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

Andrea Di Liddo
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Andrea Di Liddo: Department of Economics, University of Foggia, Largo Papa Giovanni Paolo II, Foggia 71121, Italy

Mathematics, 2016, vol. 4, issue 2, 1-27

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.

Keywords: optimal control; cost functions; epidemics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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