广西师范大学学报（自然科学版） ›› 2023, Vol. 41 ›› Issue (2): 106-117.doi: 10.16088/j.issn.1001-6600.2022033102

• 研究论文 • 上一篇    下一篇

具有饱和发生率和分布时滞的HIV免疫模型的稳定性

宋冰, 张育茹, 桑媛, 张龙*   

  1. 新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830046
  • 收稿日期:2022-03-31 修回日期:2022-05-20 出版日期:2023-03-25 发布日期:2023-04-25
  • 通讯作者: 张龙(1977—),男,新疆伊宁人,新疆大学教授,博导。E-mail:longzhang_xj@sohu.com
  • 基金资助:
    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)

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

SONG Bing, ZHANG Yuru, SANG Yuan, ZHANG Long*   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830046, China
  • Received:2022-03-31 Revised:2022-05-20 Online:2023-03-25 Published:2023-04-25

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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R0和CTL免疫再生数 R1,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。

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

Abstract: 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 R0 and CTL immunity-activated reproduction number R1. 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.

Key words: CTL immune response, distributed delay, globally asymptotically stable, Lyapunov function, saturated infection rate

中图分类号: 

  • O175
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