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.
Mots clés : virus dynamics, population dynamics, genetics, nonlinear integro-differential equations, nonlinear ordinary differential equations, dynamical systems in statistical mechanics, immunology, evolution theory
@article{M2AN_2003__37_4_709_0,
author = {Frid, Hermano and Jabin, Pierre-Emmanuel and Perthame, Beno{\^\i}t},
title = {Global stability of steady solutions for a model in virus dynamics},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {709--723},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/m2an:2003045},
mrnumber = {2018439},
zbl = {1065.92013},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003045/}
}
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: Modélisation mathématique et analyse numérique PY - 2003 SP - 709 EP - 723 VL - 37 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003045/ DO - 10.1051/m2an:2003045 LA - en ID - M2AN_2003__37_4_709_0 ER -
%0 Journal Article %A Frid, Hermano %A Jabin, Pierre-Emmanuel %A Perthame, Benoît %T Global stability of steady solutions for a model in virus dynamics %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 709-723 %V 37 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003045/ %R 10.1051/m2an:2003045 %G en %F M2AN_2003__37_4_709_0
Frid, Hermano; Jabin, Pierre-Emmanuel; Perthame, Benoît. Global stability of steady solutions for a model in virus dynamics. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 4, pp. 709-723. doi : 10.1051/m2an:2003045. http://www.numdam.org/articles/10.1051/m2an:2003045/
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