Global Asymptotic Stability of Equilibria in Models for Virus Dynamics
J. Prüss1, R. Zacher1 and R. Schnaubelt2
Institut für Mathematik, Martin-Luther-Universität, D-06099 Halle, Germany
2 Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Corresponding author: email@example.com
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