Modelling HIV In-vivo Cellular Dynamics in the Presence of Antiretroviral Therapy

A treatment strategy for the total eradication of human immunodeficiency virus (HIV) in infected individuals is presently not feasible. However, the adoption of highly-active antiretroviral therapy (HAART) has been effective in managing HIV/AIDS infected patients in recent times. In this paper, a deterministic mathematical model is proposed and used to monitor the interactions between uninfected CD4+ T-cells, Infected CD4+ T-cells, CD8+ T-cells, infectious virus and immature non-infectious virus in the course of in-host HIV cellular dynamics. The goal is to find the adequate combination of the treatment regimens that will minimize the treatment systemic costs as well as deliver maximal health benefits to the HIV-positive patients. The model analyses show that the model disease-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than unity. Thereafter, the proposed model is solved numerically and the result simulated for different combinations of the two common antiretroviral drugs effectiveness. Finding from the simulations show that treatment outcome would depend largely on patient’s HIV/AIDS status indicators before initiating treatment and his/her antiretroviral therapy history.