In this article, a stochastic SACR hepatitis B epidemic model is taken to be under consideration. We develop a stochastic epidemic model by considering the effect of environmental fluctuation on the hepatitis B dynamics and distribute the transmission rate by white noise. Using the stochastic Lyapunov function theory, we have shown the existence and uniqueness of the global positive solution. The extinction and persistence for our proposed model are derived with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme in the last section for the verification of our theoretical results.

中文翻译：

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HBV传播的随机SACR流行模型

在本文中，考虑了随机SACR乙型肝炎流行模型。我们通过考虑环境波动对乙型肝炎动力学的影响开发了一个随机流行模型，并通过白噪声分布传播率。利用随机李雅普诺夫函数理论，我们证明了全局正解的存在性和唯一性。我们提出的模型的灭绝和持久性是在充分条件下推导出来的。在最后一节中使用一阶 Itô-Taylor 随机方案进行数值模拟，以验证我们的理论结果。