Open AccessGlobal stability of infection‐free state and endemic infection state of a modified human immunodeficiency virus infection model
Author(s) -
Sun Qilin,
Min Lequan,
Kuang Yang
Publication year - 2015
Publication title -
iet systems biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.367
H-Index - 50
eISSN - 1751-8857
pISSN - 1751-8849
DOI - 10.1049/iet-syb.2014.0046
Subject(s) - equilibrium point , lyapunov function , stability theory , human immunodeficiency virus (hiv) , invariance principle , basic reproduction number , virology , stability (learning theory) , mathematics , biology , differential equation , medicine , mathematical analysis , physics , computer science , population , linguistics , philosophy , environmental health , quantum mechanics , nonlinear system , machine learning
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 R 0 < 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 R 0 = 1. The basic reproductive number R 0 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.