Table 1.
Epidemiological parameters used in the baseline simulations (R0 = 1.48, Tg = 3.1 days).
Table 2.
Correlation of population variables and epidemic statistics as observed or predicted by the model in the different European countries.
Figure 1.
Timing of the pandemic (R0UK = 1.48 Tg = 3.1 days).
(A) Distribution of the fraction of predicted attack rate (2.5%, 25%, 50%, 75% and 97.5% percentiles) by the end of August (week 35) in the different countries. In the inset, mean incidence per week in the different European countries in colour scale, from dark green (less than 5 per 1,000) to dark red (above 50 per 1,000). (B) Probability of observing a summer wave with peak incidence in a given range, in UK (blue), Germany (cyan), Netherlands (orange), Ireland (green) and Spain (red). (C) Observed peak week plotted versus predicted peak week (vertical bars represent 95% confidence intervals of the predictions) for European countries covered by the WHO/Europe weekly influenza surveillance system; only the autumn wave is considered for UK. In the inset minimum, 25%, 50%, 75% percentiles and maximum of observed minus predicted peak week. A total of 100 simulations were undertaken to produce the results shown.
Figure 2.
Spatiotemporal spread of the European pandemic (R0UK = 1.48 Tg = 3.1 days).
(A) Comparison between average weekly incidence in UK as predicted by the model (red) and weekly HPA case estimates (blue). Red shaded area represents 95% confidence intervals of the expected weekly incidence over time. (B) Comparison between average weekly incidence in Italy as predicted by the model (red) and weekly ILI cases [35] (blue). (C) Comparison between average weekly incidence in France as predicted by the model (red) and weekly ILI cases [37] (blue). (D) As (C) but assuming R0UK = 1.43. (E) Time sequence (in days) of a single simulation with the first European case in UK is shown. Colours from pink to dark red indicate an increasing number of daily cases (dark red indicates more than 10,000 daily cases). A total of 100 simulations were undertaken to produce the results shown.
Figure 3.
Variation in attack rates by age and country (R0UK = 1.48 Tg = 3.1 days).
(A) Average cumulative attack rate predicted by the model in the different European countries (black bars represent 2.5% and 97.5% percentiles of the distribution). Colours represent the fraction of individuals <15 year old in the population, increasing from yellow (13%) to red (22%). (B) Average peak weekly incidences predicted by the model in the different countries for the summer (orange) and the autumn (cyan) waves; for each country and wave, 2.5% and 97.5% percentiles of the distribution are shown (red and blue bars). (C) Post pandemic age-stratified attack rates. Estimates of post pandemic seroconvertion rates in England [34] (precisely, differences between the percentage of post pandemic (2010) serum samples from England with HI 1∶32 or more, and corresponding percentages in serum samples obtained in 2008 in England) against cumulative attack rates by age in UK predicted by the model at the end of the pandemic: red points represent the expected value of post pandemic seroconversion rates (vertical lines represent 95% confidence intervals), shaded blue areas represent 95% confidence intervals of model simulations. Cumulative attack rates by age as predicted by the model at the end of epidemic in different European countries are shown in the inset: shaded grey area represent 95% confidence interval at European level, while solid lines represent the median for Italy (blue), Germany (red) and Ireland (green). A total of 100 simulations were undertaken to produce the results shown.
Figure 4.
Sensitivity to assumed R0 and Tg.
(A) Sensitivity analysis by varying R0UK and Tg: level curves (and numbers) in black represent the mean deviation between observed and predicted peek week (in weeks). Colours represent the expected number N of countries with peak of the summer wave above 30 per 1000 individuals, ranging from dark green (N = 0) to dark red (N>30). Light green indicates 0.5<N< = 1.5, yellow indicates 1.5<N< = 2.5 and light orange indicate 2.5<N< = 5. Blue points represent possible pairs (R0UK, Tg) as resulting from the Qsurveillance data: R0UK = 1.42, Tg = 2.7 days; R0UK = 1.48, Tg = 3.1 days; R0UK = 1.55, Tg = 3.5 days. Blue vertical lines represent the uncertainty of R0UK as resulting from the uncertainty of the growth rate r of the Qsurveillance data. (B) Peak week for European countries covered by the WHO/Europe weekly influenza surveillance system as observed (cyan bars), as predicted by simulations with R0UK = 1.48 and Tg = 3.1 days (black squares), as predicted by simulations with R0UK = 1.42 and Tg = 2.7 days (green squares) and as predicted by simulations with R0UK = 1.55 and Tg = 3.5 days (red squares). (C) As (B) but for the fraction of the attack rate by end of August. (D) As (B) but for the cumulative attack rate. A total of 100 simulations were undertaken for each parameter set to produce the results shown.
Figure 5.
Effects of school holidays (R0UK = 1.48 Tg = 3.1 days).
(A) Fraction of all infections expected by end of August (week 35) as predicted by baseline simulations (actual school calendars in all countries, including autumn holidays, black squares), by assuming no holidays (green circles), by assuming the school calendar of Finland in all countries (schools close on 30 May, red circles) and by assuming the school calendar of UK in all countries (schools close on 20 July, blue circles). (B) Peak week for European countries covered by the WHO/Europe weekly influenza surveillance system as observed (cyan bars), as predicted by baseline simulations (black squares), by assuming no holidays (green circles), by assuming the school calendar of Finland in all countries (red circles) and by assuming the school calendar of UK in all countries (blue circles). A total of 100 simulations for each parameter set were undertaken to produce the results shown.
Figure 6.
Effects of age-dependent susceptibility to infection (R0UK = 1.48 Tg = 3.1 days).
(A) Peak week for European countries covered by the WHO/Europe weekly influenza surveillance system as observed (cyan bars), as predicted by baseline simulations (susceptibility of children 2 fold greater than that of adults, black), by assuming that susceptibility of children and adults was identical (red) and by assuming children were 4-fold more susceptible than adults (green). (B) As (A) but showing the fraction of the attack rate by end of August. (C) As (A) but showing mean cumulative attack rates by age in UK. The inset shows the distribution across simulations of the cumulative attack rates in UK in the three scenarios. A total of 100 simulations for each parameter set were undertaken to produce the results shown.
Figure 7.
Predictions of simpler models (R0 = 1.48 Tg = 3.1 days).
(A) Observed peak week plotted versus predicted peak week (predictions refer to the best model with coupling between European countries: R0 = 0.8 during holidays; vertical bars represent 95% confidence intervals of the predictions) for European countries covered by the WHO/Europe weekly influenza surveillance system; only the Autumn wave is considered for UK. (B) Prediction error (average of the absolute value of predicted minus observed peak week in European countries covered by the WHO/Europe weekly influenza surveillance system) as a function of the relative change of R0 during the summer for models with (red points) and without (blue points) coupling between European countries (i.e. long-distance travel). Vertical lines corresponds to the relative change of R0 during holidays in four European countries as resulting from the analysis of the POLYMOD data [39]. (C) Probability of observing a summer wave with peak incidence in a given range (predictions refer to the best model with coupling between European countries: R0 = 0.8 during holidays), in UK (blue), Germany (cyan), Netherlands (orange), Ireland (green) and Spain (red). (D) Cumulative attack rate (2.5%, 25%, 50%, 75% and 97.5% percentiles of the distribution are shown) in the different European countries (predictions refer to the best model with coupling between European countries: R0 = 0.8 during holidays). A total of 100 simulations for each parameter set were undertaken to produce the results shown.