Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T15:43:37.939Z Has data issue: false hasContentIssue false
  • English
  • Français

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
*
[email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)