To test whether these results pertain only to US or are more generally applicable to H3N2 influenza epidemiology, we collected a similar data set from Hong Kong and mainland China. Three epidemiological indicators (S-H3
) were obtained for 13 seasons (from 1997 to 2009) using data from Hong Kong Centre for Health Protection 
. Influenza epidemics in Hong Kong usually show two peaks (February-March and May-June). Both peaks were combined into the same season, and therefore a season corresponds to a calendar year in this analysis.
Because Hong Kong Centre for Health Protection data lacks ILI raw numbers, only %ILI for each month is available. Therefore, we calculated the total epidemic severity (%ILI*%Positive Specimens) for each month, and then totaled these numbers for a year to obtain. (As a test to show that this method gives results similar to the regular method (using cumulative raw numbers for each season to calculate %ILI and %Positive Specimens), we checked the correlation between the epidemic severity numbers calculated using the two methods for the USA data. The correlation between the two methods is very high (r=0.97). The H3 epidemic severity (S-H3) was calculated as the total influenza epidemic severity prorated by the fraction of H3 isolates among all isolates. These data were converted to a single epidemiological index using PCA (Figure 6). Interestingly, despite the fact that Hong Kong, like USA, is a non-tropical Northern Hemisphere country, the epidemic severity measures between the two are relatively weakly correlated (rs[epi.PC1.USA,epi.PC1.HK] = 0.36 with the p-value of 0.21). Thus the Hong Kong dataset provides a largely independent test of the model applicability.
Sequence and antigenic distances were computed in a manner similar to that for the US data (the list of Hong Kong isolates used for genetic distance calculation is in the supplementary file 
). Again, in this analysis, a season corresponds to a calendar year. Due to a low number of serologically tested isolates from Hong Kong proper, antigenic data were computed for a combined set of Hong Kong and mainland China isolates. The seasonal epidemiology seems to be the same in Hong Kong and Southern mainland China, and only Northern mainland China follows the standard Northern Hemisphere pattern 
. Moreover, the Northern China epidemics follow the Southern China epidemics and not vice versa 
. Based on this observation, two possible ways of merging these data sets were implemented, producing two versions of the serological distances (ac
in contrast to aa
serological distances for US). The first one (ac
) corresponds to the scenario where for all isolates (Hong Kong and China) the season was considered to correspond to a calendar year, following the Hong Kong pattern. The second one (as
) considers Hong Kong isolates following the Hong Kong pattern and China isolates following the Northern Hemisphere pattern with seasons starting in the fall.
Figure 6. First Principal Component (epi.PC1) of three measures of epidemiological severity for Hong Kong
There are several possible ways to apply the model derived from the US data to the Hong Kong data. One would be to directly compute the model prediction using the formula:
epi.PC1' = 1.26se.n.n2 + 1.78sn.n.n2 + 0.81ss.n.n2 - 0.41se.n1.n1 + 2.08aa.n1.n1
and replacing aa.n1.n1 (US data) with either ac.n1.n1 or as.n1.n1. Using as.n1.n1 for the serological distance variable, this formula produces a prediction that is reasonably well correlated with the real epidemiology data (rs[epi.PC1,epi.PC1’] = 0.60, with the p-value of 0.012 in a permutation test; Figure 7, "retro.direct" plot). This model allows rough prediction of the ups and downs of the H3N2 influenza epidemics in 1997-2009, but gives a relatively poor quantitative estimate.
When the model is allowed to use the actual epidemiological data from Hong Kong to adjust its coefficients (yielding 1.50, 1.46, -0.82, 0.34 and 0.64 respectively), the prediction is improved (Figure 7, "retro.adjust" plot). The adjusted model explains 0.75 of the original variance with F-statistics p-value of 2x10-2.
Finally, the stepwise reduction of the full model containing the genetic and serological distances from the corresponding seasons (se.n.n2, sn.n.n2, ss.n.n2, se.n1.n1, sn.n1.n1, ss.n1.n1, ac.n1.n1 and as.n1.n1) leads to the following 4-parameter model (Figure 7, "retro.stepwise" plot):
epi.PC1’ ~ se.n.n2 + sn.n.n2 + ac.n1.n1 + as.n1.n1 + 0
The model coefficients are 1.25, 0.75, 0.76 and 1.10 respectively; it explains 0.78 of the original variance with F-statistics p-value of 5x10-3. When trained on 8 out of the 13 seasons (leave-5-out jackknife test scheme) , this model explains 0.42 of the original variance on average.
Figure 7. Comparison of different retrospective models with observed Hong Kong epidemiological severity (epi.PC1)