Mathematical modeling of antigenicity for HIV dynamics

Dubois, François; Le Meur, Hervé V.J.; Reiss, Claude

doi:10.5802/msia.3

Dubois, François ¹ ; Le Meur, Hervé V.J.² ; Reiss, Claude ³

¹ Conservatoire National des Arts et Métiers, EA 3196, Paris, France ; univ Paris-Sud, Orsay cedex, F-91405.
² CNRS, Laboratoire de Mathématiques d’Orsay, Orsay cedex, F-91405; univ Paris-Sud, Orsay cedex, F-91405.
³ Vigilent Technologies, 38160 Chevrières, France.

MathematicS In Action, Tome 3 (2010) no. 1, pp. 1-35.

Résumé

This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define “antigenicity”, whether of the virus or of the adapted lymphocytes. We model the interaction of the immune system and the viral strains by two processes. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill only viruses for which they have been designed. We consider also the mutation and multiplication of the virus. An original infection term is derived.

So as to compare our system of differential equations with well-known models, we study some of them and compare their predictions to ours in the reduced case of only one antigenicity. In this particular case, our model does not yield any major qualitative difference. We prove mathematically that, in this case, our model is biologically consistent (positive fields) and has a unique continuous solution for long time evolution. In conclusion, this model improves the ability to simulate more advanced phases of the disease.

Publié le : 2010-04-26

MR Zbl

DOI : 10.5802/msia.3

Classification : 34-99, 65-05, 65Z05, 92B99, 92C50
Mots clés : HIV modeling, antigenic variation, mutation, immune response

Affiliations des auteurs :

Dubois, François ¹ ; Le Meur, Hervé V.J. ² ; Reiss, Claude ³

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Dubois, François; Le Meur, Hervé V.J.; Reiss, Claude. Mathematical modeling of antigenicity for HIV dynamics. MathematicS In Action, Tome 3 (2010) no. 1, pp. 1-35. doi : 10.5802/msia.3. http://www.numdam.org/articles/10.5802/msia.3/

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