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Global Asymptotic Stability of Equilibriain Models for Virus Dynamics

Published online by Cambridge University Press:  23 October 2008

J. Prüss ,
R. Zacher  and
R. Schnaubelt
J. Prüss
Affiliation:
Institut für Mathematik, Martin-Luther-Universität, D-06099 Halle, Germany
R. Zacher
Affiliation:
Institut für Mathematik, Martin-Luther-Universität, D-06099 Halle, Germany
R. Schnaubelt*
Affiliation:
Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
*
jan.pruess@mathematik.uni-halle.de
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Abstract

In this paper several models in virus dynamics with and without immune response arediscussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses andT-cells is included. It is shown that, depending on the value of the basic reproductive number R0of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then thevirus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibriumwhich takes over this property.

Keywords

May-Nowak modelimmune responsediffusionreproduction numberglobal asymptoticstabilityLyapunov function
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 7: Special issue dedicated to Glenn Webb , 2008 , pp. 126 - 142
Copyright
© EDP Sciences, 2008

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