Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 3, Issue 2


Published
on

July 15, 2018


Pages

375-402


DOI

Article

Optimal control problems for differential equations applied to tumor growth: state of the art

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Authors

Clara Rojas Affiliation:
Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain
and Juan Belmonte-Beitia Affiliation:
Department of Mathematics and Mathematical Oncology Laboratory, University of Castilla-La Mancha, 13071 Ciudad Real, Spain


Abstract

In this manuscript, we shall apply the tools and methods from optimal control to analyze various minimally parameterized models that describe the dynamics of populations of cancer cells and elements of the tumor microenvironment under different anticancer therapies. In spite of their simplicity, the analysis of these models that capture the essence of the underlying biology sheds light on more general scenarios and, in many cases, leads to conclusions that confirm experimental studies and clinical data. We focus on four applications: optimal control applied to compartmental models, brain tumors, drug resistance and antiangiogenic treatment.


Keywords

Optimal control, chemotherapy, bang-bang and singular controls, Pontryagin maximum principle, 92-02, 49J15, 49J30, 92B99, 93B27, 93C15


Citation

Rojas, C. & Belmonte-Beitia, J. (2018). Optimal control problems for differential equations applied to tumor growth: State of the art. Applied Mathematics and Nonlinear Sciences, 3(2), 375–402. https://doi.org/10.21042/AMNS.2018.2.00029

Published by: Engineering Journals

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