Mathematical modeling of antigenicity for HIV dynamics
For HIV researchers, this model offers a framework to simulate advanced disease phases, but it is an incremental contribution as it does not demonstrate novel predictions over existing models.
The authors propose a new mathematical model of HIV dynamics incorporating antigenic diversity, but in the simplified case of a single antigenicity, the model shows no major qualitative difference from existing models. The model is proven to be biologically consistent with a unique continuous solution.
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.