Singular Arcs in Cancer Chemotherapy – Are They Optimal?

A. Swierniak (Poland), U. Ledzewicz, and H. Schättler (USA)


optimal control, cancer chemotherapy, singular control, cell-cycle specificity


We recall several two- and three-compartment models considered earlier.While a killing agent which is active during cell-division is the only control considered in the two-compartment model, model (A), also two three compartment models, models (B) and (C), are analyzed, which consider a blocking agent and recruiting agent, re spectively. In model (B) a blocking agent which slows down the growth of the cells during synthesis enabling in consequence synchronization of neoplastic population is added. In model (C) the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative ef fect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal.

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