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Mathematical Methods and Models in Biomedicine pp 311–337Cite as

Tumor Development Under Combination Treatments with Anti-angiogenic Therapies

Part of the Lecture Notes on Mathematical Modelling in the Life Sciences book series (LMML)

Abstract

Tumors are a family of high-mortality diseases, each differing from the other, but all exhibiting a derangement of cellular proliferation and characterized by a remarkable lack of symptoms [52] and by time courses that, in a broad sense, may be classified as nonlinear. As a consequence, despite the enormous strides in prevention and, to a certain extent, cure, cancer is one of the leading causes of death worldwide, and, unfortunately, is likely to remain so for many years to come [4, 53].

Keywords

  • Optimal Control Problem
  • Optimal Protocol
  • Optimal Synthesis
  • Singular Control
  • Angiogenic Inhibitor

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

We would like to thank an anonymous referee for his careful reading of our chapter and several suggestions that we incorporated into the final version. The research of A.  d’Onofrio has been done in the framework of the Integrated Project “p-medicine—from data sharing and integration via VPH models to personalized medicine,” project identifier: 270089, which is partially funded by the European Commission under the 7th framework program. The research of U. Ledzewicz and H. Schättler has been partially supported by the National Science Foundation under collaborative research grant DMS 1008209/1008221.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL, 62026, USA

    Urszula Ledzewicz

  2. Department of Experimental Oncology, European Institute of Oncology, 20139, Milan, Italy

    Alberto d’Onofrio

  3. Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, 63130, USA

    Heinz Schättler

Authors
  1. Urszula Ledzewicz
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  2. Alberto d’Onofrio
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  3. Heinz Schättler
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Correspondence to Urszula Ledzewicz .

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Editors and Affiliations

  1. , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, 62026, Illinois, USA

    Urszula Ledzewicz

  2. , Electrical and Systems Engineering, Washington University, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Heinz Schättler

  3. Mathematical Biosciences Institute, Ohio State University, W. 18th Avenue 231, Columbus, 43210-1292, Ohio, USA

    Avner Friedman

  4. Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Eugene Kashdan

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Ledzewicz, U., d’Onofrio, A., Schättler, H. (2013). Tumor Development Under Combination Treatments with Anti-angiogenic Therapies. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_11

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