Threshold dynamics of a time periodic reaction–diffusion epidemic model with latent period

Abstract

In this paper, we first propose a time-periodic reaction–diffusion epidemic model which incorporates simple demographic structure and the latent period of infectious disease. Then we introduce the basic reproduction number R0 for this model and prove that the sign of R0−1 determines the local stability of the disease-free periodic solution. By using the comparison arguments and persistence theory, we further show that the disease-free periodic solution is globally attractive if R0<1, while there is an endemic periodic solution and the disease is uniformly persistent if R0>1.