二阶随机扰动下HBV流行病模型全局正解的存在唯一性与平稳分布

Existence and uniqueness of the global positive solution and the stationary distribution of HBV epidemic model with second-order stochastic perturbation

提出一个二阶随机扰动下的乙型肝炎病毒(HBV)感染模型,并在垂直传播比例μωνC不被认为是新感染的条件下研究了该模型的动力学行为。首先,证明了该随机模型全局正解的存在唯一性。其次,通过构造合适的Lyapunov函数,证明了在Ros>1的情况下,该随机模型平稳分布的存在唯一性和遍历性,并且得到了一个当噪声等于0时与基本再生数R0相等的随机临界值Ros。

This study proposes a model of hepatitis B virus infection with second-order stochastic perturbation and analyzes the dynamic behavior of the model when the fraction of vertical transmissionμωνC is not taken into account as a new infection.Firstly,the existence and uniqueness of a global positive solution to the stochastic model are verified.Secondly,by creating a suitable Lyapunov function,this study proves that if R S 0>1,there exists an ergodic stationary distribution of the stochastic HBV model,and a random critical value R S 0 is derived that is equal to the basic reproduction number R 0 when the noise is equal to zero.