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...
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...
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,...
