In the England and Wales dataset, the lowest DIC model is the single infected city parameter model in column 6 of table 1. The model is dependent on the destination population size, has estimated dependence of infectivity on mortality and an estimated intermediate degree of density dependence. The distance power g was estimated as 1.18 (0.96, 1.39). A lower value was found for models in the US, where for the most parsimonious low DIC model (density dependent, population independent), g was estimated as 0.79 (0.54, 1.00). Figure 3 shows the distance kernels for the two datasets. The credible intervals for g overlap for the two datasets.