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Modeling Cancer As An Evolutionary Game

Author

Listed:
  • THOMAS L. VINCENT

    (Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona 85745, USA)

  • ROBERT A. GATENBY

    (Department of Radiology, University of Arizona, Tucson Arizona, Tucson, Arizona 85745, USA)

Abstract

We present two different mathematical models that examine the role of cellular evolution in the development and treatment of cancer. The first is a Lotka-Volterra model of an invasive cancer subjected to chemotherapy that demonstrates rapid evolution of drug-resistant phenotypes. The second model represents a major refinement of the first one with the objective of producing a simple, but realistic model of carcinogenesis. It is a consumer-resource model (consumers = normal + mutuant cells, resource = glucose). We conclude that if mutant cells are not allowed to evolve, they will not ordinarily progress to cancer. However, if accumulating mutations allow cellular evolution and successful adaptation to proliferation constraints, normal cells will develop into invasive cancer. We find this progression is possible because normal cellular populations are not at an evolutionarily stable state and so are subject to invasion by more fit phenotypes.

Suggested Citation

  • Thomas L. Vincent & Robert A. Gatenby, 2005. "Modeling Cancer As An Evolutionary Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 331-346.
    • Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:03:n:s0219198905000557
    DOI: 10.1142/S0219198905000557
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    Keywords

    Evolutionary games; carcinogenesis; modeling cancer;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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