This paper is concerned with an SIS epidemic reaction-diffusion model with mass-action incidence incorporating spontaneous infection in a spatially heterogeneous environment. The main goal of this article is to study the influence of spontaneous infection on the endemic equilibrium (EE) of the model. To achieve this, first the existence of EE is investigated. Furthermore, we discuss the asymptotic behavior of endemic equilibrium if the migration rate of the susceptible or infected population is sufficiently small. Compared to the case without spontaneous infection, our theoretical results show that spontaneous infection can enhance persistence of infectious disease.

中文翻译：

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自发感染的空间SIS流行病模型中扩散的影响

本文关注的是一种在空间异质环境中具有自发感染并具有自发性感染的SIS流行病反应扩散模型。本文的主要目的是研究自发感染对模型的地方平衡（EE）的影响。为了实现这一点，首先要研究EE的存在。此外，如果易感或感染人群的迁移率足够小，我们将讨论地方均衡的渐近行为。与没有自发感染的情况相比，我们的理论结果表明，自发感染可以增强传染病的持久性。