• 数学 •

### 一类具有潜伏感染细胞的时滞HIV-1传染病模型

1. 安徽农业大学 理学院, 合肥 230036
• 收稿日期:2018-05-16 出版日期:2019-07-25 发布日期:2019-07-18
• 通讯作者: 谢宝英,女,讲师,研究方向为应用数学.E-mail:xieby1014@163.com. E-mail:xieby1014@163.com
• 作者简介:杨俊仙,女,副教授,研究方向为微分方程、生物数学.E-mail:yangjunxian1976@126.com.
• 基金资助:
国家自然科学基金（11201002）；安徽高校自然科学研究项目（KJ2017A815）；安徽省教育厅资助项目（KJ2011Z130）

### A class of delayed HIV-1 infection models with latently infected cells

YANG Jun-xian, XIE Bao-ying

1. School of Science, Anhui Agricultural University, Hefei 230036, China
• Received:2018-05-16 Online:2019-07-25 Published:2019-07-18

Abstract: A class of delayed HIV-1 infection models with latently infected cells was proposed. The basic reproductive number R0 was defined, and the existence conditions of disease-free equilibrium P0(x0, 0, 0, 0) and chronic-infection equilibrium P*(x*, ω*, y*, v*) were given. First, the local asymptotic stability of infection-free equilibrium and chronicinfection equilibrium was obtained by the linearization method. Further, by constructing the corresponding Lyapunov functions and using LaSalle's invariant principle, it was proved that when the basic reproductive number R0 was less than or equal to unity, the infection-free equilibrium P0(x0, 0, 0, 0) was globally asymptotically stable; moreover, when the basic reproductive number R0 was greater than unity, the chronic-infective equilibrium P*(x*, ω*, y*, v*) was globally asymptotically stable, but the infection-free equilibrium P0(x0, 0, 0, 0) was unstable. The results showed that a latently infected delay and an intracellular delay did not affect the global stability of the model, and numerical simulations were carried out to illustrate the theoretical results.