A Model for Cell Proliferation in a Developing Organism

Abstract

In mathematical biology, there is a great deal of interest in producing continuum models by scaling discrete agent-based models governed by local stochastic rules. We discuss a particular example of this approach: a model for the proliferation of neural crest cells that can help us understand the development of Hirschprung’s disease, a potentially-fatal condition in which the enteric nervous system of a new-born child does not extend all the way through the intestine and colon. Our starting point is a discrete-state, continuous-time Markov chain model proposed by Hywood et al. (2013a) for the location of the neural crest cells that make up the enteric nervous system. Hywood et al. (2013a) sc..