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Cell migration is frequently modelled using on-lattice agent-based models (ABMs) that employ the excluded volume interaction. However, cells are also capable of exhibiting more complex cell-cell interactions, such as adhesion, repulsion, pulling, pushing and swapping. Although the first four of these have already been incorporated into mathematical models for cell migration, swapping has not been well studied in this context. In this paper, we develop an ABM for cell movement in which an active agent can `swap' its position with another agent in its neighbourhood with a given swapping probability. We consider a two-species system for which we derive the corresponding macroscopic model and compare it with the average behaviour of the ABM. We see good agreement between the ABM and the macroscopic density. We also analyse the movement of agents at an individual level in the single-species as well as two-species scenarios to quantify the effects of swapping on an agent's motility.
Original languageEnglish
Article number044402
JournalPhysical Review E
Early online date27 Apr 2023
Publication statusPublished - 30 Apr 2023

Bibliographical note

Shahzeb Raja Noureen is supported by a scholarship from the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa), under the project EP/S022945/1. This research made use of the Balena High Performance Computing (HPC) Service at the University of Bath. The images in Figure 1 were taken by Dr. Matthew Ford (Centre for Research in Reproduction and Development, McGill, Canada). Richard Mort was supported by North West Cancer
Research (NWCR Grant CR1132) and the NC3Rs (NC3Rs grant NC/T002328/1). We would like to thank the members of Christian Yates’ mathematical biology reading group for constructive and helpful comments on a preprint of this paper. Finally, we would like to thank Fraser Waters for his help in managing some of the code related to this project.


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