Optimal Control of an HIV Model with Changing Behavior through an Education Campaign, Screening and Treatment

Optimal control theory was used on the system of differential equations to achieve the goal of minimizing the infected population and slow down the epidemic outbreak. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle. Three control strategies were incorporated such as human education campaign, screening and treatment of infected human and its impact were graphically observed. Runge-Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system. Numerical results with education campaign levels, screening and treatment rates as controls are illustrated.