Numerous cell migration processes exhibit travelling waves, from tumour
cell invasion to the recruitment of cells during wound healing. Using a
scrape wound healing assay, we model contact inhibited cell motility and
cell proliferation with both continuum and discrete techniques. Imaging
analysis shows that cells at the healing wavefront tend to be more motile
compared to the cells behind the wavefront. This work has applications to
the modelling of cell migration where diffusion and proliferation are the
dominant mechanisms. We use both a modified Fisher equation, and an
interacting population model to match simulation outputs with experimental
data. Discrete simulations of reaction diffusion equations using
continuous time random walkers will be also discussed.