Epidemic Waves: A Diffusion Model for Fox Rabies

Abstract

In this paper we formulate a model for the spread of vulpine rabies based on fox ecology. This model is also an approximation to the one introduced by J. D. Murray et al [MSB]. We prove that a heteroclinic spiral connection exists between the disease free and endemic equilibria of the travelling wave ODE (TWODE). The local analysis and simulation results in [MSB] motivated our proof. We hope that these results will be of interest to researchers investigating outbreaks of raccoon rabies in the United States and fox rabies in Europe as well as to epidemiologists in general.