When push comes to shove: Exclusion processes with nonlocal consequences

Authored by Kerry A Landman, Axel A Almet, Michael Pan, Barry D Hughes

Date Published: 2015

DOI: 10.1016/j.physa.2015.05.05.031

Sponsors: Australian Research Council (ARC)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case. (C) 2015 Elsevier B.V. All rights reserved.

Tags

proliferation models Populations Cell