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. 2015 Jun;9(3):95-103.
doi: 10.1049/iet-syb.2014.0046.

Global stability of infection-free state and endemic infection state of a modified human immunodeficiency virus infection model

Qilin Sun  1 , Lequan Min  2 , Yang Kuang  3
Affiliations

Global stability of infection-free state and endemic infection state of a modified human immunodeficiency virus infection model

Qilin Sun et al. IET Syst Biol. 2015 Jun.

Abstract

This study proposes 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 Lyapunov functions and LaSalle's invariance principle shows that if the model's basic reproductive number R0 < 1, the infection-free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R0 = 1. The basic reproductive number R0 of the modified model is independent of plasma total CD4⁺ T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas-De-León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients' anti-HIV infection treatments. The simulation results have shown that the first 4 weeks' treatments made the two group patients' R'0 < 1, respectively. After the period, drug resistance made the two group patients' R'0 > 1. The results explain why the two group patients' mean CD4⁺ T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.

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Figures

Fig. 1
Fig. 1
Forward bifurcation
Fig. 2
Fig. 2
Outcomes of the treatment efficacy of Group I; circles: clinical data; solid line: numerical simulation of (14) a Mean uninfected CD4+ T cell counts b Mean HIV RNA levels
Fig. 3
Fig. 3
Outcomes of the treatment efficacy of Group II; circles: clinical data; solid line: numerical simulation of (14) a Mean uninfected CD4+ T cell counts b Mean HIV RNA levels
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