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Mathematics 2016, 4(2), 21; doi:10.3390/math4020021

Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs

Department of Economics, University of Foggia, Largo Papa Giovanni Paolo II, Foggia 71121, Italy
Academic Editor: Bruno Buonomo
Received: 30 December 2015 / Revised: 7 March 2016 / Accepted: 21 March 2016 / Published: 1 April 2016
(This article belongs to the Special Issue Optimal Control and Management of Infectious Diseases)
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Abstract

The representation of the cost of a therapy is a key element in the formulation of the optimal control problem for the treatment of infectious diseases. The cost of the treatment is usually modeled by a function of the price and quantity of drugs administered; this function should be the cost as subjectively perceived by the decision-maker. Nevertheless, in literature, the choice of the cost function is often simply done to make the problem more tractable. A specific problem is also given by very expensive therapies in the presence of a very high number of patients to be treated. Firstly, we investigate the optimal treatment of infectious diseases in the simplest case of a two-class population (susceptible and infectious people) and compare the results coming from five different shapes of cost functions. Finally, a model for the treatment of the HCV virus using the blowing-up cost function is investigated. Some numerical simulations are also given. View Full-Text
Keywords: optimal control; cost functions; epidemics optimal control; cost functions; epidemics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Di Liddo, A. Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs. Mathematics 2016, 4, 21.

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