In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

中文翻译：

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具有马尔可夫切换的随机狂犬病流行模型的动力学

在本文中，我们分析了一个受白噪声和电报噪声干扰的随机狂犬病流行模型。首先，我们证明了唯一全局正解的存在。其次，通过构造适当的 Lyapunov 函数，我们建立了模型正解的唯一遍历平稳分布存在的充分条件。然后我们为疾病的灭绝建立了充分的条件。最后，引入数值模拟来说明我们的理论结果。