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

To achieve the goal of minimising the infectious population and slowing the disease spread, optimal control theory was applied to a system of differential equations. Using Pontryagin's maximum theory, the necessary conditions of an optimal control problem were thoroughly examined.  Three prevention methods were used, including human education, screening, and treatment of infected humans, and their effects were graphically depicted. The optimal control scheme is solved using the Runge-Kutta forward-backward sweep numerical approximation method. The numerical results are seen, along with the levels of education campaigns, screening, and treatment rates as controls. According to a sensitivity review, the interaction rate of susceptible to unaware HIV infective is the most sensitive parameter on the successful reproduction number, whereas the progression rate of the treated class to full-blown AIDS is the least sensitive parameter.