Geodesic
Global stability of steady solutions for a model in virus dynamics
ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 709-723.

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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.

DOI : 10.1051/m2an:2003045
Classification : 34A34, 34G20, 70K20, 92D25, 92D10, 37A60
Keywords: virus dynamics, population dynamics, genetics, nonlinear integro-differential equations, nonlinear ordinary differential equations, dynamical systems in statistical mechanics, immunology, evolution theory 
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Frid, Hermano; Jabin, Pierre-Emmanuel; Perthame, Benoît. Global stability of steady solutions for a model in virus dynamics. ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 709-723. doi : 10.1051/m2an:2003045. http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003045/

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