We have tested the effect on parameter estimates in England and Wales of relaxing the single-introduction assumption inherent in the model. We re-estimated the parameters conditioning on infections that occurred from week 3 of the epidemic onward. There is a small increase in the kernel power parameter estimate, which causes the kernel to decay more rapidly with distance (electronic supplementary material, figure S9 ). This suggests that the very long-range interactions, which are forced to occur early in the epidemic impact the shape of the kernel. However, the credible intervals largely overlap which indicates this assumption does not affect the fit of the model to a large degree.