Global Stability of Steady Solutions for a Model in Virus Dynamics

Hermano Frid; Pierre-Emmanuel Jabin; Benoît Perthame

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 4, page 709-723
  • ISSN: 0764-583X

Abstract

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We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical and theoretical arguments, we also examine how, releasing these assumptions, the system can blow-up.

How to cite

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Frid, Hermano, Jabin, Pierre-Emmanuel, and Perthame, Benoît. "Global Stability of Steady Solutions for a Model in Virus Dynamics." ESAIM: Mathematical Modelling and Numerical Analysis 37.4 (2010): 709-723. <http://eudml.org/doc/194187>.

@article{Frid2010,
abstract = { We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical and theoretical arguments, we also examine how, releasing these assumptions, the system can blow-up. },
author = {Frid, Hermano, Jabin, Pierre-Emmanuel, Perthame, Benoît},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Virus dynamics; population dynamics; genetics; nonlinear integro-differential equations; nonlinear ordinary differential equations; dynamical systems in statistical mechanics; immunology; evolution theory.; nonlinear integro-differential equations; nonlinear ordinary differential equations; dynamical systems in statistical mechanics; evolution theory},
language = {eng},
month = {3},
number = {4},
pages = {709-723},
publisher = {EDP Sciences},
title = {Global Stability of Steady Solutions for a Model in Virus Dynamics},
url = {http://eudml.org/doc/194187},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Frid, Hermano
AU - Jabin, Pierre-Emmanuel
AU - Perthame, Benoît
TI - Global Stability of Steady Solutions for a Model in Virus Dynamics
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 4
SP - 709
EP - 723
AB - We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical and theoretical arguments, we also examine how, releasing these assumptions, the system can blow-up.
LA - eng
KW - Virus dynamics; population dynamics; genetics; nonlinear integro-differential equations; nonlinear ordinary differential equations; dynamical systems in statistical mechanics; immunology; evolution theory.; nonlinear integro-differential equations; nonlinear ordinary differential equations; dynamical systems in statistical mechanics; evolution theory
UR - http://eudml.org/doc/194187
ER -

References

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  12. C.H. Taubes, Modeling lectures on differential equations in biology. Prentice-Hall (2001).  
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