Hybrid Modelling of Individual Movement and Collective Behaviour

Handle URI:
http://hdl.handle.net/10754/598524
Title:
Hybrid Modelling of Individual Movement and Collective Behaviour
Authors:
Franz, Benjamin; Erban, Radek
Abstract:
Mathematical models of dispersal in biological systems are often written in terms of partial differential equations (PDEs) which describe the time evolution of population-level variables (concentrations, densities). A more detailed modelling approach is given by individual-based (agent-based) models which describe the behaviour of each organism. In recent years, an intermediate modelling methodology - hybrid modelling - has been applied to a number of biological systems. These hybrid models couple an individual-based description of cells/animals with a PDE-model of their environment. In this chapter, we overview hybrid models in the literature with the focus on the mathematical challenges of this modelling approach. The detailed analysis is presented using the example of chemotaxis, where cells move according to extracellular chemicals that can be altered by the cells themselves. In this case, individual-based models of cells are coupled with PDEs for extracellular chemical signals. Travelling waves in these hybrid models are investigated. In particular, we show that in contrary to the PDEs, hybrid chemotaxis models only develop a transient travelling wave. © 2013 Springer-Verlag Berlin Heidelberg.
Citation:
Franz B, Erban R (2013) Hybrid Modelling of Individual Movement and Collective Behaviour. Dispersal, Individual Movement and Spatial Ecology: 129–157. Available: http://dx.doi.org/10.1007/978-3-642-35497-7_5.
Publisher:
Springer Science + Business Media
Journal:
Dispersal, Individual Movement and Spatial Ecology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2013
DOI:
10.1007/978-3-642-35497-7_5
Type:
Book Chapter
ISSN:
0075-8434; 1617-9692
Sponsors:
The research leading to these results has received funding from the EuropeanResearch Council under theEuropean Community’sSeventh Framework Programme(FP7/2007–2013)/ERCgrant agreementNo. 239870. This publication was based on work supported in partby Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology(KAUST). RE would also like to thank Somerville College, University of Oxford, for a FulfordJunior Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti JuniorFellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust fora Philip Leverhulme Prize.
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Full metadata record

DC FieldValue Language
dc.contributor.authorFranz, Benjaminen
dc.contributor.authorErban, Radeken
dc.date.accessioned2016-02-25T13:31:32Zen
dc.date.available2016-02-25T13:31:32Zen
dc.date.issued2013en
dc.identifier.citationFranz B, Erban R (2013) Hybrid Modelling of Individual Movement and Collective Behaviour. Dispersal, Individual Movement and Spatial Ecology: 129–157. Available: http://dx.doi.org/10.1007/978-3-642-35497-7_5.en
dc.identifier.issn0075-8434en
dc.identifier.issn1617-9692en
dc.identifier.doi10.1007/978-3-642-35497-7_5en
dc.identifier.urihttp://hdl.handle.net/10754/598524en
dc.description.abstractMathematical models of dispersal in biological systems are often written in terms of partial differential equations (PDEs) which describe the time evolution of population-level variables (concentrations, densities). A more detailed modelling approach is given by individual-based (agent-based) models which describe the behaviour of each organism. In recent years, an intermediate modelling methodology - hybrid modelling - has been applied to a number of biological systems. These hybrid models couple an individual-based description of cells/animals with a PDE-model of their environment. In this chapter, we overview hybrid models in the literature with the focus on the mathematical challenges of this modelling approach. The detailed analysis is presented using the example of chemotaxis, where cells move according to extracellular chemicals that can be altered by the cells themselves. In this case, individual-based models of cells are coupled with PDEs for extracellular chemical signals. Travelling waves in these hybrid models are investigated. In particular, we show that in contrary to the PDEs, hybrid chemotaxis models only develop a transient travelling wave. © 2013 Springer-Verlag Berlin Heidelberg.en
dc.description.sponsorshipThe research leading to these results has received funding from the EuropeanResearch Council under theEuropean Community’sSeventh Framework Programme(FP7/2007–2013)/ERCgrant agreementNo. 239870. This publication was based on work supported in partby Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology(KAUST). RE would also like to thank Somerville College, University of Oxford, for a FulfordJunior Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti JuniorFellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust fora Philip Leverhulme Prize.en
dc.publisherSpringer Science + Business Mediaen
dc.titleHybrid Modelling of Individual Movement and Collective Behaviouren
dc.typeBook Chapteren
dc.identifier.journalDispersal, Individual Movement and Spatial Ecologyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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