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New Challenges for Cancer Systems Biomedicine pp 249–266Cite as

On the Dynamics of Tumor-Immune System Interactions and Combined Chemo- and Immunotherapy

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Part of the book series: SIMAI Springer Series ((SEMA SIMAI))

Abstract

Tumor-immune system interplay is extremely complex, and, as such, it represents a big challenge for mathematical oncology. Here we investigate a simple general family of models for this important interplay by considering both the delivery of a cytotoxic chemotherapy and of immunotherapy. Then methods of geometrical optimal control are applied to a special case (the Stepanova model) in order to infer (under suitable constraints) the best combination of drugs scheduling to transfer — through therapy —the system from an initial condition in the malignant region of the state space into a benign region. Our findings suggest that chemotherapy is always needed first to reduce a large tumor volume before the immune system can become effective.

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Acknowledgements

This material is based upon research supported by the National Science Foundation under collaborative research grants DMS 1008209 and 1008221 (U.L. and H.S.), and by the EU project “p-Medicine: Personalized Medicine” (FP7-ICT-2009.5.3-270089) (A. d’O.). We also would like to thank our students Mohamad Naghnaeian and Mozhdeh Faraji for carrying out the numerical computations and making the figures used in the paper.

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Authors and Affiliations

  1. Department of Experimental Oncology, European Institute of Oncology, Via Ripamonti 435, 20141, Milan, Italy

    Alberto d’Onofrio

  2. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, 62026-1653, Edwardsville, IL, USA

    Urszula Ledzewicz

  3. Department of Electrical and Systems Engineering, Washington University, 631304899, St. Louis, MO, USA

    Heinz Schättler

Authors
  1. Alberto d’Onofrio
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  2. Urszula Ledzewicz
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  3. Heinz Schättler
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Corresponding author

Correspondence to Urszula Ledzewicz .

Editor information

Editors and Affiliations

  1. Department of Experimental Oncology, European Institute of Oncology, Milan, Italy

    Alberto d’Onofrio

  2. Department of Mathematics, University of Pisa, Italy

    Paola Cerrai

  3. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti“ — CNR, Rome, Italy

    Alberto Gandolfi

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d’Onofrio, A., Ledzewicz, U., Schättler, H. (2012). On the Dynamics of Tumor-Immune System Interactions and Combined Chemo- and Immunotherapy. In: d’Onofrio, A., Cerrai, P., Gandolfi, A. (eds) New Challenges for Cancer Systems Biomedicine. SIMAI Springer Series. Springer, Milano. https://doi.org/10.1007/978-88-470-2571-4_13

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