一类具有CTL免疫反应和免疫损害的HIV感染动力学模型的稳定性分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1592-1600.

• 论文 • 上一篇

一类具有CTL免疫反应和免疫损害的HIV感染动力学模型的稳定性分析

邓萌,徐瑞*()

^{山西大学复杂系统研究所太原 030006}

收稿日期:2021-10-22 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 徐瑞 E-mail:rxu88@163.com; xurui@sxu.edu.cn
基金资助:
国家自然科学基金(11871316)

Stability Analysis of an HIV Infection Dynamic Model with CTL Immune Response and Immune Impairment

Meng Deng,Rui Xu*()

^{Complex Systems Research Center, Shanxi University, Taiyuan 030006}

Received:2021-10-22 Online:2022-10-26 Published:2022-09-30
Contact: Rui Xu E-mail:rxu88@163.com; xurui@sxu.edu.cn
Supported by:
the NSFC(11871316)

摘要/Abstract

摘要：

该文研究了一类具有饱和发生率、CTL免疫反应、免疫损害和胞内时滞的HIV感染动力学模型. 利用下一代矩阵法得到了病毒感染基本再生率$ \Re_{0} $. 通过分析相应特征方程根的分布证明了: 当$ \Re_{0}<1 $时, 系统的病毒未感染平衡点是局部渐近稳定的; 当$ \Re_{0}>1 $时, 病毒感染平衡点是局部渐近稳定的. 通过构造适当的Lyapunov泛函和应用LaSalle不变性原理证明了: 当$ \Re_{0}<1 $时, 病毒未感染平衡点是全局渐近稳定的; 当$ \Re_{0}>1 $时, 病毒感染平衡点是全局渐近稳定的. 通过对病毒感染基本再生率$ \Re_{0} $进行参数敏感性分析, 确定了影响$ \Re_{0} $的关键参数.

关键词: HIV感染, 胞内时滞, CTL免疫反应, 免疫损害, 稳定性分析

Abstract:

In this paper, we study an HIV infection model with saturation incidence rate, CTL immune response, immune impairment, and intracellular delay. Firstly, the basic reproduction ratio $ \Re_{0} $ of virus infection is obtained by using the next generation matrix method. Secondly, the local stability of feasible equilibria is proved by analyzing the distribution of the root of the corresponding characteristic equations. By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle, we prove that when $ \Re_{0}<1 $, the virus infection-free equilibrium is globally asymptotically stable; when $ \Re_ {0}>1 $, the immunity-inactivated equilibrium is globally asymptotically stable. Finally, the parameter with critical influence on $ \Re_{0} $ is determined by the parameter sensitivity analysis.

Key words: HIV infection, Intracellular delay, CTL immune response, Immune impairment, Stability analysis

中图分类号:

O175.1

邓萌,徐瑞. 一类具有CTL免疫反应和免疫损害的HIV感染动力学模型的稳定性分析[J]. 数学物理学报, 2022, 42(5): 1592-1600.

Meng Deng,Rui Xu. Stability Analysis of an HIV Infection Dynamic Model with CTL Immune Response and Immune Impairment[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1592-1600.

图/表 1

参考文献 17

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一类具有CTL免疫反应和免疫损害的HIV感染动力学模型的稳定性分析

Stability Analysis of an HIV Infection Dynamic Model with CTL Immune Response and Immune Impairment

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