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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (4): 693-709.doi: 10.3969/j.issn.1005-3085.2024.04.007

• • 上一篇    下一篇

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

苗  卉1,  滕志东2   

  1. 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
  • 收稿日期:2022-02-03 接受日期:2023-07-13 出版日期:2024-08-15
  • 通讯作者: 滕志东 E-mail: zhidong@xju.edu.cn
  • 基金资助:
    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).

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

MIAO Hui1,  TENG Zhidong2   

  1. 1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006
    2. College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011
  • Received:2022-02-03 Accepted:2023-07-13 Online:2024-08-15
  • Contact: Z. Teng. E-mail address: zhidong@xju.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11901363; 12371504); the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (2021L279); the Young Talent Program for Scholars at Shanxi University of Finance and Economics (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$\tau_3$作为分支参数，可引起两个平衡点$\widetilde{E}_2$和$\widetilde{E}_4$失稳，并产生Hopf分支。结果说明$\tau_3$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$\widetilde{E}_2$和$\widetilde{E}_4$的稳定性影响。

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

Abstract:

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 $\tau_3$ as a bifurcation parameter, we show that $\tau_3$ may destabilize two equilibria $\widetilde{E}_2$ and $\widetilde{E}_4$ leading to Hopf bifurcation. The results indicate that $\tau_3$ 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 $\widetilde{E}_2$ and $\widetilde{E}_4$.

Key words: HIV infection model, adaptive immune response, cell-to-cell, Lyapunov functionals, global stability

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