Influences of Allee effects in the spreading of malignant tumours

Lotte Sewalt*, Kristen Harley, Peter van Heijster, Sanjeeva Balasuriya

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)

Abstract

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371-379, 2014] evidences that the Allee effect-in its strong form, the requirement of a minimum density for cell growth-is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Original languageEnglish
Pages (from-to)77-92
Number of pages16
JournalJournal of Theoretical Biology
Volume394
DOIs
Publication statusPublished - 7 Apr 2016
Externally publishedYes

Keywords

  • Allee effects
  • Canard theory
  • Geometric singular perturbation theory
  • Malignant tumour model
  • Travelling wave solutions

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