Dynamics Of An Almost Periodic Epidemic Model With Non-local Infectious And Latency In A Patchy Environment

Based on the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of population may disperse,combined with seasonal factors,an almost periodic SIR model with non-local infections and latency in a patchy environment is investigated.Firstly,Combining the idea of the next generation operator,the definition and calculation formula of the basic reproduction number R0 is given.Furthermore,the global dynamics theory of the model is studied using the basic regeneration number R0 as a threshold parameter.It is shown that the disease will die out in the sense that the disease-free almost periodic solution of the model is globally attractive if R0<1,while the disease is uniformly persistent when R0>1.Meanwhile,taking COVID-19 as an example,this paper numerically simulates the model in a two patch environment,verifying the propagation mechanism of the almost periodic infectious disease model.Finally,in order to provide a more intuitive understanding of the propagation mechanism of the SIR model for almost periodic infectious diseases,this paper simulates the long-term behavior of the almost periodic system under two patches(t>τ).Some numerical simulations indicate that population distribution between patches has a significant impact on the spread of COVID-19 disease and show that the periodic epidemic models may overestimate or underestimate the disease risk comparing with the almost periodic model.