Mathematical Model on the Viral Load/Burden of HIV/AIDS in the Body of a Host

Abstract

We analyze a non-linear model of the human immunodeficiency virus (HIV) infection that considers the interaction between a replicating virus, CD4⁺ T cell and the cytotoxic-T-Lymphocytes (CTL) i.e. CD8⁺ T cell. The non-negative steady state of the model equation were obtained when P₄ ≤ 1 and P₄ >1, and further analyzed for stability. We observe that the steady state of the model equation when P₄ ≤ 1 is asymptotically stable if P₄ <1 and unstable if P₄ >1. Also, we observe that the steady state of the mode equation when P₄ >1 is asymptotically stable.

Keywords: Viral load/burden, CD4⁺ T cell count, the HIV infection and immune control.