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具有两种感染模式和免疫反应的多时滞HIV模型的动力学分析

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研究了基于游离病毒和细胞-细胞两种传播机制和适应性免疫的多时滞HIV动力学模型,计算出模型存在五个平衡点和五个基本再生数.通过构造适当的Lyapunov函数,得到了模型的五个平衡点全局渐近稳定的充分条件.发现将一个时滞τ3作为分支参数,可引起两个平衡点(E)2和(E)4失稳,并产生Hopf分支.结果说明τ3可导致病毒载量出现周期振荡和免疫反应可降低感染风险.最后利用数值模拟验证所得结论,并对比了不同时滞参数对(E)2和(E)4的稳定性影响.
Dynamics of Delayed HIV Model with Two Transmission Modes and Adaptive Immune Responses
A multi time delay HIV infection model with adaptive immune responses is pro-posed,in which both the virus-to-cell infection and the cell-to-cell transmission are considered.The existence of five equilibria and five basic reproduction numbers are calculated.By using the Lyapunov functionals,the sufficient conditions on the global stability of five equilibria are established.Using a time delay τ3 as a bifurcation parameter,we show that τ3 may destabilize two equilibria(E)2 and(E)4 leading to Hopf bifurcation.The results indicate that τ3 can lead to periodic oscillations in viral load and immune responses,which can reduce the risk of infection.Finally,numerical simulations are carried out to illustrate the corresponding theoretical results,and reveal the effects of different delay parameters on the stability of the equilibria (E)2 and (E)4.

HIV infection modeladaptive immune responsecell-to-cellLyapunov function-alsglobal stability

苗卉、滕志东

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山西财经大学应用数学学院,太原 030006

新疆医科大学医学工程技术学院,乌鲁木齐 830011

HIV感染模型 适应性免疫 细胞间感染 Lyapunov函数 全局稳定性

国家自然科学基金国家自然科学基金山西省高等学校科技创新计划山财学者优秀青年人才计划

11901363123715042021L279BY-Z01087

2024

工程数学学报
西安交通大学

工程数学学报

CSTPCD北大核心
影响因子:0.302
ISSN:1005-3085
年,卷(期):2024.41(4)