一类随机SWEIA艾滋病毒传播模型的动力学分析  

Dynamic analysis of an SWEIA HIV infection model with stochastic effects

作　　者：马怡婷 张太雷[1] 邓金超 Ma Yiting;Zhang Tailei;Deng Jinchao(School of Science,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学理学院,西安710064

出　　处：《河南师范大学学报（自然科学版）》2024年第2期41-50,共10页Journal of Henan Normal University(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划(2022JM-023)。

摘　　要：研究了一类具有随机效应的SWEIA艾滋病毒传播模型.首先,通过构造Lyapunov函数证明了确定性模型平衡点的全局渐近稳定性,利用停顿理论等方法证明了随机模型正解的全局存在唯一性与有界性;其次,分析了随机模型的解在相应确定性模型的无病平衡点与地方病平衡点附近的震荡行为,并得到了随机模型解的平均持续与灭绝性的充分条件;最后,通过数值模拟进一步显示了模型的动力学行为.An SWEIA HIV epidemic model with stochastic effects is studied.Firstly,the global asymptotic stability of the equilibrium of the deterministic model is proved by constructing Lyapunov function,and the global existence,uniqueness,and boundedness of the positive solution of the stochastic model are proved by using stopping time theory.Secondly,the oscillation behavior of the solution of the stochastic model around the disease-free equilibrium and endemic equilibrium of the corresponding deterministic model is analyzed,and the sufficient conditions for the mean persistence and extinction of the solution of the stochastic model are obtained.Finally,the numerical simulation further shows the dynamic behavior of the model.

关 键 词：随机模型 It?公式 震荡行为 持久性 灭绝性 

分 类 号：O175.1[理学—数学]