The historical seasonal ILI data are temporally heterogeneous, with substantial week-to-week variability ( Figure 1 ). For making any useful and robust statistical inference the probability distribution requires smoothing. The smoothing was done assuming that the weekly reported ILI cases in a HB have a Poisson distribution with rate parameter equal to the reported total weekly ILI cases in the HB. The Poisson distribution is preferred to a binomial distribution as the numbers of weekly reported cases are very much smaller than the total population of a health board. We simulated the Poisson model to generate weekly ILI cases at the HB level (see Additional file 2). The model-generated ILI counts from individual runs for each season were then used, as described above, to calculate the joint distribution of WCR and N HB . A set of 10,000 model runs per season's data were used in the estimation of this joint distribution. A smaller (1,000) or larger (100,000) number of runs were also tested for the robustness of the results.