Mathematical models for cell migration: a non-local perspective

Li Chen, Kevin J. Painter, Christina Surulescu, Anna Zhigun

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)
152 Downloads (Pure)


We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell-cell and cell-tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Original languageEnglish
Article number20190379
JournalPhilosophical Transactions of the Royal Society B: Biological Sciences
Issue number1807
Early online date27 Jul 2020
Publication statusPublished - 14 Sept 2020


  • cell–cell and cell–tissue adhesion
  • classes of non-local models
  • haptotaxis
  • integro-differential equations
  • mathematical challenges
  • non-local and local chemotaxis

ASJC Scopus subject areas

  • General Biochemistry,Genetics and Molecular Biology
  • General Agricultural and Biological Sciences


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