Abstract In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not.

中文翻译：

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在家治疗的随机结核病传播模型的动力学

摘要 在本文中，我们考虑了具有两种治疗方式的随机结核病模型，即在家治疗和在医院治疗。首先，我们在疾病的均值中获得灭绝和持续存在的充分条件，然后在持续存在的情况下，我们通过构建合适的随机变量，为模型正解的遍历平稳分布的存在性和唯一性建立充分条件李雅普诺夫函数 理论结果表明，大白噪声有利于消除结核病地方病，而小白噪声则不然。