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Global Stability of Steady Solutions for a Modelin 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 systemin which virus are able to undergo mutations and are in competitionwith leukocytes. These mutations are related to several other concepts which havebeen proposed in the literature like those of shape or ofvirulence – a continuous notion. For a given species, the system admits aglobally attractive critical point. We prove that mutations do not affect thispicture 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 equationsnonlinearordinary differential equationsdynamical systems in statisticalmechanicsimmunologyevolution theory.

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