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Global Stability of Steady Solutions for a Model in Virus Dynamics

Published online by Cambridge University Press:  15 November 2003

Hermano Frid ,
Pierre-Emmanuel Jabin  and
Benoît Perthame
Hermano Frid
Affiliation:
Instituto de Matemática Pura e Aplicada – IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460-320, Brazil. hermano@impa.br.
Pierre-Emmanuel Jabin
Affiliation:
Département de Mathématiques et Applications, École Normale Supérieure de Paris, 45 rue d'Ulm, 75230 Paris Cedex 05, France. jabin@dma.ens.fr.
Benoît Perthame
Affiliation:
Département de Mathématiques et Applications, École Normale Supérieure de Paris, 45 rue d'Ulm, 75230 Paris Cedex 05, France. perthame@dma.ens.fr.
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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.

Keywords

Virus dynamicspopulation dynamicsgeneticsnonlinear integro-differential equationsnonlinear ordinary differential equationsdynamical systems in statistical mechanicsimmunologyevolution theory.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 709 - 723
Copyright
© EDP Sciences, SMAI, 2003

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