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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 ›› 2022, Vol. 39 ›› Issue (5): 750-762.doi: 10.3969/j.issn.1005-3085.2022.05.006

• • 上一篇    下一篇

一类具有时滞的HIV感染模型的动力学性态

邢青红,   李   灿,   马慧莲,   郭尊光   

  1. 太原工业学院理学系，太原  030008
  • 出版日期:2022-10-15 发布日期:2022-12-15
  • 通讯作者: 郭尊光 E-mail: guozg@tit.edu.cn
  • 基金资助:
    山西省自然科学基金(201901D111322)；太原工业学院青年(后备)学科带头人支持计划(201808)；太原工业学院引进人才科研资助项目(2022KJ070).

Dynamic Behavior of an HIV Infection Model with Intracellular Delay

XING Qinghong,   LI Can,   MA Huilian,   GUO Zunguang   

  1. Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
  • Online:2022-10-15 Published:2022-12-15
  • Contact: Z. Guo. E-mail address: guozg@tit.edu.cn
  • Supported by:
    The Natural Science Foundation of Shanxi Province (201901D111322); the Program for the (Reserved) Discipline Leaders of Taiyuan Institute of Technology (201808); the Scientific Research Foundation of Taiyuan Institute of Technology (2022KJ070).

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摘要：

研究一类具有胞内时滞和饱和发生率的HIV感染动力学模型，通过计算得到了病毒感染的基本再生率。进而，通过分析特征方程根的分布，讨论了系统可行平衡点的局部渐近稳定性。根据构造的Lyapunov泛函，证明了当基本再生率小于1时，病毒未感染平衡点是全局渐近稳定的。利用无穷维动力系统的持续生存理论证明了当基本再生率大于1时，系统是一致持续生存的。最后，采用比较原理和单调迭代技巧，给出了病毒感染平衡点全局吸引的充分条件。

关键词: 胞内时滞, 饱和发生率, 病毒感染的基本再生率, 稳定性

Abstract:

An HIV infection dynamics model with intracellular delay is studied. The basic reproduction ratio is obtained by calculation. By analyzing the distribution of roots of the corresponding characteristic equations, the local stability of each of feasible equilibria is established. By constructing the suitable Lyapunov functional, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. From the persistence theory of infinite dimensional dynamic system, it shows that if the basic reproduction ratio is greater than unity, the system is uniformly persistent. According to the iteration technique and comparision arguments, the sufficient conditions are obtained for the global attractivity of the chronic infection equilibrium.

Key words: intracellular time delay, saturation incidence, the basic reproduction ratio, stability

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