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Mathematical modeling of antigenicity for HIV dynamics

François Dubois;  Hervé V.J. Le Meur;  Claude Reiss — 2010

MathematicS In Action

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...

Isotropy conditions for lattice Boltzmann schemes. Application to D2Q9

Adeline Augier;  Francois Dubois;  Benjamin Graille — 2012

ESAIM: Proceedings

In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property of isotropy can be read through a group operation and then implies a sequence of relations on...

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