Multi-objective NSBGA-II control of HIV therapy with monthly output measurement

Abstract

Human immunodeficiency virus (HIV) is a worldwide dangerous and feared disease. However, when it is controlled in the body by drugs called antiretroviral therapy, the patient can have almost a normal life. This paper develops a new method based on a multi-objective controller to design an optimal treatment for a mathematical model of HIV. The suggested controller determines the control action or the drug dosage by using a non-dominating sorting binary genetic algorithm (NSBGA-II). The multi-objective approach is performed by considering the Pareto solution of two cost functions. The first cost function is based on the error between the healthy cells and the reference one, which should be minimized to improve the person’s health. Another cost function is defined to minimize the amount of drug dosage, cost, and side effects. Since the number of healthy cells and viruses is determined by a blood test, to be closer to reality, it is assumed that the number of healthy cells is only measured every month and the drug dosage is designed for a month. This is the main advantage of the proposed therapy over state-of-the-art methods. The drug dosage is computed in two ways of changing daily and weekly. Three realistic scenarios are simulated and the obtained results are compared to other metaheuristic approaches. The results show that the drug dosage planning based on the proposed NSBGA-II outperforms the state-of-the-art methods and decreases the quantity and rate of change of drug and maintains the number of healthy cells near the desired values faster. Moreover, the developed approach is robust against HIV patient model parameter uncertainties.