American Institute of Mathematical Sciences

Advanced
2010, 7(3): 675-685. doi: 10.3934/mbe.2010.7.675

Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy

Shengqiang Liu 1, and  Lin Wang 2,

1. 

Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Harbin, 150080, China
2. 

Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Received  December 2009 Revised  April 2010 Published  June 2010

Global stability is analyzed for a general mathematical model of HIV-1 pathogenesis proposed by Nelson and Perelson [11]. The general model include two distributed intracellular delays and a combination therapy with a reverse transcriptase inhibitor and a protease inhibitor. It is shown that the model exhibits a threshold dynamics: if the basic reproduction number is less than or equal to one, then the HIV-1 infection is cleared from the T-cell population; whereas if the basic reproduction number is larger than one, then the HIV-1 infection persists and the viral concentration maintains at a constant level.
Keywords: HIV-1; Global stability; delay; steady state; Lyapunov functional..
Mathematics Subject Classification: 34K20, 92D3.
Citation: Shengqiang Liu, Lin Wang. Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy. Mathematical Biosciences & Engineering, 2010, 7 (3) : 675-685. doi: 10.3934/mbe.2010.7.675
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