Controlling a model for bone marrow dynamics in cancer chemotherapy

Abstract

This paper analyzes a mathematical model for the growth of bone marrow cells under cell-cycle-speci_c cancer chemotherapy originally proposed by Fister and Panetta [8]. The model is formulated as an optimal control problem with control representing the drug dosage (respectively its e_ect) and objective of Bolza type depending on the control linearly, a so-called L1- objective. We apply the Maximum Principle, followed by high-order necessary conditions for optimality of singular arcs and give su_cient conditions for optimality based on the method of characteristics. Singular controls are eliminated as candidates for optimality, and easily veri_able conditions for strong local optimality of bang-bang controls are formulated in the form of transversality conditions at switching surfaces. Numerical simulations are given.