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Zbl 1225.92022
Souza, Max O.; Zubelli, Jorge P.
Global stability for a class of virus models with cytotoxic T Lymphocyte immune response and antigenic variation. (English)
[J] Bull. Math. Biol. 73, No. 3, 609-625 (2011). ISSN 0092-8240; ISSN 1522-9602/e

Summary: 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.

MSC 2000:: *92C50 Medical appl. of mathematical biology
92C60 Medical epidemiology
34D23 Global stability
34D05 Asymptotic stability of ODE
37N25 Dynamical systems in biology

Keywords: HIV; population dynamics; immune response; mutation; Lyapunov functions

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Zentralblatt MATH Berlin [Germany]