Opuscula Mathematica
Opuscula Math. 37, no. 3 (), 403-419
Opuscula Mathematica

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

Abstract. 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.
Keywords: optimal control, sufficient conditions for optimality, method of characteristics, pharmacodynamic model.
Mathematics Subject Classification: 49K15, 93C15, 92C45.
Cite this article as:
Maciej Leszczyński, Elżbieta Ratajczyk, Urszula Ledzewicz, Heinz Schättler, Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics, Opuscula Math. 37, no. 3 (2017), 403-419, http://dx.doi.org/10.7494/OpMath.2017.37.3.403
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.