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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 1: 1-21. doi: 10.3934/mbe.2015.12.1
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A singularly perturbed HIV model with treatment and antigenic variation

  • 1.
    Instituto Nacional de Matemática Pura e Aplicada, Rio do Janeiro, RJ 22460-320
  • Received: 01 July 2014 Accepted: 29 June 2018 Published: 01 December 2014

  • MSC : Primary: 92C50; Secondary: 34E13, 92C60.

  • We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.

    Citation: Nara Bobko, Jorge P. Zubelli. A singularly perturbed HIV model with treatment and antigenic variation[J]. Mathematical Biosciences and Engineering, 2015, 12(1): 1-21. doi: 10.3934/mbe.2015.12.1

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  • We study the long term dynamics and the multiscale aspects of a within-host HIV model that takes into account both mutation and treatment with enzyme inhibitors. This model generalizes a number of other models that have been extensively used to describe the HIV dynamics. Since the free virus dynamics occur on a much faster time-scale than cell dynamics, the model has two intrinsic time scales and should be viewed as a singularly perturbed system. Using Tikhonov's theorem we prove that the model can be approximated by a lower dimensional nonlinear model. Furthermore, we show that this reduced system is globally asymptotically stable by using Lyapunov's stability theory.


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  • This article has been cited by:

    1. Cameron J. Browne, Hal L. Smith, Dynamics of virus and immune response in multi-epitope network, 2018, 77, 0303-6812, 1833, 10.1007/s00285-018-1224-z
    2. Nara Bobko, Jorge Passamani Zubelli, Estimation of the HIV-1 infection rate and the basic reproductive ratio, 2018, 37, 0101-8205, 3267, 10.1007/s40314-017-0500-7
    3. Tongqian Zhang, Junling Wang, Yi Song, Zhichao Jiang, Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells, 2020, 2020, 1076-2787, 1, 10.1155/2020/2313102
    4. Cameron Browne, Global properties of nested network model with application to multi-epitope HIV/CTL dynamics, 2017, 75, 0303-6812, 1025, 10.1007/s00285-017-1102-0
    5. Cameron J. Browne, Fadoua Yahia, Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape, 2023, 86, 0303-6812, 10.1007/s00285-022-01843-y
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  • © 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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