A Periodic Epidemic Model With Latent Period In A Patchy Environment

The study of infectious diseases has always been an important research issue.The outbreaks of the infectious diseases are caused by the interaction of many fac-tors. The dispersal among patches and the heterogeneity of time are the main causes of disease transmission. The heterogeneity of time is caused by seasonal factors, so the characteristics of disease transmission can be described more effectively with periodical epidemic model.Firstly, we propose a non-local periodical epidemic model in a patchy environ-ment with time delay and bilinear incidence by introducing the concept of “age structure” . And then, we obtain a threshold result on its dynamics in terms of R0.When R0 > 1, the disease is uniformly persistent. When R0 < 1, the disease cannot invade the disease-free state with small initial infected individuals. In particular, if the susceptible, the latent and the infectious in each patch have the same dispersal rate, then the disease also cannot invade the disease-free state when R0 < 1,Secondly, we present the numerical simulations for the model in two patches.The numerical simulations show that the dispersal among patches has a significant impact on the control of diseases.Finally, a discussion and an outlook complete this paper.