optimal control theory

This paper continues the study of a model which was introduced in earlier work by the authors to study spontaneous and induced evolution to drug resistance under chemotherapy. The model is fit to existing experimental data, and is then validated on additional data that had not been used when fitting. In addition, an optimal control problem is studied numerically.

The primary factor 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 . In this work, the control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie techniques. A structural identfiability analysis is also presented, demonstrating that patient-specfic parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy.