Mathematical Modelling of Natural Phenomena

Research Article

Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

J. Prüssa1, R. Zachera1 and R. Schnaubelta2

a1 Institut für Mathematik, Martin-Luther-Universität, D-06099 Halle, Germany

a2 Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany

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.

(Online publication October 23 2008)

Key Words:

  • May-Nowak model;
  • immune response;
  • diffusion;
  • reproduction number;
  • global asymptotic stability;
  • Lyapunov function

Mathematics Subject Classification:

  • 35B40;
  • 92D30
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