Mathematical modeling of antigenicity for HIV dynamics

TL;DR

This paper introduces a new mathematical model of HIV dynamics that incorporates antigenic diversity, allowing for more accurate simulation of disease progression by considering virus mutation, lymphocyte adaptation, and immune response.

Contribution

The paper presents a novel HIV model that accounts for antigenic diversity and compares it with existing models, demonstrating its biological consistency and potential for advanced disease phase simulation.

Findings

Model accounts for antigenic diversity and immune response.

Mathematically proven to be biologically consistent with unique solutions.

Enhanced capability to simulate advanced HIV disease phases.

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.