Travelling Waves in Hybrid Chemotaxis Models

Benjamin Franz, Chuan Xue, Kevin J. Painter, Radek Erban

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations. © 2013 Society for Mathematical Biology.
Original languageEnglish (US)
Pages (from-to)377-400
Number of pages24
JournalBulletin of Mathematical Biology
Issue number2
StatePublished - Dec 18 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1- 013-04
Acknowledgements: The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 239870. This publication was based on work supported in part by Award No KUK-C1- 013-04, made by King Abdullah University of Science and Technology (KAUST). Radek Erban would also like to thank the Royal Society for a University Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship, and the Leverhulme Trust for a Philip Leverhulme Prize. This prize money was used to support research visits of Chuan Xue and Kevin Painter in Oxford. Kevin Painter acknowledges a Leverhulme Trust Research Fellowship award (RF-2011-045). Chuan Xue is supported by the National Science Foundation in the United States through grant DMS-1312966 and the Mathematical Biosciences Institute at the Ohio State University as a long-term visitor.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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