The Mathematical Institute, University of Oxford, Eprints Archive

Hybrid modelling of individual movement and collective behaviour

Franz, B. and Erban, R. (2011) Hybrid modelling of individual movement and collective behaviour. In: Dispersal, individual movement and spatial ecology: A mathematical perspective. Springer. (Submitted)

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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 PDEmodel 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.

Item Type:Book Section
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1393
Deposited By:Peter Hudston
Deposited On:09 Sep 2011 07:58
Last Modified:09 Feb 2012 14:01

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