Math. Model. Nat. Phenom.
Volume 15, 2020
|Number of page(s)||23|
|Published online||03 December 2020|
Optimal control for a mathematical model for chemotherapy with pharmacometrics
Institute of Mathematics, Lodz University of Technology,
2 Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Il 62026-1653, USA.
3 Department of Electrical and Systems Engineering, Washington University, St. Louis, Mo 63130 USA.
* Corresponding author: firstname.lastname@example.org
Accepted: 30 March 2020
An optimal control problem for an abstract mathematical model for cancer chemotherapy is considered. The dynamics is for a single drug and includes pharmacodynamic (PD) and pharmacokinetic (PK) models. The aim is to point out qualitative changes in the structures of optimal controls that occur as these pharmacometric models are varied. This concerns (i) changes in the PD-model for the effectiveness of the drug (e.g., between a linear log-kill term and a non-linear Michaelis-Menten type Emax-model) and (ii) the question how the incorporation of a mathematical model for the pharmacokinetics of the drug effects optimal controls. The general results will be illustrated and discussed in the framework of a mathematical model for anti-angiogenic therapy.
Mathematics Subject Classification: 92C50 / 49K15 / 92C15
Key words: chemotherapy / pharmacometrics / optimal control / singular controls
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.