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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Original Articles

Optimal Control for a Delay Differential System of Chronic Myelogenous Leukemia

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pp. 99–114Vol. 9Issue 2June 2013DOI: 10.1080/1726037X.2011.10698595XML
Published Online:
03 Jun 2013
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2011.10698595
Pages:
99–114

Abstract

A mathematical model describing the time evolution of a Cancer cell population in Chronic Myelogenous Leukemia (CML) is extended: a function modeling the treatment approach of the disease is taken into account, allowing the investigation of the most appropriate cure protocol. Because CML is believed to arise in the hematopoietic stem cell (HSC) compartment, the study in this paper starts from a delay differential system modeling CML in the stem cell compartment. Optimal control is applied to this two-dimensional system with a molecular targeted therapy, such as imatinib. The objective in this work is to minimize the cancer cell population and the negative effects of the medication to the healthy cells of a certain patient. In order to solve the delayed optimal control problem, the system is discretized and its behavior is investigated for given sets of parameters. The obtained results are illustrated by numerical simulations and discussed in view of the optimal treatment approach.

Keywords

delay differential systemoptimal controlCancer cell populationChronic Myelogenous Leukemiaimatinib

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