Impact of Case Detection and Treatment on the Spread of HIV/AIDS: a Mathematical Study

Here a simple mathematical model for HIV/AIDS with standard incidence is formulated and analyzed. It is assumed that only a fraction of total HIV and AIDS infected are detected. So only this fraction of infectives are subjected to proper counseling and are not taking part in the hetero-sexual transmission of HIV/AIDS. The model is first analyzed by considering the case detection parameters as constants. The basic reproduction number R-0 of the model is computed and its relation with the existence and stability of different equilibria of the model is investigated. It is found that the disease-free equilibrium of the model is locally and globally asymptotically stable for R-0 < 1. When R-0 > 1, the endemic equilibrium exists and is locally and globally asymptotically stable under some restriction on parameters. Next the optimal control problem is formulated by considering case detection parameters as time dependent. This problem is analyzed using Pontryagin's maximum principle. Numerical simulation is performed to show the impact of optimal control and it is found that optimal control strategy gives a better result.