A reaction–diffusion SIS epidemic model with saturated incidence rate and logistic source for the susceptible individuals is considered. We establish the uniform bounds of parabolic system and investigate the extinction and persistence of infectious diseases in terms of the basic reproduction number. We further analyze the asymptotic profiles of the endemic equilibrium for small and large movement rates and large saturate rate. In particular, it is shown that large saturation may cause the elimination of disease and the logistic source can enhance persistence of infectious disease.

中文翻译：

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具有饱和发病率和逻辑源的反应-扩散 SIS 流行病模型

考虑了针对易感个体的具有饱和发病率和逻辑源的反应-扩散 SIS 流行病模型。我们建立抛物线系统的统一界限，并根据基本繁殖数研究传染病的灭绝和持续存在。我们进一步分析了小、大移动率和大饱和率的地方性平衡的渐近曲线。特别是，表明大的饱和度可能会导致疾病的消除，而后勤来源可以增强传染病的持续性。