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Extended Abstracts Spring 2018 pp 289–294Cite as

Birkhäuser

Cancer Evolution: The Appearance and Fixation of Cancer Cells

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Part of the book series: Trends in Mathematics ((RPCRMB,volume 11))

Abstract

Cancer appears as a result of mutation of normal tissue cells. In this paper, we consider the initial stage of the cancer appearance and development. In particular, we study the conditions that are necessary for an initial fixation of the mutant cells in a patient tissue and their further successful development. In order to do this, we are using a reasonably simple mutation-selection model composed of two interacting populations, namely, the normal cells and the mutant cells. Conditions for persistence of the mutant cells are found.

A. Korobeinikov is supported by Ministerio de Economía y Competitividad of Spain via grant MTM2015-71509-C2-1-R.

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References

  1. A. Korobeinikov, S. Pedarra, A discrete variant space cancer evolution model, in Proceedings of MURPHYS-HSFS-2018 Workshop. Trends in Mathematics: Research Perspectives CRM Barcelona, Summer 2018 (Springer-Birkhäuser, Basel, 2019)

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  2. A. Korobeinikov, K.E. Starkov, P.A. Valle, Modeling cancer evolution: evolutionary escape under immune system control. J. Phys. IOP Conf. Ser. 811 (2017)

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica “Tullio Levi–Civita”, Università degli Studi di Padova, Padova, Italy

    Stefano Pedarra

  2. Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193, Barcelona, Spain

    Andrei Korobeinikov

  3. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

    Andrei Korobeinikov

Authors
  1. Stefano Pedarra
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  2. Andrei Korobeinikov
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Corresponding author

Correspondence to Stefano Pedarra .

Editor information

Editors and Affiliations

  1. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Andrei Korobeinikov

  2. Facultat de Ciències, Universitat Autònoma de Barcelona, Barcelona, Spain

    Magdalena Caubergh

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Tomás Lázaro

  4. Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

    Josep Sardanyés

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Pedarra, S., Korobeinikov, A. (2019). Cancer Evolution: The Appearance and Fixation of Cancer Cells. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25261-8_43

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