460 McBryde Hall, Virginia Tech
225 Stanger Street
Blacksburg, VA 24061-1026
My main research interest centers around mathematical modeling using ordinary differential equations and dynamical systems as well as difference equations. Particularly, I am interested in modeling biological systems, primarily in epidemiology and ecology. My recent work focuses on the formulation and analysis of population models in infectious diseases to study the evolution of pathogen-host systems. I use standard deterministic methods integrated with persistence theory, stochastic processes, and programming methods using MATLAB.
My goal in research is to build models to increase understanding of disease dynamics which in turn informs optimal strategies for controlling outbreaks. Additionally, the general framework of these models can be adapted to a variety of situations; with the appropriate modifications, we can consider different diseases, population models in ecology, or even physical systems distinct from biology. When analyzing these models, I seek to answer the following questions: "Is this model viable for this situation?" "How strong are the results?" "What does this inform us about strategies to mitigate these problems in the real world?"