Influences of Allee effects in the spreading of malignant tumours
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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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|Item Type:||Journal Article|
|Keywords:||Malignant tumour model, Alee effects, Travelling wave solutions, Geometric singular perturbation theory, Canard theory|
|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:||15 Feb 2016 18:15|
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