- - - Department of Mathematics, University of Malakand, Chakdara Dir (Lower) Khyber Pakhtunkhawa, Pakistan.
- - - Department of Mathematics, University of Malakand, Chakdara Dir (Lower) Khyber Pakhtunkhawa, Pakistan.

A double delayed- HIV-۱ infection model with optimal controls is taken into account. The proposed model consists of double-time delays and the following five compartments: uninfected cells CD۴+ T cells, infected CD۴+ T cells, double infected CD۴+ T cells, human immunodeficiency virus, and recombinant virus. Further, the optimal controls functions are introduced into the model. Objective functional is constituted which aims to (i) minimize the infected cells quantity; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood Then, the existence and uniqueness results for the optimal control pair are established. The optimality system is derived and then solved numerically using an iterative method with Runge-Kutta fourth-order scheme.

HIV-۱ model, Intracellular delay, Recombinant virus, Optimal control, Pontryagin Maximum Principle