# Global stability of steady solutions for a model in virus dynamics

Hermano Frid; Pierre-Emmanuel Jabin; Benoît Perthame

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

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topFrid, Hermano, Jabin, Pierre-Emmanuel, and Perthame, Benoît. "Global stability of steady solutions for a model in virus dynamics." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.4 (2003): 709-723. <http://eudml.org/doc/245449>.

@article{Frid2003,

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 - Modélisation Mathématique et Analyse Numérique},

keywords = {virus dynamics; population dynamics; genetics; nonlinear integro-differential equations; nonlinear ordinary differential equations; dynamical systems in statistical mechanics; immunology; evolution theory; Virus dynamics},

language = {eng},

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/245449},

volume = {37},

year = {2003},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2003

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; Virus dynamics

UR - http://eudml.org/doc/245449

ER -

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