Mathematical modeling of antigenicity for HIV dynamics

François Dubois[1]; Hervé V.J. Le Meur[2]; Claude Reiss[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 (2010)

  • Volume: 3, Issue: 1, page 1-35
  • ISSN: 2102-5754

Abstract

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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.

How to cite

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Dubois, François, Le Meur, Hervé V.J., and Reiss, Claude. "Mathematical modeling of antigenicity for HIV dynamics." MathematicS In Action 3.1 (2010): 1-35. <http://eudml.org/doc/116435>.

@article{Dubois2010,
abstract = {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.},
affiliation = {Conservatoire National des Arts et Métiers, EA 3196, Paris, France ; univ Paris-Sud, Orsay cedex, F-91405.; CNRS, Laboratoire de Mathématiques d’Orsay, Orsay cedex, F-91405; univ Paris-Sud, Orsay cedex, F-91405.; Vigilent Technologies, 38160 Chevrières, France.},
author = {Dubois, François, Le Meur, Hervé V.J., Reiss, Claude},
journal = {MathematicS In Action},
keywords = {HIV modeling; antigenic variation; mutation; immune response},
language = {eng},
number = {1},
pages = {1-35},
publisher = {Société de Mathématiques Appliquées et Industrielles},
title = {Mathematical modeling of antigenicity for HIV dynamics},
url = {http://eudml.org/doc/116435},
volume = {3},
year = {2010},
}

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
PB - Société de Mathématiques Appliquées et Industrielles
VL - 3
IS - 1
SP - 1
EP - 35
AB - 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.
LA - eng
KW - HIV modeling; antigenic variation; mutation; immune response
UR - http://eudml.org/doc/116435
ER -

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