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

A double time delayed- HIV-1 infection model with optimal controls functions is taken into account. The proposed model consists of double time delays and the following five compartments: uninfected CD4+ T cells, infected cells, double infected cells, human immunodeficiency virus and recombinant virus. The optimal control functions are introduced into the model. Then, the existence and uniqueness results for the optimal control pair are established. The optimality of system is derived and then solved numerically using a forward and backward difference scheme. The role of objective functional is to minimize the the density of infected cells; (ii) minimize free virus particles number; and (iii) maximize healthy cells density in blood