一类CD4^+T细胞感染HIV病毒模型的全局稳定性  

Global Stability of a model for HIV Infection of CD4^+T Cells

作　　者：王丽丽[1] 徐瑞[1] 王志强[2] 

机构地区：[1]军械工程学院应用数学研究所 [2]河北省科学院应用数学研究所

出　　处：《生物数学学报》2013年第4期635-642,共8页Journal of Biomathematics

基　　金：国家自然科学基金资助项目(11071254);河北省自然科学基金(A2009001426)

摘　　要：研究了一类具有标准发生率的CD4^+T细胞感染HIV病毒模型的动力学性质.通过分析,得到了病毒消除与否的阈值一基本再生数.证明了当基本再生数小于1时,未感染病毒平衡点全局渐近稳定,病毒将在宿主体内被清除.当基本再生数大于1时,病毒将在宿主体内持续生存,进一步给出了病毒感染平衡点全局渐近稳定的条件.最后对所得结论进行了数值模拟.A mathematical model of virus infected by HIV of CD4＋T cells is investigated. The basic reproductive ratio which determines whether a virus is cleared or not is obtained. If the basic reproduction ratio is less than one, the infection-free equilibrium is global asymptoticMly stable, and the HIV virus is cleared from T-cell population. If the basic reproduction ratio is greater than one, the HIV infection persists. Further more, sufficient conditions are derived for the global stability of the chronic-infection equilibrium. At last, numerical simulations are carried out to illustrate the main result.

关 键 词：HIV感染 CD4+T细胞 标准发生率 

分 类 号：O175.13[理学—数学]