Collective Behavior: Macroscopic versus Kinetic Descriptions

Modelling collective cell migration in biology

Philip Maini

Oxford University

Collective cell motion in biology can arise in a number of different ways and this talk will review three of them. We will consider a classical partial differential equation approach to investigate tumour cell invasion, then we will present a hybrid individual-based model for neural crest cell invasion and finally a model for epithelial sheet movement. We will show that in very simple cases, all these models reduce at the macroscopic level to a nonlinear diffusion equation where the microscopic level description is encoded in the nonlinearity of the diffusion coefficient