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In this paper, we have proposed a reaction-diffusion SIRS epidemic model with a general incidence function f(S,I) in a spatially heterogeneous environment. For this model, we derive the basic reproduction number R0 and establish the results of the threshold dynamics with respect to the basic reproduction number R0. Specifically, the disease-free equilibrium is globally asymptotically stable when R01. Especially, under the spatially homogeneous condition, the SIRS model admits a unique steady state, which is globally asymptotically stable under some assumptions when R0>1. Finally, we take the Beddington-DeAngelis-type incidence function and perform some numerical simulations to illustrate the dynamics of the solutions as the model parameters are varied.
Zhi et al. (Sun,) studied this question.