Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

J. Prüss; R. Zacher; R. Schnaubelt

Mathematical Modelling of Natural Phenomena (2008)

  • Volume: 3, Issue: 7, page 126-142
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Prüss, J., Zacher, R., and Schnaubelt, R.. "Global Asymptotic Stability of Equilibria in Models for Virus Dynamics." Mathematical Modelling of Natural Phenomena 3.7 (2008): 126-142. <http://eudml.org/doc/222370>.

@article{Prüss2008,
abstract = { 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. },
author = {Prüss, J., Zacher, R., Schnaubelt, R.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {May-Nowak model; immune response; diffusion; reproduction number; global asymptotic stability; Lyapunov function; global asymptotic stability},
language = {eng},
month = {10},
number = {7},
pages = {126-142},
publisher = {EDP Sciences},
title = {Global Asymptotic Stability of Equilibria in Models for Virus Dynamics},
url = {http://eudml.org/doc/222370},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Prüss, J.
AU - Zacher, R.
AU - Schnaubelt, R.
TI - Global Asymptotic Stability of Equilibria in Models for Virus Dynamics
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/10//
PB - EDP Sciences
VL - 3
IS - 7
SP - 126
EP - 142
AB - 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.
LA - eng
KW - May-Nowak model; immune response; diffusion; reproduction number; global asymptotic stability; Lyapunov function; global asymptotic stability
UR - http://eudml.org/doc/222370
ER -

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