In this paper, we are concerned with an SIRS epidemic reaction–diffusion system with standard incidence infection mechanism in a spatially heterogeneous environment. We first establish the uniform bounds of solutions and then derive the threshold dynamics in terms of the basic reproduction number \(\mathcal {R}_0\). Our main focus is on the asymptotic profile of endemic equilibria (when exists) if the diffusion (migration) rate of the susceptible, infected or recovered population is small, and our results show that the disease always exists in the entire habitat in each case of small diffusion rate. This suggests that restricting the diffusion (migration) rate of population is not an effective strategy of disease eradication.

在本文中，我们关注的是在空间异质环境中具有标准发病率感染机制的SIRS流行病反应扩散系统。我们首先建立解的统一边界，然后根据基本复制数\（\ mathcal {R} _0 \）得出阈值动态。如果易感，感染或恢复的人群的扩散（迁移）率很小，我们的重点是在地方均衡（如果存在）的渐近分布上，我们的结果表明，在每种情况下，该疾病始终存在于整个栖息地中扩散率小。这表明限制人口的扩散（迁移）率不是根除疾病的有效策略。