Optimal treatment strategies derived from a HIV model with drug-resistant mutants

This paper presents a mathematical model which is in the form of a system of ordinary differential equations. These equations describe the dynamics of the immune system, human immunodeficiency virus (HIV), and drug-resistant mutants. We derive optimal treatment strategies for the HIV infection by formulating and then analyzing an optimal control problem with a structured treatment interruptions (STI) control approach. The continuous optimal treatment strategy is found by solving the corresponding optimality system. Moreover, using a direct search approach, a suboptimal STI in therapy is also obtained. We demonstrate, by numerical simulation, that the optimal treatment strategies reduce the mutant virus particles and increase the uninfected CD4+ T-cell count.