In this paper, we formulate a stochastic model for hepatitis B virus transmission with the effect of fluctuation environment. We divide the total population into four different compartments, namely, the susceptible individuals in which the disease transmission rate is distributed by white noise, the acutely infected individuals in which the same perturbation occur, the chronically infected individuals and the recovered individuals. We use the stochastic Lyapunov function theory to construct a suitable stochastic Lyapunov function for the existence of positive solution. We also then establish the sufficient conditions for the hepatitis B extinction and the hepatitis B persistence. At the end numerical simulation is carried out by using the stochastic Runge–Kutta method to support our analytical findings.

本文在环境波动的影响下，建立了乙型肝炎病毒传播的随机模型。我们将总人口分为四个不同的区室，即，通过白噪声分布疾病传播率的易感人群，发生相同扰动的急性感染人群，慢性感染人群和恢复的人群。我们使用随机李雅普诺夫函数理论来构造适合于存在正解的随机李雅普诺夫函数。然后，我们还为乙型肝炎的灭绝和乙型肝炎的持久性建立了充分的条件。最后，使用随机的Runge-Kutta方法进行了数值模拟，以支持我们的分析结果。