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

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  • Andrea Di Liddo

    (Department of Economics, University of Foggia, Largo Papa Giovanni Paolo II, Foggia 71121, Italy)

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.

Suggested Citation

  • Andrea Di Liddo, 2016. "Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs," Mathematics, MDPI, vol. 4(2), pages 1-27, April.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:2:p:21-:d:67152
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    References listed on IDEAS

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    1. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
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