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  

Dynamics of Delayed HIV Model with Two Transmission Modes and Adaptive Immune Responses

作　　者：苗卉 滕志东 MIAO Hui;TENG Zhidong(School of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006;College of Medical Engineering and Technology,Xinjiang Medical University,Urumqi 830011)

机构地区：[1]山西财经大学应用数学学院,太原030006 [2]新疆医科大学医学工程技术学院,乌鲁木齐830011

出　　处：《工程数学学报》2024年第4期693-709,共17页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11901363,12371504);山西省高等学校科技创新计划(2021L279);山财学者优秀青年人才计划(BY-Z01087).

摘　　要：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τ_(3)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τ_(3)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。A multi time delay HIV infection model with adaptive immune responses is proposed,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 τ_(3) as a bifurcation parameter,we show that τ_(3) may destabilize two equilibria E_(2) and E_(4) leading to Hopf bifurcation.The results indicate that τ_(3) 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).

关 键 词：HIV感染模型 适应性免疫 细胞间感染 LYAPUNOV函数 全局稳定性 

分 类 号：O29[理学—应用数学]