In this paper, we discuss the global dynamics of a general susceptible-infected-recovered-susceptible (SIRS) epidemic model. By using LaSalle’s invariance principle and Lyapunov direct method, the global stability of equilibria is completely established. If there is no input of infectious individuals, the dynamical behaviors completely depend on the basic reproduction number. If there exists input of infectious individuals, the unique equilibrium of model is endemic equilibrium and is globally asymptotically stable. Once one place has imported a disease case, then it may become outbreak after that. Numerical simulations are presented to expound and complement our theoretical conclusions.

中文翻译：

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具有恒定移民的广义SIRS传染病模型的全局动力学。

在本文中，我们讨论了一般的易感者感染恢复易感性（SIRS）流行病模型的全局动力学。通过使用LaSalle不变性原理和Lyapunov直接方法，完全建立了全局均衡的稳定性。如果没有传染性个体的输入，则动力学行为完全取决于基本繁殖数。如果存在传染性个体的输入，则模型的唯一均衡是地方均衡，并且全局渐近稳定。一旦一个地方输入了一个疾病病例，则此后可能爆发。数值模拟被提出来解释和补充我们的理论结论。