Influences of Allee effects in the spreading of malignant tumours

Journal of Theoretical Biology
Lotte SewaltSanjeeva Balasuriya

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.

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Citations

Nov 18, 2017·PLoS Computational Biology·Zoltan NeufeldAndras Czirok
Jun 21, 2019·PloS One·Marcelo A Pires, Sílvio M Duarte Queirós
Nov 2, 2017·Korean Journal of Radiology : Official Journal of the Korean Radiological Society·Carole DurotChristine Hoeffel
Mar 25, 2017·Bulletin of Mathematical Biology·Wang JinMatthew J Simpson
Nov 21, 2020·Journal of Mathematical Biology·Yifei LiMatthew J Simpson
Mar 13, 2021·NPJ Breast Cancer·Yael Artzy-RandrupRobert A Gatenby
Mar 31, 2021·ELife·Jean-Pascal CappFrédéric Thomas
Dec 21, 2021·Bulletin of Mathematical Biology·Yifei LiMatthew J Simpson

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