In this paper, we are concerned with the global dynamical behavior of a multigroup SVIR epidemic model, which is formulated as a piecewise-deterministic Markov process. We first obtain sufficient criteria for extinction of the diseases. Then we establish sufficient criteria for persistence in the mean of the diseases. Moreover, in the case of persistence, we find a domain which is positive recurrence for the solution of the stochastic system by constructing an appropriate Lyapunov function with regime switching.

中文翻译：

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具有马尔可夫切换的多组 SVIR 流行病模型的全局动力学行为

在本文中，我们关注多组 SVIR 流行病模型的全局动态行为，该模型被表述为分段确定性马尔可夫过程。我们首先获得足够的疾病灭绝标准。然后我们为疾病的平均值建立足够的标准。此外，在持久性的情况下，我们通过构造具有状态切换的适当 Lyapunov 函数来找到随机系统解的正递归域。