Reactions, diffusion and volume exclusion in a heterogeneous system of interacting particles

Cellular migration can be affected by short-range interactions between cells such as volume exclusion, long-range forces such as chemotaxis, or reactions such as phenotypic switching. In this talk I will discuss how to incorporate these processes into a discrete or continuum modelling frameworks. In particular, we consider a system with two types of diffusing hard spheres that can react (switch type) upon colliding. We use the method of matched asymptotic expansions to obtain a systematic model reduction, consisting of a nonlinear reaction-diffusion system of equations. Finally, we demonstrate how this approach can be used to study the effects of excluded volume on cellular chemotaxis. This is joint work with Dan Wilson and Helen Byrne.