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Global Stability for a Class of Virus Models with Cytotoxic T Lymphocyte Immune Response and Antigenic Variation

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Abstract

We study the global stability of a class of models for in-vivo virus dynamics that take into account the Cytotoxic T Lymphocyte immune response and display antigenic variation. This class includes a number of models that have been extensively used to model HIV dynamics. We show that models in this class are globally asymptotically stable, under mild hypothesis, by using appropriate Lyapunov functions. We also characterise the stable equilibrium points for the entire biologically relevant parameter range. As a by-product, we are able to determine what is the diversity of the persistent strains.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidade Federal Fluminense, R. Mário Santos Braga, s/n, Niterói, RJ, 22240-120, Brazil

    Max O. Souza

  2. IMPA, Est. D. Castorina 110, Rio de Janeiro, RJ, 22460-320, Brazil

    Jorge P. Zubelli

Authors
  1. Max O. Souza
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  2. Jorge P. Zubelli
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Correspondence to Max O. Souza.

Additional information

The authors thank an anonymous referee for suggesting that an early version of Theorem 1 could be extended as presented here. MOS is partially supported by FAPERJ grants 170.382/2006 and 110.174/2009, and by CNPq grant 309616/2009-3. JPZ was supported by CNPq under grants 302161/2003-1 and 474085/2003-1.

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Souza, M.O., Zubelli, J.P. Global Stability for a Class of Virus Models with Cytotoxic T Lymphocyte Immune Response and Antigenic Variation. Bull Math Biol 73, 609–625 (2011). https://doi.org/10.1007/s11538-010-9543-2

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  • DOI: https://doi.org/10.1007/s11538-010-9543-2

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