A singularly perturbed HIV model with treatment and antigenic variation

Nara Bobko; Jorge P. Zubelli

doi:10.3934/mbe.2015.12.1

Mathematical Biosciences and Engineering, 2015, 12(1): 1-21. doi: 10.3934/mbe.2015.12.1. Primary: 92C50; Secondary: 34E13, 92C60.

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A singularly perturbed HIV model with treatment and antigenic variation

Nara Bobko, Jorge P. Zubelli

1. Instituto Nacional de Matemática Pura e Aplicada, Rio do Janeiro, RJ 22460-320

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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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Keywords: immune response; Lyapunov functions.; Global stability; multiscale analysis; HIV; mutation

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

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