Interacting motile agents: taking a mean-field approach beyond monomers and nearest-neighbor steps

Catherine J. Penington, Barry D. Hughes, Kerry A. Landman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Original languageEnglish
Article number032714
Pages (from-to)1-12
Number of pages12
JournalPhysical Review E
Issue number3
Publication statusPublished - Mar 2014
Externally publishedYes

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