Optimal Control of Combined Therapy in a Single Strain HIV-1 Model

Highly active antiretroviral therapy (HAART) is administered to symptomatic human immunodeficiency virus (HIV) infected individuals to improve their health. Various administration schemes are used to improve patients?lives and at the same time suppressing development of drug resistance, reduce evolution of new viral strains, minimize serious side effects, improve patient adherence and also reduce the costs of drugs. We deduce an optimal drug administration scheme useful in improving patients? health especially in poor resourced settings. In this paper we use the Pontryagin?s Maximum Principle to derive optimal drug dosages based on a mathematical dynamical model. We use methods of optimal control to determine optimal controls analytically, and then use the Runge-Kutta scheme of order four to numerically simulate different therapy effects. We simulate the different effects of a drug regimen composed of a protease inhibitor and a nucleoside reverse transcriptase inhibitor. Our results indicate that for highly toxic drugs, small dosage sizes and allowing drug holidays make a profound impact in both improving the quality of life and reducing economic costs of therapy. The results show that for drugs with less toxicity, continuous therapy is beneficial.