Others have developed theoretical lattice-based models for epidemics (and see my comment below), but a highly significant aspect of the current work is that the authors took a rigorous approach to fitting their models to actual epidemic data, estimating parameters, and comparing predictions (including the heterogeneity of the predictions).
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Fitting a lattice model with local and global transmission to spread of a plant disease.
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We see a clear trend of increasing times to reach each row, and the dispersal model visually matches the data better than the equivalent plots for the lattice model ( Fig 3 B).