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

a. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
b. Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

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 $R_0$ for the model via the next generation operator method. We then establish the threshold dynamics of the model in terms of $R_0$, that is, the disease is uniformly persistent if $R_0 > 1$, while the disease goes to extinction if $R_0 < 1$. Finally, we study the global dynamics for the model in a special case when all the coefficients are independent of spatio–temporal variables.

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