We used data from the French General Practitioner (GP) Sentinel network 21 . The network is a continuous epidemiological surveillance system based on voluntary GPs and operating since 1984 in France. Sentinel GPs report cases of influenza-like illness (ILI), defined as abrupt-onset fever above 39°C accompanied by respiratory signs and symptoms and myalgia or stiffness. Weekly national ILI incidence was estimated from the average number of ILI cases reported by GPs participating in surveillance during a week, multiplied by the ratio of all French GPs to participating sentinel GPs 22 . Surveillance criteria and procedures were not modified during the first pandemic season.

Three age groups were considered: children (0-18 years), younger adults (< 65 years), and the elderly (≥65 years). In order to estimate the total size of the infected population, we took into account the fact that some cases of ILI might have been caused by other pathogens (poorly specific case definition), and that not all cases of influenza virus infection would result in ILI corresponding to the case definition (lack of sensitivity). The latter cases would include asymptomatic and paucisymptomatic infection. We also took into account the fact that not all patients with typical ILI seek medical advice (figure 1).

To overcome the poor specificity of the clinical case definition, we calculated the excess of GP consultations by children and adults under 65, relative to baseline rates, using seasonal regression models fitted to historical data since 1985, as described elsewhere 23 . The seasonal regression model was used to fit all-ages weekly incidence data between 1985 to 2010, defining the first French pandemic season as the period during which the incidence of medical visits for ILI exceeded the upper 90% limit of the predicted incidence for at least two consecutive weeks. The excess attributed to 2009 H1N1 was calculated in the same way, using a separate model for each age group, by summing the weekly differences between the observed and predicted incidence rates during the first pandemic season. We used a different method for elderly subjects, among whom the seasonality of medical visits for ILI was less clear-cut. We assumed that 50% of medical visits for ILI in this age group during the first pandemic season were associated with 2009 H1N1 infection, while rates of 0-100% were used to calculate confidence intervals. In children and younger adults, excess medical visits attributed to 2009 H1N1 represented, on average, 85% of all medical visits for ILI during the first pandemic season.

The proportion of patients with ILI who did not seek medical advice was estimated from a monthly telephone survey, conducted since May 2009, of a representative sample of 800 members of the general population (unpublished data). Overall, approximately 40% of persons who reported having typical 'flu-like symptoms did not consult a GP, which is consistent with the results of a prospective follow-up survey of 817 household contacts of index cases with seasonal influenza virus infection (43%) 24 . Finally, we used values from a meta-analysis of experimental human influenza challenge studies showing that approximately 65% of infected volunteers did not develop typical 'flu-like illness (33% did not have symptoms, 32% did not have fever), and who would not thus have matched our case definition 25 . The proportion of infections not matching the ILI definition was assumed to be lower in children (45%), who are considered more likely than adults to develop fever 26 .

Population data and demographic parameters were obtained from national censuses 27 . In France, pandemic influenza vaccination started in November 2009, initially in groups at risk of complications. Influenza vaccine coverage rates were obtained from the French national security database. Adjuvanted vaccines were used in the vast majority of cases. At the end of first pandemic season the vaccine coverage rates were 12.6% in children, 6.8% in younger adults, and 6.7% in the elderly, most subjects having received a single injection. Confidence limits for proportions were calculated with the delta method.

We used an individual-centred model, which permits rich parameterization of the simulated population 20 . The model included detailed descriptions of healthcare use and interventions aiming at controlling influenza. It also included demographic characteristics and household sizes, and simulated the spread of influenza through the use of randomly generated graphs. The random graphs were a mixture of bidirectional graphs, comprising fully-connected graphs for describing contact pattern within the household, and Barabasi-Albert scale free graphs 28 for describing other social contacts. The networks exhibit a substantial level of clustering meaning that two simulated individuals have an increased chance to be contacts of each other given that they share a common network contact. The connectivity of the simulated network followed a power law distribution, with some individuals having a large number of contacts which allows generation of superspreading events

The mean number of contacts per subject (the connectivity of the network) was 13.9 overall (standard deviation SD = 0.4), 15.3 (SD = 0.06) for children, 14.6 (SD = 0.59) for younger adults, and 5.1 (SD = 0.16) for the elderly, in keeping with the results of recent large surveys 29 30 . New networks were generated at each simulation.

We made the following assumptions:

- We used realistic modelling of infectivity based on experimental infection viral shedding data 25 . Rather than assuming that infectivity was constant, we modelled it as a function depending on the time elapsed from infection 31 . We assumed the kinetics of infectivity had a gamma density function form (shape parameter = 5.2, scale parameter = 1), with an offset of 0.5 day (a latent period) and the function was truncated at ten days. Infectivity did not depend on age 32 and peaked at 2.1 days, with a calculated generation time of 2.6 days 33 34 35 . Infectivity was scaled during the fitting process to adjust the observed data. The resulting probability of transmission during a hypothetical meeting lasting throughout the infective period between a susceptible and a single infected individual was 40%.

- Children were fully susceptible to infection, and unknown proportions of the younger adult and elderly populations (to be calculated) were immune to 2009 H1N1 before it started to circulate. We assumed that these immune subjects could not be infected, irrespective of the number of contacts with infectious persons ("all-or-nothing" protection) 36 .

- Subjects with asymptomatic infection were half as infective as other subjects, and, among subjects who consulted a GP, 40% did so the first day after symptom onset, 30% the second day, and 30% later than the second day 24 .

- We postulated that 70% of individuals who consulted a GP would remain confined to home for five days, as recommended 37 .

- We assumed that 50% of patients who visited a doctor within two days of symptom onset received antiviral therapy. We also assumed that antiviral treatment reduced an individual's infectiousness by 28% 38 , and their risk of severe influenza by 80% 5 7 12 13 . Antiviral prophylaxis was not considered, as it was not recommended in France during the first H1N1 season.

- For consistency with observed vaccine coverage rates, we assumed that vaccination started 4 weeks after the outset of the epidemic and increased linearly over the next 7 weeks. We assumed that influenza vaccination was 80% protective against infection and illness, irrespective of age, starting 15 days after vaccination. Vaccination was administered irrespective of the individual's history of exposure or immunity to influenza viruses.

The model was calibrated by varying the proportion of younger adults and elderly subjects with pre-exposure immunity to fit the excess rates of medical visits attributed to 2009 H1N1 in the relevant age group. For each set of parameters we ran 400 simulations, starting with a single infectious individual at the first day of the first French pandemic season. We classified as "outbreaks" situations in which more than 5 per 1000 subjects were infected 20 . Goodness-of-fit was optimized by minimising the difference by age group between the observed and average rates in simulated outbreaks. The size of the post-exposure immunized population was estimated in each of the three age groups as the proportion of individuals who were infected during the first pandemic season or who were immunized naturally or by vaccination prior to the first pandemic season. Confidence limits for the rates of post-exposure immunity were calculated, assuming that the rate of pre-exposure immunity could vary between +5% and -5% of the values obtained in the fitted model.

We also simulated a scenario in which the entire population was susceptible before introducing infectious individuals, all other parameters being equal, in order to examine how a total lack of pre-exposure immunity might influence the first pandemic season.

We calculated the effective reproductive number by simulating the first generation of secondary cases after introducing a single infectious subject, as described elsewhere 20 . We also calculated a basic reproductive number by setting all parameters related to healthcare use (treatment, isolation, etc.), and the size of the pre-exposure immune population, to zero.

We simulated reintroduction of individuals infected by a pandemic H1N1 virus exhibiting modified antigenic properties (due to antigenic drift for example), at a rate of 2/1000, in a population in which individuals who were immune after the first season had varying levels of persistent protective cross-immunity against the new virus 39 . For these individuals, the chance of being infected during contact with an infected individual was reduced by 90% to 30%. All other parameters (transmission parameters, pathogenicity, contact networks and healthcare use) remained identical to those used to adjust the first epidemic curve. We completed each scenario by postulating that 10% to 50% of the entire population (or children) who were not vaccinated during the first pandemic season would receive the 2009 H1N1 vaccine before the reintroduction of infectious individuals. Vaccine effectiveness was reduced in proportion to the postulated cross-protection (vaccine effectiveness = 80% x cross-protection), as the mechanism underlying the loss of naturally acquired immunity would also concern vaccination-induced immunity, as vaccines being prepared for the 2010-2011 season cover 2009 H1N1 40 .

The first pandemic season in France lasted 16 weeks, from 7 September 2009 to 27 December 2009. The incidence of medical visits for ILI increased moderately and remained at a stable low level during the first 6 weeks, then increased more sharply and peaked between 6 and 12 December.

During the course of the first pandemic season, we estimated that the proportions of the population who consulted a GP for ILI were 4.86% overall (95%CI 3.62%-6.11%), 12.7% among children (95%CI 11.3%-14.0%), 3.11% (95%CI 1.67%-4.56%) among younger adults, and 0.34% among the elderly (95%CI 0-0.68%) (figure 2). The estimated proportion of the population infected by pandemic H1N1 was 18.1% overall (95%CI 12.2%-23.9%), 38.3% (95%CI 30.8%-45.9%) among children, 14.8% (95%CI 7.01%-22.6%) among younger adults, and 1.62% (95% CI 0%-3.60%) among the elderly.

The model was fitted to the excess rates of medical visits attributed to 2009 H1N1 by setting the pre-exposure immune populations to 36% among younger adults and 85% among the elderly. The simulated proportion of infected persons was 18.2% overall (InterQuartile Range (IQR) 17.2%-20.7%), 39.3% in children (IQR 37.3%-44.0%), 14.8% in younger adults (IQR 13.0%-17.1%) and 1.49% in the elderly (IQR 1.21%-1.76%). The simulated outbreaks lasted an average of 13.1 weeks (IQR 11-14 weeks), 10% of outbreaks exceeding 16 weeks.

The post-exposure immune population represented 57.3% overall (95%CI 49.6%-65.0%), 44.6% (95% CI 35.5%-53.6%) in children, 53.8% (95%CI 44.5%-63.1%) in younger adults, 87.4% (82.0%-92.8%) in the elderly.

Postulating no pre-exposure immunity in younger adults and elderly persons, the simulated proportions of infected persons would be 47.9% overall (IQR 46.2%-49.7%), 64.2% in children (IQR 62.6%-65.4%), 47.6% in younger adults (IQR 45.4%-49.7%) and 26.7% among the elderly (IQR 25.2%-27.9%). An estimated 11.9% (11.4%-12.4%) of the total population would consult a GP for ILI caused by 2009 H1N1.

The effective reproductive number was 1.03 and the basic reproductive number 1.54 (figure 3). An average of 1.57 persons were infected (1.11 children, 0.45 younger adults and 0.01 elderly persons) when the index patient was a child, 0.96 (0.23 children, 0.72 younger adults, 0.01 elderly) when the index patient was a younger adult, and 0.43 (0.14 children, 0.25 younger adults, 0.04 elderly persons) when the index patient was an elderly person.

As shown in Table 1, persistent cross-protection above 70% would be necessary to markedly limit the size of a second pandemic season due to a virus with different antigenic properties. Cross-protection of 50% would imply attack rates of 23.1% overall, and rates notably higher in younger adults and the elderly than during the first pandemic season. Influenza vaccination of 30 to 50% of the population, in addition to the population vaccinated during the first pandemic season, would halve the attack rates, provided that cross-protection was not below 50%. With cross-protection below 30%, vaccination of 50% of the population would have little impact. Vaccination of children alone would limit the burden of influenza in all age groups if cross-protection was between 50% and 70% and the vaccine coverage rate exceeded 50%; in contrast, this measure would have little impact in case of cross-protection greater than 70%; and would be barely effective in case of cross-protection below 50%.