A singularly perturbed HIV model with treatment and antigenic variation

  • 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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