The top row of figure 4 corresponds to the unlikely scenario when each spatial district has identical parameters; in reality, there is likely to be significant heterogeneity in transmission between different areas owing to social and demographic factors. In the 2009 influenza pandemic in the UK, it was observed that the epidemic grew more rapidly in London and the West Midlands, possibly owing to such a mixture of socio-demographic factors. Unfortunately, the degree of such heterogeneity is difficult to estimate and is likely to vary between outbreaks; we therefore force the transmission rate within each district to be lognormally distributed about the mean, with the variance of the distribution controlled by the spatial heterogeneity (H ). (In particular, the transmission rate is given