Influences of Allee effects in the spreading of malignant tumours

Sewalt, Lotte, Harley, Kristen, van Heijster, Peter, & Balasuriya, Sanjeeva (2016) Influences of Allee effects in the spreading of malignant tumours. Journal of Theoretical Biology, 394, pp. 77-92.

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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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2 citations in Scopus
2 citations in Web of Science®
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ID Code: 92730
Item Type: Journal Article
Refereed: Yes
Keywords: Malignant tumour model, Alee effects, Travelling wave solutions, Geometric singular perturbation theory, Canard theory
DOI: 10.1016/j.jtbi.2015.12.024
ISSN: 0022-5193
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2016 Elsevier
Copyright Statement: Licensed under the Creative Commons Attribution; Non-Commercial; No-Derivatives 4.0 International. DOI: 10.1016/j.jtbi.2015.12.024
Deposited On: 08 Feb 2016 23:45
Last Modified: 17 May 2017 05:01

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