Long Term Optimal Control for HIV Treatment Using Spline Functions

This paper presents a long-term optimal control treatment of human immunodeficiency virus (HIV) infection. HIV destroys the body immune system, increases the risk of certain pathologies, damages body organs such as the brain, kidney, and heart, and causes death. Unfortunately, this infectious disease currently has no cure; however, there are effective retroviral drugs for improving the patients’ health conditions. In this paper, two treatment drugs are considered to decrease the free HIV virus particles in the blood. Since excessive use of these drugs is not without harmful side effects, the prescription dosage should be minimum. Thus, we formulate an optimal control problem to reduce the HIV virus particles in the blood by using minimum drugs. To solve the obtained optimal control, direct method and spline functions are utilized. The main advantage of the direct method to the indirect method is the low computational cost of this solution. Spline functions are tools used in the direct solving approach to achieve the better solutions. Also, three different models are considered in this paper to evaluate the effectiveness of the proposed method in different conditions. In addition, in the end, we compare the results from the proposed approach with the results of the problem solving by indirect method. Furthermore, the sensitivity analysis is checked to demonstrate the performance of control system against parametric uncertainties.