Tumour Modelling

  • Nicholas Ferris Britton
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


In the prosperous countries of the world, about one person in five will die of cancer. But why is it so common for cells to act in such a way as to kill their host, and therefore themselves, in apparent contradiction to the principles of natural selection? Natural selection works in two ways here. On the one hand, it acts on the population of cells within the animal. Although these cells are initially genetically identical, natural selection is strong because of high mutation rates leading to genetic variation for it to work on, high rates of reproduction, and high selective advantages. On the other hand, natural selection acts on the population of animals, and provides them with a battery of controls to guard against cancer. This is not as strong as might be expected because the heritable component of most cancers is small, as they are usually the result of a cascade of random somatic mutations, and because cancer is often a disease of old age, so that the selective advantages of not having it are small. Since there are about 1010 mutations per gene in a typical human lifetime, the fact that more cells do not escape from the controls that prevent them becoming cancerous shows how strong these controls are.


Bifurcation Diagram Free Boundary Problem Necrotic Core Gompertz Equation Avascular Tumour 
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Copyright information

© Springer-Verlag London 2003

Authors and Affiliations

  • Nicholas Ferris Britton
    • 1
  1. 1.Centre for Mathematical Biology, Department of Mathematical SciencesUniversity of BathBathUK

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