<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this manuscript, we shall apply the tools and methods from optimal control to analyze various minimally parameterized models that describe the dynamics of...

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

Published Online: Jul 15, 2018

Page range: 375 - 402

Received: Feb 09, 2018

Accepted: Jul 15, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00029

Keywords
Optimal control, chemotherapy, bang-bang and singular controls, Pontryagin maximum principle

© 2018 C. Rojas, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Jul 15, 2018

Page range: 375 - 402

Received: Feb 09, 2018

Accepted: Jul 15, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00029

KeywordsOptimal control, chemotherapy, bang-bang and singular controls, Pontryagin maximum principle

© 2018 C. Rojas, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Optimal control, chemotherapy, bang-bang and singular controls, Pontryagin maximum principle