Ricerc@Sapienza

Mathematical modeling represents a useful instrument to describe epidemic spread
and to propose useful control actions, such as vaccination scheduling, quarantine, informative
campaign, and therapy, especially in the realistic hypothesis of resources limitations. Moreover, the
same representation could efficiently describe different epidemic scenarios, involving, for example,
computer viruses spreading in the network. In this paper, a new model describing an infectious
disease and a possible complication is proposed; after deep-model analysis discussing the role of the
reproduction number, an optimal control problem is formulated and solved to reduce the number
of dead patients, minimizing the control effort. The results show the reasonability of the proposed
model and the effectiveness of the control action, aiming at an efficient resource allocation; the model
also describes the different reactions of a population with respect to an epidemic disease depending
on the economic and social original conditions. The optimal control theory applied to the proposed
new epidemic model provides a sensible reduction in the number of dead patients, also suggesting
the suitable scheduling of the vaccination control. Future work will be devoted to the identification
of the model parameters referring to specific epidemic disease and complications, also taking into
account the geographic and social scenario.