Analysis of a degenerate reaction-diffusion host-pathogen model with general incidence rate

Abstract

In this paper, we deal with the sharp threshold results for a host-pathogen model with general incidence rates. We formulate the model by a system of degenerated reaction-diffusion equations with heterogeneous parameters, where the movement of pathogens are ignored. The basic reproduction number, ℜ0, is defined to govern and it is shown to be a threshold determining whether or not the disease will be extinct or be persistent. We also confirm that disease will be extinct in the critical case ℜ0=1. By three examples of homogeneous cases in the sense that parameters are all constants, we obtain the specific formula for ℜ0, and explore the stability problems of the unique constant positive equilibrium by using the technique of Lyapunov function. Our theoretical results can also be potentially applied to explore the effect of the spatial heterogeneity on disease dynamics, and also evaluate the risk of disease transmission.