Stochastic individual-based modelling approaches allow for the investigation of complex biological systems, for example cell populations that exhibit single cell dynamics. These models generally include rules that each cell follows independently of other cells in the population. We have developed a range of IB models that describe biological systems in the context of pattern formation. From these models we have derived the continuum limits from the underlying random walk, providing a deterministic PDE description of these processes. Ultimately, the results illustrate how the simple rules governing the dynamics of single cells in an individual-based model can lead to the emergence of complex spatial patterns of population growth.
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