A reaction–diffusion SIS epidemic model in a time-periodic environment

In this paper, we consider a susceptible–infected–susceptible (SIS) reaction–diffusion model, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and temporally periodic and the total population number is constant. We introduce a basic reproduction number and establish threshold-type results on the global dynamics in terms of . In particular, we obtain the asymptotic properties of with respect to the diffusion rate dI of the infected individuals, which exhibit the delicate influence of the time-periodic heterogeneous environment on the extinction and persistence of the infectious disease. Our analytical results suggest that the combination of spatial heterogeneity and temporal periodicity tends to enhance the persistence of the disease.