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.

A two-group age of infection epidemic model with periodic behavioral changes

“…Periodic delay differential equations have also gained many attentions and several works have been done in this subject. We refer among other to the works of [3,11,13,24,37,32,36]. The definition of a threshold by the basic reproduction number to know if it will be extinguished or persistence of a disease in the case of non-autonomous models has receive a lot of attentions.…”