# 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

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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 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 -

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