具有时滞和免疫反应的离散HIV感染模型的稳定性分析  

Stability Analysis of a Discrete HIV Infection Model withDelay and Immune Response

作　　者：雷学红 许云霞 LEI Xuehong;XU Yunxia(College of Science,Kaili University,Kaili 556011,China)

机构地区：[1]凯里学院理学院,贵州凯里556011

出　　处：《湖北民族大学学报（自然科学版）》2021年第3期291-298,共8页Journal of Hubei Minzu University:Natural Science Edition

基　　金：贵州省教育厅青年科技成长项目(黔教合KY字[2019]189);贵州省教育厅青年科技成长项目(黔教合KY字[2019]186).

摘　　要：本文考虑具有时滞和免疫反应的离散HIV感染模型,该模型采用非标准有限差分法(NSFD)对连续模型进行离散化.通过构造合适的Lyapunov函数和利用LaSalle's不变性原理,研究所给模型在无感染平衡点、无CTL平衡点及CTL平衡点处的全局稳定性.研究表明,该离散模型和原连续模型的解有一致的正性、有界性及稳定性等性质.最后,通过数值模拟验证了所得结论.In this paper,the discrete HIV infection model with delay and immune response is considered,by using nonstandard finite difference scheme to discretize the continuous model.By constructing the suitable Lyapunov function and using the LaSalle's invariance principle,the global stability of the given model at the infection-free equilibrium,the CTL-absent infection equilibrium and the CTL-present infection equilibrium are studied.The results show that the solution of the discrete model and the original continuous model have the consistent positiveness,boundedness and stability properties.Finally,numerical simulations are carried out to the theoretical results.

关 键 词：离散HIV模型 基本再生数 非标准有限差分方法 LYAPUNOV函数 

分 类 号：O175.1[理学—数学]