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.
DOI : 10.5802/msia.3
Keywords: HIV modeling, antigenic variation, mutation, immune response
Dubois, François 1 ; Le Meur, Hervé V.J. 2 ; Reiss, Claude 3
@article{MSIA_2010__3_1_1_0,
author = {Dubois, Fran\c{c}ois and Le Meur, Herv\'e V.J. and Reiss, Claude},
title = {Mathematical modeling of antigenicity for {HIV} dynamics},
journal = {MathematicS In Action},
pages = {1--35},
year = {2010},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {3},
number = {1},
doi = {10.5802/msia.3},
mrnumber = {2647440},
zbl = {1197.34072},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/msia.3/}
}
TY - JOUR AU - Dubois, François AU - Le Meur, Hervé V.J. AU - Reiss, Claude TI - Mathematical modeling of antigenicity for HIV dynamics JO - MathematicS In Action PY - 2010 SP - 1 EP - 35 VL - 3 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - http://geodesic.mathdoc.fr/articles/10.5802/msia.3/ DO - 10.5802/msia.3 LA - en ID - MSIA_2010__3_1_1_0 ER -
%0 Journal Article %A Dubois, François %A Le Meur, Hervé V.J. %A Reiss, Claude %T Mathematical modeling of antigenicity for HIV dynamics %J MathematicS In Action %D 2010 %P 1-35 %V 3 %N 1 %I Société de Mathématiques Appliquées et Industrielles %U http://geodesic.mathdoc.fr/articles/10.5802/msia.3/ %R 10.5802/msia.3 %G en %F MSIA_2010__3_1_1_0
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
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