Hybrid Modelling of Individual Movement and Collective Behaviour

Benjamin Franz, Radek Erban

Research output: Chapter in Book/Report/Conference proceedingChapter

12 Scopus citations

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.
Original languageEnglish (US)
Title of host publicationDispersal, Individual Movement and Spatial Ecology
PublisherSpringer Nature
Pages129-157
Number of pages29
ISBN (Print)9783642354960
DOIs
StatePublished - Jan 3 2013
Externally publishedYes

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