In this paper we develop mathematical models for collective cell motility. Initially we develop a model using a linear diffusion-advection type equation and fit the parameters to data from cell motility assays. This approach is helpful in classifying the results of cell motility assay experiments. In particular, this model can determine degrees of directed versus undirected collective cell motility. Next we develop a model using a nonlinear diffusion term that is able capture in a unified way directed and undirected collective cell motility. Finally we apply the nonlinear diffusion approach to a problem in tumor cell invasion, noting that neither chemotaxis or haptotaxis are present in the system under consideration in this article.
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