Optimal control of double delayed HIV-1 infection model of ghting a virus with another virus

A double delayed- HIV-1 infection model with optimal controls is taken into account. The proposed model consists of double time delays and the following ve compart- ments: uninfected cells CD4+ T cells, infected CD4+ T cells, double infected CD4+ T cells, human immunodeciency 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 par- ticles number; and (iii) maximize healthy cells density in blood Then, the existence and uniqueness results for the optimal control pair are established. The optimal- ity system is derived and then solved numerically using an iterative method with Runge-Kutta fourth order scheme.