中山大学学报(自然科学版) ›› 2020, Vol. 59 ›› Issue (4): 158-167.doi: 10.13471/j.cnki.acta.snus.2019.07.17.2019A058

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一类具有潜伏感染细胞的时滞病毒感染模型

杨俊仙, 于淑妹   

  1. 安徽农业大学理学院,安徽 合肥 230036
  • 收稿日期:2019-07-17 出版日期:2020-07-25 发布日期:2020-07-25
  • 通讯作者: 于淑妹(1983年生),女;研究方向:微分方程、生物数学;E-mail:yushumei@ahau.edu.cn
  • 作者简介:杨俊仙(1976年生),女;研究方向:微分方程、生物数学;E-mail:yangjunxian@ahau.edu.cn

A delayed virus infection model with latent infection cells 

YANG Junxian, YU Shumei   

  1. School of ScienceAnhui Agricultural UniversityHefei 230036China
  • Received:2019-07-17 Online:2020-07-25 Published:2020-07-25

摘要: 提出了一类具有潜伏感染细胞的时滞病毒感染模型,定义了基本再生数,给出了每个平衡点存在的充分条件。通过构造 Lyapunov函数和利用 LaSalle不变集原理,证明了当基本再生数小于或等于 1时,无病平衡点是全局渐近稳定的;当基本再生数大于 1时,慢性感染平衡点是全局渐近稳定的,但无病平衡点是不稳定的。结论表明, 模型中的潜伏感染时滞、内时滞和病毒产生时滞并不影响模型的全局稳定性,并通过数值模拟验证了所得理论结果。

关键词: 潜伏感染细胞, Beddington-DeAngelis发生率, 时滞, 病毒感染模型, 全局稳定性

Abstract: A class of delayed virus infection models with latently infected cells are investigated. The basic reproduction number is defined, and the sufficient conditions for the existence of each feasible equilibrium are given. By using Lyapunov functionals and LaSalle's invariance principle, it is proved that when the basic reproduction number is less than or equal to unity, the infection-free equilibrium is globally asymptotically stable; when the basic reproduction number is greater than unity, the chronic-infection equilibrium is globally asymptotically stable, but the infection-free equilibrium is unstable. The results show that the latently infected delay, the intracellular delay, and virus production period in the model do not affect the global stability of the model, and numerical simulations are carried out to illustrate the theoretical results.

Key words: latently infected cells,  , Beddington-DeAngelis incidence,  , delay,  , virus infection model,  , global stability

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