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 by a specific variable. We model two processes in the interaction of the immune system and the viral strains. On the one hand, the presence of a given viral quasi-species generates antigenically adapted lymphocytes. On the other hand, the lymphocytes kill viruses for which they have been designed. We consider also the mutation and multiplication of the virus. A new infection term is derived. So as to compare our system of differential equations with some well-knowns models, we study all of them mathematically 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 differences. We prove 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.