Ricerc@Sapienza

The paper addresses the problem of human virus spread reduction when the resources
for the control actions are somehow limited. This kind of problem can be successfully solved in the
framework of the optimal control theory, where the best solution, which minimizes a cost function
while satisfying input constraints, can be provided. The problem is formulated in this contest for the
case of the HIV/AIDS virus, making use of a model that considers two classes of susceptible subjects,
the wise people and the people with incautious behaviours, and three classes of infected, the ones
still not aware of their status, the pre-AIDS patients and the AIDS ones; the control actions are
represented by an information campaign, to reduce the category of subjects with unwise behaviour,
a test campaign, to reduce the number of subjects not aware of having the virus, and the medication
on patients with a positive diagnosis. The cost function considered aims at reducing patients with
positive diagnosis using as less resources as possible. Four different types of resources bounds
are considered, divided into two classes: limitations on the instantaneous control and fixed total
budgets. The optimal solutions are numerically computed, and the results of simulations performed
are illustrated and compared to put in evidence the different behaviours of the control actions.