title: Influences of Allee effects in the spreading of malignant tumours.
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.
authors.affiliation: Mathematisch Instituut, Leiden University, 2300 RA, Leiden, The Netherlands. Electronic address: lotte@math.leidenuniv.nl.
authors.forename: Lotte
authors.initials: L
authors.lastname: Sewalt
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia.
authors.forename: Kristen
authors.initials: K
authors.lastname: Harley
authors.affiliation: School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia.
authors.forename: Peter
authors.initials: P
authors.lastname: van Heijster
authors.affiliation: School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia.
authors.forename: Sanjeeva
authors.initials: S
authors.lastname: Balasuriya
mesh_terms: D003198:Computer Simulation; D005109:Extracellular Matrix / Q000378:metabolism; D006801:Humans; D008954:Models, Biological; D009362:Neoplasm Metastasis / Q000473:pathology*; D009369:Neoplasms / Q000473:pathology*
keywords: Allee effects; Canard theory; Geometric singular perturbation theory; Malignant tumour model; Travelling wave solutions