| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Cancer modelling
|
|
|---|---|---|
| Article Number | 69 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/mmnp/2020008 | |
| Published online | 03 December 2020 | |
Optimal control for a mathematical model for chemotherapy with pharmacometrics
1
Institute of Mathematics, Lodz University of Technology,
90-924
Lodz, Poland.
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: uledzew@siue.edu
Received:
16
January
2019
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
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