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Mathematical Biosciences and Engineering

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

  • 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: 01 December 2009 Accepted: 29 June 2018 Published: 01 June 2010

  • MSC : 34K20, 92D30.

  • 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.

    Citation: Shengqiang Liu, Lin Wang. Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy[J]. Mathematical Biosciences and Engineering, 2010, 7(3): 675-685. doi: 10.3934/mbe.2010.7.675

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  • 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.


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