Optimal control for SIRC epidemic outbreak

Authors:
Daniela Iacoviello;Nicolino Stasio
Affiliations:
Department of Computer, Control and Management Engineering Antonio Ruberti - Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy;Sapienza University of Rome, Italy
Venue:
Computer Methods and Programs in Biomedicine
Year:
2013

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Abstract

In this paper the mathematical SIRC epidemic model is considered. It efficiently describes diseases in which a cross immune class (C) is present, along with the susceptible (S), the infected (I) and the removed (R) ones. Controlling epidemic diseases corresponds to the introduction of vaccination, quarantine and treatment strategies; generally only one of these actions is considered. In this paper the possibility of optimal controls both over the susceptible and the infected subjects is assumed, taking into account also limitations of resources. A suitable cost index is introduced and via the Pontryagin's Minimum Principle the optimal control strategy is determined and the existence of the optimal solution is assessed. Numerical results are developed analyzing the effects of different control strategies.