Investigations on the HIV dynamics with a system of time delayed functional equations

A model of time delayed ordinary functional equations for the description of the dynamics of the human Immuno-deficiency(HIV) and its interaction with the human immune system is considered. The model focuses on the evolution of TCD4^+ cells on the lymphoid tissue and takes into account the same steps included in a cellular automaton (CA) which describes, with one single set of parameters, three distinct phases of the HIV infection: the primary infection, the latency period, and the AIDS phase. The primary infection occurs on the short time interval (~weeks), while the second phase occurs in the much larger time scale (~years). The proposed model reproduces the same features of its CA counterpart, attesting that the mechanism based on the interaction of TCD4^+ cells and time delay captures essential aspects of the HIV infection dynamics. Results are based on the analysis of fixed points, numeric integration of differential equations, and characterization of the phase space structure of the model.