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

Shengqiang Liu; Lin Wang

doi:10.3934/mbe.2010.7.675

Article Contents

2010, Volume 7, Issue 3: 675-685. Doi: 10.3934/mbe.2010.7.675

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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
2.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3

Received: November 30, 2009

Revised: March 31, 2010

Published: May 2010

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Abstract

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, 92D30.

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