TY  - JOUR
ID  - Leszczyński2017
LB  - Leszczyński2017
AU  - Leszczyński, Maciej
AU  - Ratajczyk, Elżbieta
AU  - Ledzewicz, Urszula
AU  - Schättler, Heinz
TI  - Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
ST  - Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 3
SP  - 403
EP  - 419
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.3.403
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.3.403
AB  - 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.
KW  - optimal control
KW  - sufficient conditions for optimality
KW  - method of characteristics
KW  - pharmacodynamic model
SN  - 1232-9274
ER  -