Speaker
Dr. Zoi Rapti, Professor, Department of Mathematics, University of Illinois Urbana-Chanpaign
Title
Mathematics Seminar
Subtitle
Title: Stability and Bifurcations in Coupled Ordinary and Partial Differential Equations Systems
Physical Location
Allen Hall 14
Abstract: Many phenomena in mathematical biology are modeled by systems of coupled ordinary and partial differential equations (ODEs-PDEs). In this talk, we will provide motivating examples, and we will then investigate the stability of certain types of biologically relevant steady state and spatially uniform solutions. We will show that when reaction-diffusion terms exist, the stability problem may give rise to operator eigenvalue problems that can be studied using Herglotz functions and Sturm-Liouville type theory. We will demonstrate that when the ODE-PDE system contains a transport equation, the basic reproductive number can be obtained through linear stability analysis and certain bifurcations of solutions can also be studied analytically. We will apply our mathematical methods to animal epidemics and will make connections with strategies for containment.