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

摘要

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 R-0 for this model and prove that the sign of R-0 - 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 R-0 < 1, while there is an endemic periodic solution and the disease is uniformly persistent if R-0 > 1. (C) 2015 Elsevier Inc. All rights reserved.