The analysis requires an estimate of when each city became infected to allow potential sources of that infection to be identified. For each city infected in week t, the candidate infectors are those infected in any week before t. We define the infection week of city i, t i , to be the first that meets a set of conditions on mortality in weeks t i þ 1, t i þ 2 and t i þ 3. We use mortality values ahead of t i to include the time from infection to death. A week could be designated the infection week if either (or both) of two sets of criteria were met for mortality in the following weeks. The first set of criteria required the mortality rate in week t i þ 1 to be above a certain threshold, to have increased in t i þ 2 and to be above a higher threshold in t i þ 3. These criteria are intended to ensure that the epidemic in that city is patently increasing. The second set of criteria was designed to capture cities where there was a rapid onset of increased influenza-related mortality. They therefore used a higher threshold on mortality in week t i þ 1, but less strict conditions on rate of growth in the following two weeks. The week of infection determined was found to be relatively robust to the precise choice of thresholds used. For further details on the algorithm and a spatio-temporal display of the result, see the electronic supplementary material.