具有二阶扰动的乙型肝炎传染病模型平稳分布研究  

Study on the Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Second-Order Perturbation

作　　者：张艳敏 刘明鼎 孙荣庭[2] Zhang Yanmin;Liu Mingding;Sun Rongting(Qindao City University;Chang’an University)

机构地区：[1]青岛城市学院 [2]长安大学

出　　处：《哈尔滨师范大学自然科学学报》2024年第5期42-49,共8页Natural Science Journal of Harbin Normal University

基　　金：山东省本科高校研究项目(M2023185)

摘　　要：针对一类具有二阶非线性干扰的乙型肝炎病毒传播(hepatitis B virus,HBV)模型,完成了对模型正解全局唯一性的证明,并利用随机Lyapunov分析法以及Itô公式得到了该模型存在唯一遍历平稳分布的条件R_(0)^(S),以及病毒灭绝条件R_(1)^(S).因为存在二阶非线性扰动增加了模型的复杂性,所以构造的随机Lyapunov函数具有一定的创新性.最后证明了当R_(0)^(S)>1时,模型存在唯一遍历平稳分布,当R_(1)^(S)<1时,具有灭绝性.证明方法可以应用在类似的二阶非线性扰动模型中.For a class of stochastic hepatitis B epidemic model with second-order perturbation,the global uniqueness of positive solution is proved.Then,by using the stochastic Lyapunov analysis and Itôformula,the conditions for the existence of unique ergodic stationary distribution R_(0)^(S)and the extinction of the disease R_(1)^(S)are obtained.Because the model has second-order nonlinear perturbation,a novel stochastic Lyapunov function is constructed.Finally,it is proved that the model has a unique ergodic stationary distribution at R_(0)^(S)>1,and has extinction at R_(1)^(S)<1.The proof method can be applied to similar second-order nonlinear perturbation model.

关 键 词：乙型肝炎传染病模型 二阶扰动 LYAPUNOV函数 平稳分布 灭绝性 

分 类 号：R512.62[医药卫生—内科学]