Optimal control of combined antiretroviral therapies in an HIV infection model with cure rate and fusion effect

Abstract

This paper mainly targets to deduce an optimal treatment strategy for combined antiretroviral drugs, which can maximize healthy CD4+ T cells level with minimum side effects and cost. For this purpose, we consider a within-host treatment model for the HIV infection with two controls incorporating full logistic proliferation of healthy CD4+ T cells, cure rate and fusion effect. These two controls represent the effects of reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs), respectively. The model analysis begins with proving different basic properties like non-negativity, boundedness of the model solutions and calculation of the basic reproduction number of the model under consideration. Then, stability results are obtained for HIV infection-free equilibrium point and also, a critical efficacy for the combined therapies is calculated. After that, the optimal control problem is proposed and solved numerically using a forward–backward iterative method. Finally, we obtain an optimal treatment strategy that can maximize healthy CD4+ T cells count and control the viral load, and HIV-infected CD4+ T cells count to an undetectable level resulting in improved health conditions of infected individuals.