A new mathematical model for cell motility with nonlocal repulsion from saturated areas

Abstract: The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for a single population confined to an isolated domain. Our most relevant contribution is to derive a mathematical model including a nonlocal saturation coefficient as part of an appropriate nonlocal drift term, including repulsion effects, depending on the level of saturation of the area. For this purpose, we use two discrete approaches taking into account different perspectives: Eulerian and Lagrangian reference systems.