Abstract
In this paper, we deal with an SIRS reaction–diffusion epidemic model with saturation infection mechanism. Based on the uniform boundedness of the parabolic system, we investigate the extinction and persistence of the infectious disease in terms of the basic reproduction number. To better investigate the effects of infection mechanism and individual diffusion, we further analyze the asymptotic profiles of the endemic equilibrium for small or large motility rate and large saturation rate. In particular it is shown that large saturation may cause the elimination of disease. Our study may provide some significant useful insight on disease control and prevention.
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