Analytical Solution of the T, T*, VI, VNI Model for HIV-1 Dynamics

Abstract

This paper investigates a model for cellular and viral interactions following Human Immunodeficiency Virus Type 1 (HIV-1) infection. A simplified version of this model, which considers interactions between the populations of susceptible CD4+ T cells, infected CD4+ T cells, infectious virus, and non-infectious virus, under the effects of reverse transcriptase and protease inhibitors, is presented and solved analytically. The solution is obtained through an iterative method after isolating one dependent variable and performing various substitutions. Although an analytical solution is more difficult to obtain than numerical approximations, it produces exact results to the system of equations. As such, the analytical solution can be used to study the behavior of HIV-1 and its interactions with various treatment methods in an infected patient.