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Optimal Control for Mathematical Models of Cancer Therapies pp 171–235Cite as

Optimal Control of Mathematical Models for Antiangiogenic Treatments

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Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 42))

Abstract

In the models considered so far, the focus was on the cancerous cells progressing from mathematical models for homogeneous tumor populations of chemotherapeutically sensitive cells to heterogeneous structures of cell populations with varying sensitivities or even resistance. From an optimal control point of view, optimal treatment schedules change from bang-bang solutions with upfront dosing (that correspond to classical MTD approaches in medicine) to administrations that also include singular controls (which correspond to time-varying dosing schedules at less than maximum rates) as heterogeneity of the tumor population becomes more prevalent. In this chapter, we begin to analyze mathematical models that also take into account a tumor’s microenvironment.

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Authors and Affiliations

  1. Electrical and Systems Engineering, Washington University, St. Louis, MO, USA

    Heinz Schättler

  2. Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, USA

    Urszula Ledzewicz

Authors
  1. Heinz Schättler
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  2. Urszula Ledzewicz
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Schättler, H., Ledzewicz, U. (2015). Optimal Control of Mathematical Models for Antiangiogenic Treatments. In: Optimal Control for Mathematical Models of Cancer Therapies. Interdisciplinary Applied Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2972-6_5

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