Traveling Waves in Modeling of a Fungal Disease over a Vineyard

Dr. Shangbing Ai

Department of Mathematical Sciences
UA Huntsville

September 19, 2008
219 Shelby Center
3:00 PM (Refreshments at 2:30)

Abstract

We study traveling wave solutions for a model of a fungal disease propagating over a vineyard. The model consists of a reaction-diffusion equation and two ODEs of the SIR-type. We consider the case that one of the parameters involved is sufficiently small and the model system is then singularly perturbed. Employing the recent theory in dynamical systems, we establish the existence of a family of traveling wave solutions for the model.