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A 3-Compartment Model for Chemotherapy of Heterogeneous Tumor Populations

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We consider a mathematical model for cancer chemotherapy with a single agent that distinguishes three levels of sensitivities calling the subpopulations ‘sensitive’, ‘partially sensitive’ and ‘resistant’. We analyze the dynamic properties of the system under what could be considered metronomic (continuous, low-dose, constant) chemotherapy and, more generally, also consider the optimal control problem of minimizing the tumor burden over a prescribed therapy interval. Interestingly, when several levels of chemotherapeutic sensitivities are taken into account in the model, lower time-varying dose rates as they are given by singular controls become a treatment option. This is only the case once a significant residuum of resistant cells has been created in a simpler 2-compartment model that only considers sensitive and resistant cells. For heterogeneous tumor populations, a more modulated approach that varies the dose rates of the drugs may be more beneficial than the classical maximum tolerated dose approach pursued in medical practice.

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This material is based upon work supported by the National Science Foundation under collaborative research Grants Nos. DMS 1311729/1311733. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Correspondence to Urszula Ledzewicz.

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This material is based upon work supported by the National Science Foundation under collaborative research Grants Nos. DMS 1311729/1311733. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Ledzewicz, U., Bratton, K. & Schättler, H. A 3-Compartment Model for Chemotherapy of Heterogeneous Tumor Populations. Acta Appl Math 135, 191–207 (2015).

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