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 random diffusion. We focus on cell–cell interaction mechanisms for a single population confined to an isolated domain. We derive a macroscopic mathematical model including a nonlocal saturation coefficient depending on a crowding capacity, as part of a nonlocal drift term. Then, this capacity acts as a threshold above which repulsion effects appear. This macroscopic model is approached using two different microscopic discrete models based on Eulerian or Lagrangian reference systems, respectively.