Effective reproduction numbers, $\mathcal{R}_E$ , provide a means of evaluating the effectiveness of interventions to control the transmission of pathogens in host populations. They can be estimated empirically from reported infections via a renewal equation or analytically via next generation matrices derived from mechanistic models. Both approaches have advantages and disadvantages, with one...
The population-level burden of an influenza season depends strongly on the proportion of people vaccinated beforehand. Being able to predict whether a given season is on track to have low, high or average uptake would provide a critical piece of highly actionable intelligence for all stakeholders involved: Governments, public health authorities, healthcare providers, vaccines manufacturers,...
Mathematical modelling is a valuable tool in assessing disease dynamics and interventions. Models may be deterministic, stochastic, data driven, network-based, or hybrid, combining multiple approaches. Advances in computing power, data collection, and simulation frameworks have made it possible to create dynamic models that integrate individual behaviour, environmental context and policy...
About half of the world's population, about 4 billion people, live in areas with a risk of dengue infection. Recent evolutionary adaptations of dengue-transmitting mosquitoes to colder regions, such as the Himalayas of Nepal, have raised severe public health concerns about dengue pandemics. In this talk, I will demonstrate how machine-learning techniques and mathematical models can be combined...
Natural populations exhibit complex class structures that shape evolutionary trajectories. While evolutionary demography provides a formal framework to predict adaptation using invasion fitness, the high mathematical dimensionality of these models often precludes interpretable analytical solutions. We introduce two complementary tools to simplify complex life cycles. First, we formulate the...
To better understand SARS-CoV-2 variant succession during the COVID-19 pandemic, we developed multi-variant transmission models, derived conditions for novel variants to invade and coexist with or replace ancestral ones, and explored phenomena that might explain observed patterns. To invade, novel variants require reproduction numbers greater than unity when ancestral ones are at their endemic...
Measles is currently affecting many countries globally. In recent studies we have shown that measles vaccine induced immunity can wane over time. In this talk we will determine the control reproduction number and the critical vaccination threshold under these conditions. We will then present a case study for measles infection in Ontario, Canada and determine the effective size of the...
Social dilemmas featuring tension between the individual incentive to cheat and a collective goal to maintain cooperative behavior arise across a range of natural and social systems, from the origins of multicellular life to the sustainable manage of shared natural resources. Evolutionary game theory provides a helpful analytical framework for describing this conflict between individual and...
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. A reaction-diffusion-aggregation system coupled with a separate dynamically updating map is proposed to describe the animal population movement. We show that when an asymmetric cognitive map influences instantaneously, a...
Consider the first order Caputo fractional differential equation (FDE)
$$(D^{1-\alpha}_{C,a^+}u)(x):= (I^\alpha_{a^+} u')(x)=f(x,u(x))\quad \mbox{for almost every } x\in [a,b],$$
where $\alpha\in(0,1)$, $I^\alpha_{a^+}$ is the Riemann-Liouville fractional integral, $u'$ is the traditional first-order derivative and $f: [a,b] \times [0,\infty) \to \mathbb{R}$ is a function. The Caputo FDE can...
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...
Population models have long been grounded in natural intelligence: the human-driven theoretical frameworks that include nonlinear dynamics, bifurcation theory, PDEs, structured population models, and stochastic processes. These classical approaches remain indispensable for explaining underlying mechanisms, generating deep insight, and ensuring interpretability. In parallel, artificial...
