Locally Optimal Pumping and Treatment Rates in Uncertain Environments

by John J. Westman, Bruce R. Fabijonas, Daniel L. Kern and Floyd B. Hanson

appearing in:
Proceedings of Sixteenth International Symposium of Mathematical Theory of Networks and Systems, MTNS2002

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ABSTRACT:

A compartmental model for the evolution of cancer subject to multiple chemotherapeutic agents is presented. The formulation presented accounts for the heterogeneous nature of cancer and drug resistance, leading to a system that can be useful as a tool for the optimizing of treatments. Chemotherapeutic or cytotoxic agents have limited effectiveness due to effects of toxicity and the development of drug resistance. Toxicity limits the amount of the agent that can be used and acts as an upper bound on the dosage. Drug resistance causes the clinical value of the cytotoxic agent to become nominal after a small number of treatments. Therefore, several non-cross resistant cytotoxic agents are used to extend the number of treatments that a given agent can be administered.