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

Content Provider	IET Digital Library
Author	Sun, Qilin Min, Lequan Kuang, Yang
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 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.
Starting Page	95
Ending Page	103
Page Count	9
ISSN	17518849
Volume Number	9
e-ISSN	17518857
Issue Number	Issue 3, Jun (2015)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-syb/9/3
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-syb.2014.0046
Journal	IET Systems Biology
Publisher Date	2015-04-10
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Blood Cellular Biophysics Differential Equation (numerical Analysis) Differential Equation Model Drugs Endemic Infection Equilibrium Point Endemic Infection State Forward Bifurcation Global Stability HIV HIV Drug Resistance Database Infection-free Equilibrium Point Infection-free State LaSalle Invariance Principle Lyapunov Function Lyapunov Method Mean HIV RNA Levels Microorganisms Modified Human Immunodeficiency Virus Infection Model Numerical Approximation And Analysis Patient Care And Treatment Patient Treatment Physics of Subcellular Structure Plasma Total CD4+ T Cell Counts RNA Saturated Infection Rate
Content Type	Text
Resource Type	Article
Subject	Cell Biology Genetics Molecular Biology Modeling and Simulation Biotechnology

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