Migration can be divided into temporary and permanent migration, which is related to the residence time of people in the patch, thus we consider an SIS epidemic model with migration and residence time in a patchy environment. If R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease dies out. With the same migration rate of susceptible and infectious individuals and without disease-induced death, when R0 > 1, the endemic equilibrium is unique and globally asymptotically stable. Numerical simulations are carried out to show the effects of residence time and the migration rate on disease prevalence.

中文翻译：

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具有迁移和停留时间的SIS流行病模型的动态分析

迁移可分为临时迁移和永久迁移，这与人在斑块中的停留时间有关，因此我们考虑在斑块环境中迁移和停留时间的SIS流行病模型。如果R0 ≤ 1，无病平衡是全局渐近稳定的，疾病消失了。在易感个体和传染性个体的迁移率相同且无疾病引起的死亡的情况下，当R0 > 1，地方性均衡是唯一的并且全局渐近稳定。进行数值模拟以显示停留时间和迁移率对疾病流行率的影响。