Global stability of a modified HIV infection model with saturation incidence

YANG Junxian; WANG Leihong

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Global stability of a modified HIV infection model with saturation incidence

更新时间：2023-12-11

- Global stability of a modified HIV infection model with saturation incidence
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 57, Issue 3, Pages: 64-69(2018)
- 作者机构：
  
  1. 安徽农业大学理学院,安徽,合肥,230036
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2018，
  
  Published Online：25 May 2018，
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YANG Junxian, WANG Leihong. Global stability of a modified HIV infection model with saturation incidence. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(3):64-69(2018)
DOI：

YANG Junxian, WANG Leihong. Global stability of a modified HIV infection model with saturation incidence. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 57(3):64-69(2018) DOI：

摘要

提出了一类具有饱和发生率的被修正HIV传染病模型。首先通过分析相应的特征方程，得到了无病平衡点E

0)和正平衡点E

)的局部渐近稳定性。进一步构造Lyapunov函数和利用LaSalle不变集原理，证明了当基本再生数R

1时

无病平衡点E

0)是全局渐近稳定的; 利用第二加性复合矩阵，证明了当基本再生数R

1时

正平衡点E

)是全局渐近稳定的。最后通过数值模拟，验证了所得主要理论结果。

Abstract

A modified HIV infection model with saturation incidence is studied. By analyzing the corresponding characteristic equations

the local stability of an infectionfree equilibrium E

0) and a positive equilibrium E

) is discussed. By using suitable Lyapunov functions and the LaSalle invariant principle

it is proved that if the basic reproductive number R

the infectionfree equilibrium E

0) is globally asymptotically stable. If the basic reproductive number R

by means of the second additive compound matrix

the globally asymptotical stability of the positive equilibrium E

) is obtained. Numerical simulations are carried out to illustrate the main theoretical results.

关键词

HIV传染病饱和发生率Lyapunov函数LaSalle不变集原理第二加性复合矩阵

Keywords

HIV infectionsaturation incidenceLyapunov functionLaSalle invariant principlethe second additive compound matrix

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