Ricerc@Sapienza

The control of the HIV infection is considered in the framework of the optimal control theory within the problem of resource allocation. A control action, changing the intervention strategy on the basis of the updated situations, is proposed. The switching instants are not fixed in advance but are determined along with the final control time. A constructive algorithm to compute iteratively the switching control is outlined. The solutions obtained provide interesting and promising results.

In optimal control problems, once the model, the boundary conditions and the constraints are fixed, the result depends obviously on the choice of the cost index and, in particular, on the weights assumed for the variables considered. The weights take into account the different mutual influence of the elements included in the cost index; therefore different choices yield to different control strategies.

In this paper, we consider the fractional SIS (susceptible-infectious-susceptible) epidemic model (α-SIS model) in the case of constant population size. We provide a representation of the explicit solution to the fractional model and we illustrate the results by numerical schemes. A comparison with the limit case when the fractional order α converges to 1 (the SIS model) is also given. We analyze the effects of the fractional derivatives by comparing the SIS and the α-SIS models.