Global dynamics for an SVEIR epidemic model with diffusion and nonlinear incidence rate

Abstract

In this paper, we investigate an SVEIR epidemic model with reaction–diffusion and nonlinear incidence. We establish the well-posedness of the solutions and the basic reproduction number mathfrak{R}_{0}. Moreover, we show that the disease-free steady state is globally asymptotically stable when mathfrak{R}_{0}<1, whereas the disease will be persistent when mathfrak{R}_{0}>1. Furthermore, using the method of Lyapunov functional, we prove the global stability of the positive steady state for the spatial homogeneous model.