Global dynamics of a class of HIV-1 infection models with latently infected cells
Articles
Haibin Wang
Shijiazhuang Mechanical Engineering College, China
Rui Xu
Shijiazhuang Mechanical Engineering College, China
Zhaowei Wang
Shijiazhuang Mechanical Engineering College, China
Hui Chen
Shijiazhuang Mechanical Engineering College, China
Published 2015-01-20
https://doi.org/10.15388/NA.2015.1.2
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Keywords

HIV-1 infection model
nonlinear infection rate
global stability
LaSalle's invariance principle

How to Cite

Wang H., Xu R., Wang Z. and Chen H. (2015) “Global dynamics of a class of HIV-1 infection models with latently infected cells”, Nonlinear Analysis: Modelling and Control, 20(1), pp. 21-37. doi: 10.15388/NA.2015.1.2.

Abstract

In this paper, the global dynamics of a class of HIV-1 infection models with different infection rates and latently infected cells are investigated. We first modify the basic virus infection model and propose two models with bilinear infection rate and saturation infection rate, respectively, which take HIV-1 latency into consideration, and then study a model with a general nonlinear infection rate. By using proper Lyapunov functions and LaSalle's invariance principle, it is proved that in the first two models, if the basic reproduction ratio is less than unity, each of the infection-free equilibria is globally asymptotically stable; if the basic reproduction ratio is greater than unity, each of the chronic-infection equilibria is globally asymptotically stable. For the last model with general nonlinear infection rate, we obtain sufficient conditions for the global stability of both the infection-free and chronic-infection equilibria of the model.

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