Controlling a model for bone marrow dynamics in cancer chemotherapy - Urszula Ledzewicz; Heinz Schättler (Mathematical Biosciences and Engineering)
This paper analyzes a mathematical model for the growth of bonemarrow cells under cell-cycle-specic cancer chemotherapy originally proposedby Fister and Panetta [8]. The model is formulated as an optimal controlproblem with control representing the drug dosage (respectively its effect)and objective of Bolza type depending on the control linearly, a so-called $L^1$-objective. We apply the Maximum Principle, followed by high-order necessaryconditions for optimality of singular arcs and give sufficient conditions for optimality based on the method of characteristics. Singular controls are eliminatedas candidates for optimality, and easily veriable conditions for strong localoptimality of bang-bang controls are formulated in the form of transversalityconditions at switching surfaces. Numerical simulations are given.