AUTHOR=Greene James M. , Sanchez-Tapia Cynthia , Sontag Eduardo D. 

TITLE=Mathematical Details on a Cancer Resistance Model

JOURNAL=Frontiers in Bioengineering and Biotechnology

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/bioengineering-and-biotechnology/articles/10.3389/fbioe.2020.00501

DOI=10.3389/fbioe.2020.00501

ISSN=2296-4185

ABSTRACT=One of the most important factors} limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance.  We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy~\cite{Greene2019,Greene2018}.  In this work, we expound on the details relating to an optimal control problem outlined in~\cite{Greene2018}.  The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebraic techniques.  A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy.  For completeness, a detailed analysis of existence results is also included.