Optimal Control to reduce the HIV/AIDS spread

In this paper the problem of the HIV/AIDS spread reduction is addressed in the framework of optimal control theory. A model recently proposed has been adopted; it considers two classes of susceptible subjects, the wise people and the people with incautious behaviors, and three classes of infected, the ones still not aware of their status, the pre-AIDS patients and the AIDS ones. The control actions involve prevention by information campaign, to reduce the category of subjects with unwise behavior, by test campaign, to reduce the number of subjects not aware of having the virus, and medication on patients with a positive diagnosis. A cost index aiming at the reduction of patients with positive diagnosis is introduced with the conflicting requirements of using as less resources as possible.