Spatial Spread of Rabies in China∗

The reported data on human rabies in Mainland China in the past 10 years demonstrate that the number of counties with human rabies cases has increased dramatically and the disease has spread from southern provinces to northern provinces. The aim of this paper is to study how the movement of dogs impacts the spatial spread of rabies and to find effective strategies for controlling rabies. We firstly construct a reaction-diffusion model for dogs and humans and obtain the minimal wave speed. Then we consider the existence of traveling waves and the influences of parameters on human rabies cases and the minimal wave speed by numerical simulations. Lastly, we discuss the local stability of the endemic equilibrium. Our analysis indicates that dog movement leads to the traveling wave of dog and human rabies and has a large influence on the minimal wave speed. Thus restricting the movement of dogs, in particular the exposed and infected dogs, is an effective way to prevent the spatial spread of rabies.