HIV/Aids - <i>in vivo</i> model with the roles of CTL immune cells and antiretroviral theraphy

Abstract

In this work, we formulated a mathematical model to study the interaction between HIV/AIDS and Cluster of Differentiation 4 cells (CD4⁺T), incorporating the roles of Cytotoxic T- lymphocytes (CTLs) cells and antiretroviral therapy. The proliferation of CD4⁺T cells was considered to follow the logistic growth pattern. The presence of HIV in the CD4⁺T cells stimulates the recruitment of CD4⁺T and CTL cells. The recruitment of uninfected CD4⁺T and CTL immune cells fall purely as an exponential function of time in the presence of HIV. The basic reproduction number (R₀) was obtained using the next generation matrix method. We adopted the Jacobian stability criterion and the Lyaponuv second method of stability to establish the local and global stabilities of the equilibrium states and show that HIV can be eliminated from CD4⁺T cells when R₀ ≤ 1 but will continue to persist within CD4⁺T cells when R₀ >1. Early medication therapy was observed to reduce viral load and increase the number of CTL cells, while CD4⁺T cells is kept above the AIDS bar. A high initial viral load was noticed to induce rapid decline in the number of CD4⁺T cells. To keep a healthy system, we recommended that the CTL and uninfected CD4⁺T cells population should be maintained by reducing viral load through early medication therapy and cloning of CTL cells within infected human, which fights and kills infected cells.

Keywords: Basic Reproduction Number (R₀), Virus-free Equilibrium (VFE), Endemic Equilibrium (EE), Locally Asymptotically Stable (LAS) and Globally Asymptotically Stable (GAS)