Dynamics of a reaction-diffusion SIRS model with general incidence rate in a heterogeneous environment.

Abstract

In this paper, we study a diffusive SIRS-type epidemic model with transfer from the infectious to the susceptible class. Our model includes a general nonlinear incidence rate and spatially heterogeneous diffusion coefficients. We compute the basic reproduction number mathcal {R}_0 of our model and establish the global stability of the disease-free steady state when mathcal {R}_0<1. Furthermore, we study the uniform persistence when mathcal {R}_0>1 and perform a bifurcation analysis for a special case of our model. Some numerical simulations are presented to illustrate the dynamics of the solutions as the model parameters are varied.