Issue Math. Model. Nat. Phenom. Volume 3, Number 7, 2008 Special issue dedicated to Glenn Webb Page(s) 126 - 142 DOI 10.1051/mmnp:2008045 Published online 23 October 2008

Math. Model. Nat. Phenom. Vol. 3, No. 7, 2008, pp. 126-142
DOI: 10.1051/mmnp:2008045

Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

J. Prüss¹, R. Zacher¹ and R. Schnaubelt<sup>2

1</sup>  Institut für Mathematik, Martin-Luther-Universität, D-06099 Halle, Germany
²  Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany

jan.pruess@mathematik.uni-halle.de

Published online: 23 October 2008

Abstract
In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R₀ of the virus, the corresponding equilibrium is globally asymptotically stable. If R₀ < 1 then the virus-free equilibrium has this property, and in case R₀ > 1 there is a unique disease equilibrium which takes over this property.

Mathematics Subject Classification. 35B40, 92D30

Key words: May-Nowak model -- immune response -- diffusion -- reproduction number -- global asymptotic stability -- Lyapunov function

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