Stability Analysis and Optimal Control of a Fractional Order Model for HIV Infection

Abstract: In this article, a mathematical model of HIV infection is developed using fractional-order differential equation consisting uninfected CD4+T cells, infected CD4+T cells and CTL effectors (i.e. immune response cells). The fractional order model possesses non-negative solutions. The system has three equilibria: infectionfree equilibrium, infected equilibrium and CTL equilibrium. Stability conditions of the model system around the equilibria are derived. Numerically it is observed that the system is Global MittagLeffler stabile. Moreover, the necessary conditions for the optimality of the system are derived whose fractional derivative is described in the Riemann and Caputo sense. Using an objective functional, the fractional optimal control problem is solved with minimal dosage of anti-HIV drugs with an aim to minimize the infectious viral load and count of infected CD4+T cells. Efficient numerical technique is provided for solving the FOCP. Numerical simulation has been done to elucidate the analytical results.