How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models

Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal continuum models by Falc\'o, Baker, and Carrillo (2023). We apply their theoretical results by specifying biologically-based cell-cell interactions, showing how such cell communication results in an effective attraction-repulsion Morse potential. We then explore the clustering instability, the existence and size of the cluster, and its stability. We also extend their work by investigating the accuracy of the local approximation relative to the full nonlocal model.