Traveling Epizootic Waves of a Fox Rabies Model with Small Spatial Diffusion

Abstract

In this paper, to describe the spread of fox rabies, a degenerate SEI epidemic model with small spatial diffusion equipped by infectious foxes due to rabies is investigated. In particular, the existence of traveling waves is established by the geometric singular perturbation theory for the larger speeds, while the non-existence of traveling wave is still derived for the smaller speeds. Moreover, some numerical simulations are implemented to illustrate the propagation dynamics driven by traveling waves.