In this paper, we consider an SIS epidemic reaction–diffusion model with spontaneous infection and logistic source in a heterogeneous environment. The uniform bounds of solutions are established, and the global asymptotic stability of the constant endemic equilibrium is discussed in the case of homogeneous environment. This paper aims to analyze the asymptotic profile of endemic equilibria (when it exists) as the diffusion rate of the susceptible or infected population is small or large. Our results on this new model reveal that varying total population and spontaneous infection can enhance persistence of infectious disease, which may provide some implications on disease control and prediction.

在本文中，我们考虑了在异构环境中具有自发感染和后勤来源的SIS流行病反应扩散模型。建立了统一的解边界，并讨论了在均质环境下常地方平衡的全局渐近稳定性。本文旨在分析当易感人群或受感染人群的扩散率较小或较大时，地方平衡（当存在时）的渐近分布。我们在这个新模型上的结果表明，总人口的变化和自发感染可以增强传染病的持久性，这可能对疾病的控制和预测具有一定的意义。