On the modeling of long-term HIV-1 infection dynamics

In this paper, we propose and study models of long-term Human Immunodeficiency Virus (HIV-1) infection. Our aim is to identify model mechanisms that allow one to explain the trends observed in clinical measurements of the number of CD4+ T-cells and virus throughout the long-term HIV-1 infection, from the acute phase until the onset of AIDS. To achieve our goal, we apply some standard methods of modeling and analysis of dynamical systems. Among these methods, are model development and validation processes such as parameter estimation, as well as Painleve and bifurcation analysis.