[HIV-1 quantitative dynamics in vivo: a review of mathematical models]

Over the last years, mathematical models have been applied in HIV infection to investigate the population dynamics of HIV-1 and cells of the immune system in infected hosts. They have contributed to a better understanding of the pathogenesis of AIDS. Among the model-based works, the quantitative studies carried out by two teams, during the years 1995, 1996 and 1997, have brought important results on HIV infection dynamics, reminding that HIV belonged to the lentivirus family, which had not been integrated in research of the previous years. In the studies on HIV dynamics, solutions of mathematical models were fitted to viral and/or immunological markers data in order to estimate the parameters of the viral and cellular production kinetics in infected patients. The present paper is a critical review of these studies. The methods and the most important results are presented. We explain why their impact was so considerable, but also show how the simplicity of modelling could result in conceptual errors. We finally discuss the contribution and the limits of mathematical models in the analysis of experimental data.