Abstract:
Ever since the emergence of Human immunodeficiency virus (HIV) disease in early 1980s, the understanding of the conditions necessary for the effective treatment of HIV in infected individuals has been a global health challenge. Though, there have been some major advances in the understanding of HIV pathogenesis, researches are still on-going regarding the optimal treatment regimen for infected individuals. In this research work, a model for the cellular dynamics of the virus and its interacting immune cells in the presence of antiretroviral therapy (ART) is proposed. The model considers five different cell populations which include the uninfected CD4+ T- cells, infected CD4+ T- cells, CD8+ T- cells, infectious virus and immature non-infectious virus. The model steady states were determined and the criteria for their stability were well established. Thereafter, an optimal control problem was formulated with the goal of finding the optimal levels of effectiveness of each of the drugs in the multidrug ART that would minimize patients’ viral load and side-effects of the drugs while, at the same time, boosting the patients’ immune system. Based on Pontryagin’s maximum principle, the optimality system for the optimal control of the problem was derived and solved numerically using Runge-Kutta forth order scheme based on forward-backward sweep approach. The results were simulated for different treatment scenarios. Findings from our simulations showed that there was no definitive way to combine the ART drugs for optimal patient’s benefit. Rather, the drug combination that would be most effective for a particular patient at a point in time would depend on patient’s viral load and CD4+ T- cells count as well as his/her history of ARV treatment.
