My team integrates nonlinear dynamics, bifurcation analysis, and climate modeling to study infectious-disease dynamics and ecological systems. Using a One Health framework, we analyze vector-borne diseases and zoonotic spillover while incorporating environmental drivers such as temperature. We also apply advanced methods—including Filippov (piecewise-smooth) systems—to optimize and evaluate public health interventions.
Bifurcation and Dynamics
The research explores complex nonlinear dynamics in epidemiology and ecology through rigorous bifurcation analysis.
Key findings highlight backward bifurcations, where diseases persist even when R0<1, driven by resource constraints or media impact. Hopf bifurcations induce sustained oscillations due to maturation delays and population competition. High-codimension bifurcations, such as Bogdanov-Takens and nilpotent singularities, serve as organizing centers for multistability and multiple limit cycles. Additionally, the studies integrate Filippov systems for discontinuous interventions, adaptive networks for shifting topologies, and stochasticity to determine extinction risks, providing a robust framework for optimizing disease control and pest management.
Projects and Reports
- Dynamical Systems and Differential equations; Bifurcation theory and applications; Hilbert’s Sixteenth Problem;
- Mathematical ecology and epidemiology, Population dynamics;
- Ontario Climate Indices (CMIP6)
- Climate Data portal
- Mosquito Data portal
- Climate change modeling and impact studies
- Mosquitoes and mosquito-borne diseases, West Nile virus.
Climate change
Our research investigates high-resolution climate projections and their multifaceted impacts throughout Ontario. Central to this is the Ontario Climate Data Portal (OCDP), which disseminates a super ensemble of 209 climate projections (~10km resolution) to support regional adaptation. We examine shifting environmental patterns, specifically the projected significant increase in extreme precipitation events. Additionally, we model ecological consequences, such as northward mosquito range expansion and West Nile virus transmission risks driven by climate warming. This integrated research framework ensures consistency and comparability across Ontario's climate risk assessments.
Population dynamics
Population dynamics research utilizes delay differential equations—discrete, distributed, and fractional—to analyze biological systems ranging from disease vectors to the immune response. Key mechanisms include maturation delays and negative feedback, triggering Hopf and Neimark-Sacker bifurcations that produce sustainable periodic oscillations. Environmental drivers, specifically temperature, regulate survival thresholds like R0. Spatial fragmentation dictates metapopulation persistence through fast-slow dynamics. Notably, immune models reveal that antigen-antibody spatial interactions are essential for realizing the memory stage. Modern strategies integrate biological controls and fractional-order memory intensity to suppress disease-carrying populations.
Vector-borne diseases
Our research investigates the complex population dynamics of disease vectors, primarily mosquitoes and ticks, through advanced mathematical modeling. We analyze how environmental drivers, such as temperature and climate warming, influence maturation delays, spatial spreading, and range movement. Crucially, our studies examine transmission mechanisms for diseases like West Nile virus, Zika, and Dengue, incorporating factors like vertical transmission and host diversity. Finally, we evaluate integrated control strategies, including Wolbachia-based biological interventions and insecticide use, to optimize public health responses and predict future outbreaks.
Zoonoses & one-health
Zoonoses like monkeypox and swine viral diseases illustrate the inextricable links between human, animal, and environmental health. Utilizing a One Health framework, our research employs spatial epidemiology and mathematical modeling to assess transmission risks at this critical interface. By integrating GIS and compartmental models, we identify key drivers of virus spillover—ranging from animal reservoirs and climate shifts to socio-behavioral patterns. Effective control necessitates interdisciplinary collaboration to implement targeted measures like case isolation and integrated surveillance. Ultimately, we aim to enhance global health security against emerging infectious threats.
Disease Modelling
Modern disease modeling has shifted from basic tracking to sophisticated predictive frameworks integrating climate dynamics and cross-species interactions. Researchers use Bayesian hierarchical models to link environmental variables like temperature to vector life cycles, identifying thermal optima for disease transmission. Advanced analysis utilizes bifurcation theory, revealing that reducing R0 below 1 is sometimes insufficient for eradication due to stable endemic states. Additionally, the One Health framework tracks pathogens across animal reservoirs, environment, and humans to predict zoonotic spillover. These mathematical tools, including Filippov systems, allow for realistic simulations of pandemic management.
