Invasive species pose major challenges for biodiversity and ecosystem management. In this talk, I present mathematical models to understand how biological invasions emerge, spread, and can be controlled. I first focus on early invasion stages, where stochastic effects are important, and discuss extinction probabilities and invasion thresholds. I then address invasion dynamics at larger spatial...
In this talk, we discuss a hybrid modeling framework to analyze measles transmission and vaccination strategies during the 2025 Texas outbreak. A deterministic model incorporating single- and double-dose vaccination with vaccine efficacy was calibrated to reported Texas measles data from January 20 to May27, 2025. To complement the mechanistic analysis, time-series forecasting methods,...
The simultaneous escalation of COVID-19 and drug overdose deaths motivates the development of mathematical frameworks capable of capturing interacting population-level processes across disparate time scales. We propose a coupled dynamical systems formulation that represents the joint evolution of an infectious disease process and a mortality process associated with substance use. The framework...
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number R0 of the pathogen can be defined in that case and corresponds to a threshold between the persistence ($R_0 > 1$) and the extinction ($R_0 \leq 1$) of the pathogen. When $R_0>1$ and the maximal fitness is...
This mini-symposium centers on the development and analysis of mathematical models arising from public health and ecological threats, including infectious diseases, substance-use–related mortality, and biological invasions. The talks emphasize the formulation and study of coupled, multi-scale, and non-autonomous dynamical systems, with attention to qualitative properties such as stability,...
