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Mathematical modeling of antigenicity for HIV dynamics. (English) Zbl 1197.34072

Summary: This contribution is devoted to a new model of HIV multiplication. 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.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
92C60 Medical epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
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