Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives

In this paper, we study the impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. Initially we consider constant controls and thereafter treat control measures as time dependent control parameters. In the constant controls case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit transcritical bifurcation. For the time dependent controls, we formulate the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of unaware infectives in the spread of HIV/AIDS. We observed that unawareness by infectives has a great cost impact on the community. We further investigate the impact of combinations of the strategies in the control of HIV/AIDS. Carrying out cost-effectiveness analysis, we found that the most cost-effective strategy is the combination of all the control strategies.