Mathematical Modeling of the Dynamics between CD4+ T Cell Depletion and Antigen Variation

Abstract

This research involves the formulation of mathematical models representing the dynamics between CD4+ T cell depletion and antigen variation, subject to the initial conditions. The study considered some assumptions where the interaction of the HIV cells with the immune cells leads to the depletion of the immune system. The study further considers that immune cells and the HIV cells grow logistically, excluding a constant supply of the T immune cells from the thymus. Moreover, the HIV cells are considered autonomous external invaders. The steady-state solution of the system was obtained, linearisation of the system was carried out, and characteristic eigenvalues were obtained. In addition, numerical simulation using Wolfram Mathematica, version 12, on the models was performed, where the impact of the pertinent parameters on the system was considered. The results showed that increases in viral replication rate accelerate immune cell depletion and destabilise the system, while higher immune response rates promote stability and delay progression toward immune collapse.