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Bulletin of Mathematical Biology

, Volume 73, Issue 1, pp 2–32 | Cite as

Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models

  • Raluca EftimieEmail author
  • Jonathan L. Bramson
  • David J. D. Earn
Review Article

Abstract

We briefly review spatially homogeneous mechanistic mathematical models describing the interactions between a malignant tumor and the immune system. We begin with the simplest (single equation) models for tumor growth and proceed to consider greater immunological detail (and correspondingly more equations) in steps. This approach allows us to clarify the necessity for expanding the complexity of models in order to capture the biological mechanisms we wish to understand. We conclude by discussing some unsolved problems in the mathematical modeling of cancer-immune system interactions.

Keywords

Cancer Immunology Tumor-immune system interaction Ordinary differential equations (ODEs) 

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Copyright information

© Society for Mathematical Biology 2010

Authors and Affiliations

  • Raluca Eftimie
    • 1
    Email author
  • Jonathan L. Bramson
    • 2
    • 3
  • David J. D. Earn
    • 1
    • 3
  1. 1.Department of Mathematics and StatisticMcMaster UniversityHamiltonCanada
  2. 2.Centre for Gene Therapeutics, Department of Pathology and Molecular MedicineMcMaster UniversityHamiltonCanada
  3. 3.Michael G. DeGroote Institute for Infectious Disease ResearchMcMaster UniversityHamiltonCanada

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