一类具有Beddington-DeAngelis功能性反应的时滞HIV模型全局性分析

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摘要：

研究了一类四维的HIV传染病动力学时滞模型,模型使用的是Beddington-DeAngelis功能性反应形式的非线性发生率.考虑了受感染细胞CD4-T细胞的潜伏特性,也就是说被感染后没有传染性,只有被激活后才产生病毒细胞.通过构建Lyapunov函数,利用LaSalle不变集原理,给出了疾病平衡点,包括无病平衡点和地方性平衡点的全局渐近稳定.证明了当基本再生数小于1,无病平衡点全局渐近稳定;当基本再生数大于1,地方性平衡点全局也是渐近稳定.还考虑了具有n阶潜伏阶段的模型,并给出了平衡点的全局渐近稳定.

This paper investigates the global stability of an HIV dynamics model with discrete delays incorporating Bed- dington-DeAngelis functional response infection rate. An eclipse stage of infected cells（i, e. latently infected cells）, not yet pro- ducing virus, is included in our model. We consider nonnegativity, boundedness of solutions and global asymptotic stability of the uninfected and infected equilibria （steady states） by constructing suitable Lyapunov functionals and using LaSalle invariance principle. It is proved that if the basic reproduction number R0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The results show that the global dynamics are completely determined by the basic reproduction number R0. That is, time delay has no effect on the global asymptotic stability of our model. What is more, we develop and analyze an n-stage-structured HIV model including Beddington-DeAngelis functional response. We also prove the global asymptotical stability of two equilibria by con- structing suitable Lyapunov functionals.

作者：

刘永奇熊建栋

机构地区：

北京师范大学珠海分校应用数学学院 betway官方app 数学与信息科学学院

出处：

《betway官方app 学报：自然科学版》 CAS 北大核心 2016年第4期14-20,共7页

基金：

国家社会科学基金(14BKS121) 珠海市哲学社科十二五规划课题(2015YB115) 河南省科技攻关计划(162102210265) betway官方app 博士科研启动课题(qd13045)

关键词：

HIV模型全局稳定分析 BEDDINGTON-DEANGELIS功能性反应时滞模型

HIV model global stability analysis Beddington-DeAngelis functional response discrete intracellular delays

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