Abstract
In this paper, we study a time-periodic nonlocal dispersal susceptible-infected-susceptible epidemic model with Neumann boundary conditions, where the total population number is constant. We first investigate limiting profile of the spectral bound for a time-periodic nonlocal dispersal operator, and then obtain asymptotic behavior of the basic reproduction ratio of the model as the dispersal rates go to zero and infinity, respectively. Next, we establish the existence, uniqueness and stability of steady states of the model in terms of the basic reproduction ratio. Finally, we discuss the impacts of small and large diffusion rates of the susceptible and infectious populations on the persistence and extinction of the disease.
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