Optimal Control of a Fractional-Order HIV-Immune System With Memory

The fact that fractional-order models possess memory leads to modeling a fractional-order HIV-immune system. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. Using an objective function that minimizes the infectious viral load and count of infected T cells, the optimal control problem is solved for the fractional-order optimality system with minimal dosage of anti-HIV drugs and the effects of mathematically optimal therapy are demonstrated. Simulation results show that the fractional-order optimal control scheme can achieve improved quality of the treatment.