We used the posterior median parameter estimates fitted to the England and Wales dataset to calculate a likelihood value in the US dataset. By likelihood ratio test, this value was not different from the most parsimonious low DIC US model (255.23, 257.72, p . 0.97). We therefore cannot reject the assumption that spread had the same characteristics in the US and England and Wales, though clearly the smaller size of the US dataset reduces inferential power. the epidemic during which each city was infected. Inferred city-to-city infection events more frequent than 70 per cent (in 1000 trees) are shown in black, events of lower frequency are shown in grey. Interactions in weeks 0 -3 are longer range than those in weeks 4 -7 ( p , 0.01), which are in turn longer range than those in weeks 8 -10 ( p , 0.01) (figure 4d ). The probability that the most likely infector was responsible for each infection falls as the epidemic progresses because there are many more potential infectors available later (figure 4e). Cities infected early give rise to more infections than those infected late in the wave, as expected, but the range is large, with some early cities giving rise to no new infections (figure 4f ). Figure 5 shows results for two models using the US data. We compare the most likely infection trees for the distance-only constant infectivity model with parameters inferred from the US data (figure 5a) with a model where parameters used to generate the trees are taken from the England and Wales single-infected city parameter model (figure 5c). In the distance-only constant infectivity model, the nearest infected city is always the most likely infector. In contrast, with the England and Wales parameters, some links between cities are high frequency, while other cities have several potential infectors of intermediate frequency ( figure 5b) . As in England and Wales, infection events inferred early in the epidemic have a higher support than those later in the epidemic. There are some exceptions owing to the distribution of cities in the US dataset-Oakland and San Francisco are distant from all other cities but very close to each other. In the distance-only constant infectivity model, some cities may give rise to a large number of new infections (e.g. Pittsburgh gives rise to nearly a quarter of infections) (figure 5d ). The effect of a city acting as a hub of infection is reduced in the more complex model, as the risk of infection from one city to another is the combined effect of several factors including distance.