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


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