  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.
