From individual-based models to continuum descriptions: Modelling and analysis of interactions between different populations.

First we will show that the continuum counterpart of the discrete individual-based mechanical model that describes the dynamics of two contiguous cell populations is given by a free-boundary problem for the cell densities. Then, in addition to interactions, we will consider the microscopic movement of cells and derive a fractional cross-diffusion system as the many-particle limit of a multi-species system of moderately interacting particles.