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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
  • 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

    Related Papers:

  • 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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    [1] Nature, 333 (1988), 514-519.
    [2] Proceedings of the Royal Society of London. Series B: Biological Sciences, 270 (2003), 1651-1657.
    [3] Mathematical Biosciences and Engineering, 10 (2013), 499-521.
    [4] (2010).
    [5] Proceedings of the National Academy of Sciences, 94 (1997), 6971-6976.
    [6] Proceedings of the National Academy of Sciences, 83 (1986), 9159-9163.
    [7] Ministério da Saúde, 2013.
    [8] Journal of Differential Equations, 31 (1979), 53-98.
    [9] JAIDS Journal of Acquired Immune Deficiency Syndromes, 7 (1994), 236-244.
    [10] PLoS computational biology, 9 (2013), e1002971, 12 pp.
    [11] Current HIV research, 2 (2004), 23-37.
    [12] Nature, 373 (1995), 123-126.
    [13] Cambridge University Press, 1998.
    [14] vol. 114, Springer New York, 1996.
    [15] AMS notices, 43 (1996), 191-202.
    [16] Bulletin of Mathematical Biology, 66 (2004), 879-883.
    [17] Proceedings of the Royal Society of London. Series B: Biological Sciences, 268 (2001), 847-854.
    [18] Journal of Clinical Investigation, 105 (2000), R1-R8.
    [19] Immunology and cell biology, 85 (2006), 6-15.
    [20] Mathematical Biosciences, 179 (2002), 73-94.
    [21] Oxford University Press, 2000.
    [22] Science, 272 (1996), 74-79.
    [23] (2012).
    [24] Mac Graw Hill, 1978.
    [25] Ph.D. thesis, IMPA, 2005.
    [26] Mathematical biosciences, 114 (1993), 81-125.
    [27] SIAM review, 41 (1999), 3-44.
    [28] The Hopkins HIV Report, 8 (1996), no. 3.
    [29] Nature Reviews Genetics, 5 (2004), 52-61.
    [30] Journal of molecular evolution, 40 (1995), 249-259.
    [31] no. Ed. 4, WB Saunders, 1995.
    [32] Ph.D. thesis, AIMS, 2012.
    [33] Nature Reviews Microbiology, 1 (2003), 181-190.
    [34] SIAM Journal on Applied Mathematics, 63 (2003), 1313-1327.
    [35] Science, 242 (1988), 1554-1557.
    [36] Journal of mathematical biology, 68 (2014), 1269-1293.
    [37] Bull. Math. Biol., 73 (2011), 609-625.
    [38] Journal of Theoretical Biology, 203 (2000), 285-301.
    [39] Journal of differential equations, 92 (1991), 252-281.
    [40] Springer-Verlag Berlin, 1984.
    [41] Moskva: Vysshaya Shkola, 1990 (Russian).
    [42] Advances in Complex Systems, 10 (2007), 495-503.
    [43] Dover Publications, Inc., New York, 1987.
    [44] (2013).
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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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