Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics

• Autorzy: Leszczynski M. , Ratajczyk E. , Ledzewicz U. , Schättler H.

Identyfikatory

DOI

10.7494/OpMath.2017.37.3.403

• Języki publikacji: EN

Abstrakty

EN

We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.

Słowa kluczowe

EN

optimal control; sufficient conditions for optimality; method of characteristics; pharmacodynamic model

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 3
• Strony: 403--419
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Leszczynski M.

• Lodz University of Technology Institute of Mathematics 90-924 Lodz, Poland

autor

Ratajczyk E.

• Lodz University of Technology Institute of Mathematics 90-924 Lodz, Poland

autor

Ledzewicz U.

• Lodz University of Technology Institute of Mathematics 90-924 Lodz, Poland
• Southern Illinois University Edwardsville Department of Mathematics and Statistics Edwardsville, Il, 62026-1653, USA

autor

Schättler H.

• Washington University Department of Electrical and Systems Engineering St. Louis, Mo, 63130, USA

Bibliografia

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Uwagi

EN

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).