Threshold dynamics of a time periodic and two--group epidemic model with distributed delay

Abstract

In this paper, a time periodic and two--group reaction--diffusion epidemic model with distributed delay is proposed and investigated. We firstly introduce the basic reproduction number R0 for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of R0, that is, the disease is uniformly persistent if R0>1, while the disease goes to extinction if R0< 1. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio--temporal variables.