具有饱和发生率和分布时滞的HIV免疫模型的稳定性  

Stability of an HIV Immune Model with Saturation Incidence and Distributed Delays

作　　者：宋冰 张育茹 桑媛 张龙[1] SONG Bing;ZHANG Yuru;SANG Yuan;ZHANG Long(College of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《广西师范大学学报（自然科学版）》2023年第2期106-117,共12页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11861065,12261087);新疆维吾尔自治区自然科学基金(2019D01C076);新疆维吾尔自治区应用数学重点实验室开放课题(2021D04014);新疆维吾尔自治区高校科研重点项目(XJEDU2021I002);新疆维吾尔自治区优秀青年科技创新人才项目(2019Q017)。

摘　　要：本文提出一类具有饱和发生率和抗体免疫反应的细胞内感染的时滞HIV感染模型,包括未感染细胞、潜伏感染细胞、感染细胞、游离HIV病毒和CTL免疫反应细胞。考虑4种时滞:潜伏感染时滞、细胞内时滞、感染细胞转化病毒时滞和CTL免疫反应时滞。定义2个阈值:感染基本再生数R 0和CTL免疫再生数R 1,得到了模型的3类平衡点:无感染平衡点、免疫灭活感染平衡点和免疫激活感染平衡点。通过分析特征方程、构造Lyapunov函数和LaSalle不变原理,建立了各平衡点局部以及全局渐近稳定性的判定准则。A delayed HIV model of intracellular infection with saturated infection rate and antibody immune response is presented here.Including uninfected cells,latently infected cells,infected cells,free HIV virus,and CTLs.The following four delays are considered:latently infected delay,intracellular delay,the time lag between an infected cell and a virus,and CTL response delay.Two threshold conditions are defined:infection reproduction number R 0 and CTL immunity-activated reproduction number R 1.It obtains three equilibria of this model:disease-free equilibrium,immune-free infection equilibrium and immune-activated equilibrium.By analyzing the characteristic equation,Lyapunov function and LaSalle’s invariance principle,the locally and globally asymptotic stable criteria of each equilibrium are established.

关 键 词：CTL免疫反应 分布时滞 全局渐近稳定 LYAPUNOV函数 饱和发生率 

分 类 号：O175[理学—数学]