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Description

Many PDE-based models of collective cell behaviour implicitly assume that the population of cells is ‘well mixed’. This is called a spatial mean-field assumption. In reality, populations often have a more complex spatial structure, such as clusters and/or spatial segregation of cells. This spatial structure is both a cause and an effect of interactions among neighbouring cells and can make a significant difference to model predictions about, for example, cell densities and invasion speeds. I will describe an individual-based model of collective cell behaviour that is based on interactions between pairs of cells. I will show how a neighbour-dependent directional bias can be included in the model and how spatial moment dynamics can be used to give a continuum-level description of the population that retains spatial structure beyond the mean-field.