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Optimal control of a delayed breast cancer stem cells nonlinear model
Author(s) -
Barrea Andrés,
Hernández Matias E.
Publication year - 2015
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2164
Subject(s) - optimal control , pontryagin's minimum principle , breast cancer , nonlinear system , control theory (sociology) , maximum principle , ordinary differential equation , mathematical optimization , mathematics , control (management) , computer science , cancer , differential equation , medicine , artificial intelligence , physics , mathematical analysis , quantum mechanics
Summary In this article, we consider a nonlinear model, which is governed by an ordinary differential equations system with time delays in state and control. The model is used in order to describe the growth of breast cancer cells under therapy. We seek optimal therapies to minimize the number of cancer cells as well as the total quantity of drug used in the treatment. In this way, we formulate an optimal control problem. We prove the existence of an optimal therapy and use Pontryagin's maximum principle in order to find optimality conditions, which characterize such optimal therapy. At last, both numerical results and conclusion are presented. Copyright © 2015 John Wiley & Sons, Ltd.