through simulation but are inefficient and rely on hand-crafted summary statistics. Neural Posterior Estimation (NPE) is a scalable and flexible...
Soil organisms regulate essential ecological processes such as nutrient cycling and pest suppression \cite{bardgett2014belowground}, yet much about them is still unknown. At the global scale, soil degradation causes substantial economic losses each year \cite{sutton2016ecological}. Understanding how soil biota responds to land-use and climate change is therefore vital for ecosystem services...
Acoustic boundary conditions strongly influence pressure fields and biological responses in in-vitro ultrasound experiments, yet their mechanistic role remains poorly quantified. This study investigates the effects of standing waves on acoustic pressure and cell viability. A multiphysics finite-element model integrating pressure acoustics, solid mechanics, and electrostatics was developed to...
We consider the problem of inferring $R_0$ for an epidemic where contact tracing data are available, from which we observe the size of several infectious clusters within a large population. By fitting the observed cluster sizes to the total progeny of a branching process, we use the Dwass formula for total progeny to estimate both $R_0$ and the index of dispersion of the offspring...
Melanoma cells can transition between cell states, contributing to therapy resistance and immune evasion. These state changes involve dynamic and reversible shifts in gene expression, making it essential to understand the underlying regulatory mechanisms for developing effective therapies. We present a mathematical model of a minimal gene regulatory network comprising key transcription factors...
Understanding how structural synaptic connectivity shapes neuronal network function remains a fundamental challenge in neuroscience. While optical imaging now allows the simultaneous recording of thousands of neurons, most studies rely on calcium signals, which lack the temporal resolution to capture fast spiking and synaptic dynamics \cite{Pa17}. Recent advances in Genetically Encoded Voltage...
Parasite virulence, the harm parasites cause to host survival and fitness, shapes hostโparasite dynamics in both pathogenic and social parasites. Although high virulence can limit parasite persistence, outcomes depend on ecological context and can even lead parasites to function as net mutualists. Fungus-growing ants (Myrmicinae: Attini: Attina) form a well-studied symbiotic system that is...
Phenotypic plasticity underlies cancer progression and metastasis \cite{c1}, yet how distinct regulatory axes interact to shape tumour progression and patient outcomes remains unresolved. We investigated major axes of plasticity in ER-positive breast cancer, including metabolic reprogramming, epithelial-to-mesenchymal plasticity, and drug-resistance using ODE-based gene regulatory network...
Myeloproliferative neoplasms (MPN) are a group of hematological malignancies characterized by an overproduction of myeloid blood cells. A recent mathematical model (\cite{B}) coupling hematopoiesis, inflammation, MPN progression and treatment inhibiting inflammation is here analyzed from a dynamical systems perspective.
The model includes time varying populations of stem cells, progenitor...
Parameter estimation for ODE models of biological systems is commonly based on continuous or semi-quantitative measurements. Many relevant observations are however inherently binary โ such as gene essentiality classifications from CRISPR knockout screens. Treating such data as continuous introduces statistical misspecification, biasing parameter estimates and undermining uncertainty...
Background: A fundamental challenge in clinical hematology is the inability to monitor bone marrow dynamics in real time without invasive procedures.
Objective: We present an Extended Kalman Filter (EKF) framework that reconstructs unobservable bone marrow cell populations (stem, progenitor, differentiated) from noisy measurements of peripheral blood inflammation.
Methods: The hematopoietic...
The focus of the presentation is the development, numerical simulation and parameter analysis of a model of the transcription of ribosomal RNA in highly transcribed genes. The well-known nonlinear Lighthill-Whitham-Richards (LWR) equation is used to model the transcription process. The numerical treatment for model simulations includes introducing a low complexity time accurate method by...
Across living systems, oscillations support coordination, information flow, and decision making, from neural rhythms to calcium signaling in single cells. While most studies focus on organisms with nervous systems, growing interest concerns how similar abilities arise in non-neural organisms. The unicellular slime mold Physarum polycephalum is a key example, exhibiting decision-like behaviors...
Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals disperse across interconnected patches. We consider an intraspecific competition model, where individuals compete for space while dispersing according to a...
The liver contributes to maintaining metabolic homeostasis by clearing toxins from the bloodstream. Blood enters through portal veins, flows through the tissue where hepatocytes remove toxins, and exits through central veins. This process occurs within a highly organized microarchitecture in which portal and central veins form repeating functional units called lobules. In cross-section,...
This work focuses on hyperspectral imaging in biomedical applications, particularly fluorescence microscopic hyperspectral imaging (FMHSI) of unstained biological tissue, a foundational tool in diagnostic pathology and biomedical research due to its high spectral and spatial resolution. Semantic segmentation of FMHSI images is essential for generating labeled HSI data and enabling downstream...
Cell movement is an important part of many biological processes, such as collective cell migration and the immune response to cancer. In many systems interactions between nearby cells are a key driver of cell movement, yet it can be difficult to infer and express the rules governing cell-cell interactions in a manner that is biologically interpretable. Here we present a model, based on the...
Predicting disease progression hinges on understanding how innate immune responses regulate viral spread at the tissue level. Type I interferon (IFN) induces local antiviral protection in epithelial cells, yet the combined effects of virion diffusion, IFN transport, and cellular heterogeneity remain difficult to capture in spatial models. We present a spatial agent-based model of influenza A...
Social structure influences ecological dynamics, fitness, and evolution in animal populations. Network science provides tools to link individual interactions to emergent social organisation, which are increasingly used in behavioural ecology [1,2]. In animal societies, this approach explains how individual and relational characteristics influence the formation, stability, and evolution of...
Volume-exclusion interactions play a crucial role in the self-organisation observed in many biological systems. In particular, they are fundamental to explain the spontaneous emergence of nematic order in populations of anisotropic particles, as observed, for example, in dense suspensions of myxobacteria \cite{balagam2015mechanism}. More generally, they also play an important role in cell...
Active surveillance is a common management strategy for patients with low-risk prostate cancer, aiming to delay or avoid invasive treatment while monitoring disease progression. However, interpreting longitudinal observations is challenging because the prostate itself can undergo significant physiological growth due to aging or benign prostatic hyperplasia. These baseline changes may obscure...
Biological condensates are membraneless organelles within the cell or the nucleus which perform an array of different tasks and typically consist of DNA/RNA and protein. Actin is a protein that exists in most eukaryotic cells and transitions between monomeric and filamentous states. In its filamentous state, actin forms networks, which perform vital tasks inside the cell. Recent research has...
Efforts to suppress glioblastoma (GBM) recurrence include targeting peritumoral regions by increasing extent of tumor resection and volume/dose of radiotherapy. Due to their broad application, these methods include risks of radiation toxicity and excess healthy tissue excision. Techniques to better predict where GBM recur could circumvent these limitations. Recent evidence indicates that...
We present the Multiple Clone Cancitis (MCC) model describing the blood
cancers AML, CML, and MPNs despite its differences [1]. The MCC model is
based on biological mechanisms, basic cell descriptors such as proliferation rates,
and apoptosis rates connecting stem cell dynamics with mature blood cells and
immune mediated feedback including an explicitly cytotoxic T-cell mediated
death of...
Sickle cell anaemia is a genetic and molecular disease that affects the structure and dynamics of red blood cells (RBCs), leading to a variety of complications in blood circulation. A single amino-acid mutation in the haemoglobin molecule leads to the polymerization of long, rigid fibres that deform the cell from the inside, affecting its morphology and the blood's rheological properties...
Many modelled biological systems are data-limited, due to the costs, time constraints, invasiveness or untrustworthiness of data collection. However, ecologists and biologists often possess valuable knowledge about how systems should behave, derived from theory, experiments, or expert understanding. We develop a new statistical framework for incorporating expert knowledge directly into...
Understanding how spatial structure and environmental variability shape microbial colony growth and inter-strain interactions remains a central challenge in systems biology. I will present an integrated experimentalโcomputational framework for the quantitative analysis of Saccharomyces cerevisiae colonies on solid media under both standard and non-standard environmental conditions....
The Sterile Insect Technique (SIT) is an environmentally friendly strategy for suppressing mosquito populations that transmit diseases such as dengue, Zika, and Chikungunya. We investigate SIT-based control of Aedes aegypti mosquitoes using a spatially explicit reactionโdiffusion model describing the dynamics of wild males, wild females, and released sterile males. The model incorporates...
This contribution studies the dynamics of an infectious disease outbreak in a closed homogeneously mixed population using a stochastic SVIR model with a pre-epidemic vaccination program and imperfect vaccine protection \cite{Gamboa2024}. The model is formulated as an absorbing continuous-time Markov chain with susceptible, vaccinated, infected, and recovered compartments. We focus on two key...
Background: Several PK/PD models are used for propofol delivery via target-controlled infusion (TCI). The Schnider PK model \cite{schnider1998influence} was developed in younger healthy volunteers. The Eleveld PK/PD model \cite{eleveld2018pharmacokinetic} is a newer general-purpose model for children, elderly, and obese patients. The models differ in effect-site equilibrium rates, with...
Spatial networks reconstructed from microscopy such as mitochondrial, neuronal, and vascular networks are frequently modelled as embedded graphs whose edge weights depend on interโvertex distance. Uncertainty in vertex localisation arising from segmentation, registration, or temporal sampling introduces geometric perturbations that propagate nonlinearly into graph Laplacians. These...
This work explores the dynamics of a multistage SIRS model. Using the Lyapunov method as our primary tool, we begin by revisiting the stability analysis of the disease-free and endemic equilibria in a single-stage SIRS model. We then extend the techniques employed in this analysis to enable a similar stability analysis of multistage infection models. In particular, we propose a systematic...
The increasing availability of experimental data has motivated interest in calibrating stochastic models, raising fundamental questions about parameter identifiability. Structural identifiability analysis determines whether parameters can be uniquely inferred from idealised, noise-free data; however, existing methods are not suited to partially-observed stochastic processes with hidden...
Structural identifiability in chemical reaction networks is often studied for kinetic parameters, but much less is known about identifiability of the stoichiometric structure itself. We study this question for non-autocatalytic mass-action biochemical reaction networks with fixed rate constants. We ask when the stoichiometric matrix can be uniquely recovered (identifiable) from the induced...
In this talk, I will describe my group's ongoing research into designing mathematical models that can learn from different data modalities simultaneously: such as clinical reports, whole-genome sequencing, and medical images. We apply these to describe risk stratification, patient outcomes, and subclonal evolution for several different pre-cancerous conditions. In my lab, we draw from both...
Intraperitoneal (IP) chemotherapy is a promising treatment for peritoneal carcinomatosis because it provides high local drug exposure to tumours within the abdominal cavity. However, its efficacy is limited by tumour microenvironmental barriers and rapid drug clearance from the peritoneal cavity. Nanosized drug carriers have attracted increasing interest because evidence suggests that they...
