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.

中文翻译：

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具有饱和感染机制的SIRS反应扩散模型的定性分析

在本文中，我们处理具有饱和感染机制的SIRS反应扩散模型。基于抛物线系统的一致有界性，我们根据基本繁殖数来研究传染病的灭绝和持续性。为了更好地研究感染机制和个体扩散的影响，我们进一步分析了小或大运动率和大饱和率时地方病平衡的渐近曲线。特别地，显示出大的饱和度可以引起疾病的消除。我们的研究可能会在疾病控制和预防方面提供一些重要的有用见解。