HIV Inside the Body: A Review of Mathematical Modeling.

This paper presents a review of works devoted to studies on Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS) dynamics through mathematical modeling. The analysis is performed over about a hundred papers from 1989 to the present day, distinguishing models according to the presence or absence of variables such as infected T-lymphocytes and immune effectors or precursors, and the presence or absence of differentiation in uninfected T cells, infected T cells and viruses. The review also cites the optimal control approaches to the topic and some recent formulations in terms of differential game theory, aimed at predicting the effects of different dosage schedules or drug combinations. For each group of works we describe the significant variables and underline their role in the dynamics. The survey also proposes a frequency table over the most commonly used parameters. Finally, building on the previous analysis, we resume the main features a mathematical model should have in order to describe faithfully the complex interactions between the immune system and HIV.