- Tytuł:
- Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
- Autorzy:
-
Leszczynski, M.
Ratajczyk, E.
Ledzewicz, U.
Schättler, H. - Powiązania:
- https://bibliotekanauki.pl/articles/255130.pdf
- Data publikacji:
- 2017
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
optimal control
sufficient conditions for optimality
method of characteristics
pharmacodynamic model - Opis:
- 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.
- Źródło:
-
Opuscula Mathematica; 2017, 37, 3; 403-419
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł