Global Stability of  Infection-free State and Endemic Infection State of An Amended HIV Infection Model

SUN Qi-Lin; Min Le-Quan; CHEN Xiao

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Global Stability of Infection-free State and Endemic Infection State of An Amended HIV Infection Model

SUN Qi-Lin 1 #,Min Le-Quan 2 *,CHEN Xiao 1

1.School of Automation and Electrical Engineering, University of Science andTechnology Beijing Beijing 100083

2.School of Automation and Electrical Engineering, University of Science and Technology Beijing Beijing 100083,School of Mathematics and Physics, University of Science and Technology Beijing Beijing 100083

*Correspondence author

#Submitted by

Subject:

Funding: National Natural Science Foundation of China （No.No.61074192）, and Doctoral Research Fundsof University of Science and Technology Beijing (USTB)（No.No.06108126）

Opened online: 5 February 2013

Accepted by: none

Citation: SUN Qi-Lin,Min Le-Quan,CHEN Xiao.Global Stability of Infection-free State and Endemic Infection State of An Amended HIV Infection Model[OL]. [ 5 February 2013] http://en.paper.edu.cn/en_releasepaper/content/4518830

We consider a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection-free equilibrium point and an endemic infection equilibrium point. Using LaSalle's invariance principle, we show that if the basic infection reproductive number $R_0$ of the model is less than one, then the infection-free equilibrium point of the model is globally asymptotically stable, otherwise the endemic infection equilibrium point of the model is globally asymptotically stable. Based on the clinic data from the HIV drug resistance database of StanfordUniversity, this paper simulates the dynamics of two group patients' anti-HIVinfection therapy. The simulation results show that thetreatments cannot make the two group patients' $R_0$ less than one,which can interpret why the two group patients were still at endemic infection state during the entire trail.

Keywords:differential equation model; basic infectionreproductive number; globally asymptotically stable; LaSalle'sinvariance principle; numericalsimulation.

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