| Issue |
Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008
Special issue dedicated to Glenn Webb
|
|
|---|---|---|
| Page(s) | 126 - 142 | |
| DOI | https://doi.org/10.1051/mmnp:2008045 | |
| Published online | 23 October 2008 | |
Global Asymptotic Stability of Equilibria in Models for Virus Dynamics
1
Institut für Mathematik, Martin-Luther-Universität, D-06099 Halle, Germany
2
Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Corresponding author: jan.pruess@mathematik.uni-halle.de
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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