  We propose a model for the human immunodeficiency virus type 1 (HIV-1)
infection with intracellular delay and prove the local asymptotical stability
of the equilibrium points. Then we introduce a control function representing
the efficiency of reverse transcriptase inhibitors and consider the
pharmacological delay associated to the control. Finally, we propose and
analyze an optimal control problem with state and control delays. Through
numerical simulations, extremal solutions are proposed for minimization of the
virus concentration and treatment costs.
