








key: cord-002138-uywz5nqw
authors: Boëlle, Pierre‐Yves; Ansart, Séverine; Cori, Anne; Valleron, Alain‐Jacques
title: Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review
date: 2011-03-31
journal: Influenza Other Respir Viruses
DOI: 10.1111/j.1750-2659.2011.00234.x
sha: 
doc_id: 2138
cord_uid: uywz5nqw

Please cite this paper as: Boëlle P‐Y et al. (2011) Transmission parameters of the A/H1N1 (2009) influenza virus pandemic: a review. Influenza and Other Respiratory Viruses 5(5), 306–316. Background The new influenza virus A/H1N1 (2009), identified in mid‐2009, rapidly spread over the world. Estimating the transmissibility of this new virus was a public health priority. Methods We reviewed all studies presenting estimates of the serial interval or generation time and the reproduction number of the A/H1N1 (2009) virus infection. Results Thirteen studies documented the serial interval from household or close‐contact studies, with overall mean 3 days (95% CI: 2·4, 3·6); taking into account tertiary transmission reduced this estimate to 2·6 days. Model‐based estimates were more variable, from 1·9 to 6 days. Twenty‐four studies reported reproduction numbers for community‐based epidemics at the town or country level. The range was 1·2–3·1, with larger estimates reported at the beginning of the pandemic. Accounting for under‐reporting in the early period of the pandemic and limiting variation because of the choice of the generation time interval, the reproduction number was between 1·2 and 2·3 with median 1·5. Discussion The serial interval of A/H1N1 (2009) flu was typically short, with mean value similar to the seasonal flu. The estimates of the reproduction number were more variable. Compared with past influenza pandemics, the median reproduction number was similar (1968) or slightly smaller (1889, 1918, 1957).

In April 2009, a new influenza virus A ⁄ H1N1 (2009) was isolated in Mexico and has rapidly spread over the world, being reported in 214 countries 1 year after its first identification. 1 The spread of the virus was extremely fast worldwide. 2 As soon as the new virus was identified, a major issue was to estimate the transmissibility of the new virus. In the guidance document 'Global surveillance during an influenza pandemic' released by the World Health Organization, three parameters were highlighted that should be documented quickly in this respect: the incubation period (time between infection and symptoms), the serial interval (time between symptoms onset in primary case and secondary case), and the reproduction ratio ⁄ number (average number of secondary cases per primary case). 3 These parameters are instrumental to assessing the feasibility and efficacy of intervention strategies against pandemic influenza. 4 Information regarding the serial interval and the reproduction number from past pandemics has been limited. For the serial interval, the best information concerned sea-sonal influenza infections 5, 6 and no information was available regarding past pandemics. There was comparatively more information regarding reproduction numbers, with estimates obtained in the last four pandemics (1889, 1918, 1957, 1968) . [7] [8] [9] [10] [11] [12] Estimates have ranged between 1 and 6 depending not only on place, time, wave, but also on the methods and assumptions used in estimation.

As we have now entered the post-pandemic period for H1N1(2009), 13 it is timely to review the results of all studies regarding the serial interval or generation time for the A ⁄ H1N1 flu, as well as the reproduction numbers, to allow comparison with previous pandemics and help in planning. Here, we present the results of a systematic review of published estimates concerning the first wave of A ⁄ H1N1 (2009) concerning the serial interval and the reproduction number.

The generation time (GT) is the time interval between the date of infection in one case and that in its infector. 14 It is difficult to measure in practice, as the actual time of infection is not observed. The serial interval (SI), i.e., the time interval between the date of symptoms onset in one case and that in its infector, is therefore often considered instead of the GT because it has the same mean. 14 The GT or SI informs on the speed of transmission of the disease. It is not an intrinsic property of the disease, but a combination of biology (how much and when is a person infectious) and behavior (how many and when contacts leading to infection occur). 15 A random sample of pairs of secondary case and their infector would allow unbiased estimation of the SI but is seldom available. In practice, various designs are used to observe pairs of infectee ⁄ infector, and this may impact the observed distribution. 16 For example, cases may be observed in households, where common exposure may have led to coprimary cases and ongoing transmission to an overlap of secondary and tertiary cases. Statistical modeling is therefore required to recover the true SI distribution.

The reproduction number (or reproduction ratio), denoted R, is defined as the average number of secondary cases caused by one index case. 17 A reproduction number may be calculated at any time during an outbreak, a value larger than 1 corresponding to epidemic spread of the disease. In practice, additional qualifiers are often used when reporting a reproduction number: 'initial' in the beginning of an epidemic; 'basic' when the whole population is initially susceptible to the disease -R is in this case denoted R 0 ; 'effective' when the natural course of the outbreak is altered, for example, by interventions. Several methods are available to estimate reproduction numbers: using attack rates, 18 the exponential growth rate, 19 averaging over transmission chains. 20 An assumption regarding the GT distribution may be required to estimate the reproduction number; in this case, a shorter mean GT will likely lead to a smaller reproduction number estimate. For all studies, we abstracted the date of publication, the place and date where the data were collected, the estimate of the reproduction number and of the mean SI or GT and its confidence interval when reported; we summarized how the data were collected and the method for analysis. We focused on reproduction number estimates described as 'basic' or 'initial'. In studies where the reproduction number was estimated as a function of time, we reported the range of R(t) values.

Seventeen independent estimates of the mean SI or GT during the 2009 H1N1 pandemic were reported in sixteen studies. Details are reported in Table 1 and Figure 1 . The data were collected early in the pandemic, between April and August 2009.

In a first group of 13 studies, estimation was based on the analysis of observed time intervals between cases and their close contacts, especially in households. Cases and their households or contacts were included as part of the local health authorities response to the pandemic, except in one study where households had been included in a prospective clinical trial. 21 Whether the data were prospective or retrospective was not reported except in two retrospective cases. 22, 23 Household contacts only were used in eight studies, 21,23-29 yielding mean SIs in the range of 2AE6-4AE4 days. In all but one study, the index case was the first case in the household. Household observed serial intervals were defined as the difference in date of symptoms onset between incident cases and the index case. In the study where the index case could be different from the first, all cases after the index were considered as secondary cases of the index case. 27 The other five studies included contacts not limited to the household, 22, [30] [31] [32] [33] with mean SIs in the range of 2AE5-3AE5 days. Here, pairs of infector ⁄ infectee were identified where the infector was the only, or most probable, source of infection.

The largest estimate (4AE4 days; range = [1, 9] ) was obtained from only five serial intervals observed in three households. 29 One estimate (2AE6 days, range = [1, 3] ) was based on eight observed household SI; however, only the first non-index-case in the household was used. 28 In four instances, only the median SI was reported, 22 23 very similar to the reported medians. In these calculations, coprimary cases (same day as index case) and those occurring more than 7 days after the index case were excluded. In all but two cases, the mean SI was calculated as the empirical mean of observed intervals, excluding the possibility of tertiary transmission. More sophisticated modeling allowing for several generations of transmission was carried out in the two other cases. In the first case, a householdbased study, the empirical mean SI (excluding coprimary cases and cases >7 days after) was 2AE9 days (95% CI [2AE7, 3AE1]). 24 After modeling, the reported mean SI decreased to 2AE6 days (95% CI [2AE2, 3AE5]). In the second case, derived from the FF100 cohort in the UK, the empirical mean SI of observed serial intervals was 3AE4 days (95% CI [2AE9, 3AE9]) and the reported mean SI decreased to 2AE5 days (95% CI [2AE1, 2AE9]) after modeling. 31 An overall estimate of the mean SI derived from these studies (excluding 28 ), weighting by the number of observed SIs used for estimation in each study, was 3AE0 days (CI 95% [2AE4, 3AE6]). No correlation was found between the reported SI and the size of the study (P = 0AE3) or the date of report (P = 0AE3). Household-based studies did not yield different estimates of the mean SI than close-contact studies (P = 0AE15).

A second group of four studies reported the SI or GT estimated by modeling epidemic curves. These included the smallest estimate of all, a mean GT of 1AE9 days (CI 95% [1AE3, 2AE7]) in a Mexican village, 34 and the largest, a mean GT of 4-5 days in Ontario. 35 The two other estimates used epidemic curves in the United States and Mexico, with results in the range of 2AE6-3AE2 days for the mean SI or GT. White estimated the mean SI at 2AE6 days (CI 95% [1AE9, 3AE3]), but accounting for increased case ascertainment in time reduced this estimate to 2AE2 days. 36 In Yang, the mean GT was 2AE7 or 3AE2 days depending on the assumed parametric form (Weibull or gamma). 29 

Reproduction numbers were reported in 24 studies (see Table 2 and Figure 2 ) for 20 countries. All studies focused on the first few months of the pandemic, with data obtained between March and October 2009. Overall, the estimates at the community level (town, region or country) varied between 1AE1 and 3AE1, with a median value of 1AE6. In the Netherlands, as in other European countries (except the UK), the reproduction number was smaller than 1 (R = 0AE5) in the period considered. 32, 37 The largest estimate (R = 3AE3) was obtained from the analysis of a school outbreak. 22 Ten papers qualified the reproduction number as 'basic', with a range from 1AE3 to 2AE3, all assuming that the whole population was susceptible at first; this range was not significantly different from that of the otherwise reported R values. In 15 analyses, the exponential growth rate estimated from the initial epidemic curve was used to estimate the reproduction number, with a range of values between 0AE5 and 3AE1. The method for estimating the exponential growth rate was variable (for example, Poisson regression, 38 birth and death process, 39 least squares, 40 modified logistic growth 41 ), as was the GT distribution (mean GT between 1AE9 and 4AE1) and the formula linking the exponential growth rate to the reproduction number. Other methods of estimation included fitting the output of transmission models to the data. 34, 35, 42 In two instances, the reproduction number was estimated using cases seen in tourists returning from Mexico, yielding 1AE4 (95% CI [1AE2, 1AE8]) 34 when comparing the number of cases in 9 countries to model predictions and 1AE7 (CI 95% [1AE6, 1AE9]) using only the date of first introduction in 12 countries. 43 No correlation was found in the reported reproduction number and the GT used in its computation (r = )0AE04; P = 0AE83). There was a decreasing trend in the reported values with time (r = )0AE5, P = 0AE004), large estimates being more frequent at first. A first explanation was the inclusion of correction for under-reporting: while no correction was applied for an early estimate in Mexico (R = 2AE2 38 ) and another analysis (R = 2AE3 29 ), accounting for an increasing trend in case reporting led to large differences, from 2AE4 to 1AE6 after such correction in Australia, 44 from 2AE2 to 1AE7 in the United States, 36 and from 2 to 1AE4 in Mexico. 42 Another issue was the importance of school outbreaks in the early epidemic curve, so that the estimated reproduction number was not representative of transmission in the community. For example, the R estimate was 2AE3 in Japan with a GT of 1AE9 days, 39 but the reproduction number was approximately 1AE3 when transmission was later established in the community. 45 Considering only estimates for which underdeclaration was taken into account and the generation time was close to 3 days, the reproduction number was between 1AE2 and 2AE3, with median value 1AE5.

Using all published information as of July 2010 regarding the A ⁄ H1N1 (2009) pandemic shows that the mean SI was <3 days and the reproduction number typically close to 1AE5.

A striking feature of the household ⁄ close-contact studies for the mean SI was that most estimates were in the range of 2AE5-3AE5 days, although the sampling as well as the meth-

Fraser (34) White (36) Yang (29) Yang (29) Tuite (35) Yang (29) Suess (28) Cowling (21) Leung (25) Lessler* (22) Hahné (32) SG-Spain* (30)

McBryde (33) Ghani (31) Cauchemez (24) France (23) Pedroni* (27) Morgan (26) Epidemic curve modelling ods of analysis was different. Overall, the weighted mean SI of all estimates was 3AE0 days (CI 95% [2AE7, 3AE3]), but this reduced to 2AE6 days in the studies where tertiary transmission was accounted for. Studies in households may have provided the best framework to estimate the SI, as potential contacts could be more easily identified. The only truly prospective study yielded little information (8 events), 21 so that the best evidence remains that from American households. 24 The number of studies documenting the serial interval in the 2009 influenza pandemic contrasts with the relative absence of information for past pandemics or seasonal influenza. Indeed, before 2009, the two best documented values for the mean SI concerned seasonal influenza, with two estimates obtained in household-based studies: 2AE6 days (CI 95% 2AE1, 3AE0) 6 and 3AE6 days (CI 95% [2AE9, 4AE3]) 5 ; no information was available for past pandemics. The current estimate for A ⁄ H1N1 (2009) was somewhat closer to the first estimate; it was also in good agreement with the 2AE8 days obtained by using the profile of viral excretion as a indicative of the GT distribution. 46 As reported mean SIs are rather short, it is worth examining whether the mean SI could have been biased downwards. Changes in behavior and interventions may make long serial intervals unlikely. There was little information regarding behavior change and interventions in the reported studies: household members were, for example, instructed in simple hand-hygiene, 21 some index cases received antiviral treatment, 26 but neither isolation nor quarantine was reported. As all studies concerned the early phase of the pandemic, differences in attitude toward the A ⁄ H1N1 flu may have been limited. A second issue is that the combination of rapid transmission and limited number of contacts in households may lead to small intervals. 16 The secondary attack rates were modest (13%, 24 11AE2%, 31 11AE3%, 23 8% 21 ), arguing against a large effect in this respect because of susceptible depletion. A short follow-up could also limit the possibility of observing long serial intervals. In most studies when this was reported, the duration of follow-up in households was approximately 1 week so that few secondary cases should have been missed. Finally, some cases counted as secondary may have been attributed to common exposure (coprimary cases), leading to a downward bias. However, in most cases, cases occurring on the same date as the index case were excluded from the calculations, therefore limiting this bias.

Upward bias could occur because of successive generations of influenza overlapping in small time periods. 15 Indeed, some observed serial intervals in close-contact studies may be between primary and tertiary cases rather than secondary cases. Two studies used modeling to explicitly account for such phenomenon: in both approaches, the modeled mean SI was shorter than the empirical mean of observed values (2AE6 vs. 2AE9 24 ; 2AE5 vs. 3AE4 31 ). This suggests that tertiary transmission is always an issue for estimating the serial interval of influenza, and further implies that estimates reported in the other 11 studies could have been biased upwards.

The GT or SI estimates obtained by modeling epidemic curves were more variable. In such approaches, the mean GT depends on the structure of the model 14 : in the classical SEIR model, it is L + I, where L and I are the average durations of the latent and infectious period, so that the mean GT should have been 6 days instead of 4-5 days in Canada 35 ; when the E and I stages are split into two (as in 34, 46 ) , the mean GT is L + 3 ⁄ 4 · I, so that it should have been 1AE6 days rather than 1AE9 days in the La Gloria epidemic in Mexico. 34 The two other modeling approaches yielded estimates similar to those in households ⁄ closecontact studies.

Reproduction numbers for the A ⁄ H1N1 2009 pandemic varied according to place, methods, and hypotheses, with a reported range from 1AE1 to 3AE3. While the most used approach relied on determining the initial exponential growth, the formulas and fitting methods changed with authors and how the initial exponential growth period was chosen was little documented. When provided, the sensitivity analyses illustrated that somewhat arbitrary hypotheses (choice of the GT, correction for under-reporting, exponential growth period,…) had a large effect on the reported value. In Mexico alone, estimates ranged between 1AE2 and 3AE1 during the same period. 29, 34, 38, 40, 42 Factors explaining these differences were numerous. The first is differences in data, either by nature (travelers back from Mexico or suspected ⁄ confirmed cases in Mexico or local epidemics or genetic sequence) or by collection time. For example, cases were added to the epidemic curve in retrospect, so that early estimates were biased upwards. 38 A second factor was the choice of the GT distribution, shorter mean GTs leading to smaller reproduction number estimates: from 3AE1 (mean GT = 4 days) to 2AE2 (mean GT = 3 days), 38 from 3AE4 (mean GT = 5AE5 days) to 1AE9 (mean GT = 2AE3 days; supplementary material 29 ), and from 2AE0 (mean GT = 2AE6days) to 1AE4 (mean GT = 1AE9 days 34 ). When similar mean GTs were allowed (approximately 3 days), less variability was present (2AE2, 38 2AE0, 34 2AE3 29 ). A third factor was underdeclaration in the initial period of the pandemic, leading to smaller estimates: from 2 to 1AE4 42 and from 2AE6 to 2AE4. 29 Methods less dependent on the completeness of the data (genetic sequences, travelers out of Mexico) consistently led to lower estimates, from 1AE2 to 1AE7. The short mean GT (1AE9 days 34 ) estimated early in Mexico may have led to underestimation when it was used to estimate the reproduction number in later studies. The impact was moderate: for example, the reproduction number in several countries from the southern hemisphere ranged between 1AE2 to 1AE6 using a GT of 1AE9 days 41 and increased by approximately 10% when a mean GT of 2AE8 days was used. In practice, collecting data that allow the joint estimation of the serial interval and reproduction ratio should be encouraged to limit these uncertainties. 48 In approximately one report of two, the authors described the estimated reproduction ratio as 'basic' (i.e., R 0 ), while others used 'initial', 'effective', several qualifiers or none. Estimating R 0 requires an additional assumption on the initial susceptibility of the population, and all authors reporting R 0 assumed, often implicitly, that the whole population was initially susceptible. It is now known that adults over 50 years of age were less susceptible to the disease, 24,49 making this assumption incorrect. Practically, this means that it is unlikely that any of the reported estimates were truly 'basic' and that accounting for differential susceptibility will be required to obtain R 0 estimates. For public health purposes, however, it is the initial R which is the most relevant estimates as it informs on the required strength of interventions and is useful to calibrate mathematical models. In this respect, the reproduction number may have been poorly estimated at the start of the pandemic, as a result of poor case ascertainment; how imported cases in the course of the outbreak were accounted for in estimation; and the over-representation of places like schools where transmission was large. 45 Several new methods have been proposed to estimate the reproduction number during the pandemic, 34, 36, 42, 50, 51 which should now be compared in terms of data requirements, applicability, and how they deal with the issues listed earlier to help select best practice.

Overall, the initial reproduction number estimates of A ⁄ H1N1 (2009) pandemic ranged from 1AE2 to 2AE3 with median value 1AE5 when correction for underdeclaration was applied and the mean GT was approximately 3 days. This was lower than the median for 1889, 1918, and 1957, but compared with 1968 (see Figure 2 ). For example, the reproduction number (using a mean GT of 2AE8 days) was between 1AE7 and 3AE0 (median 2AE1) in 96 cities in 1889, 7 between 1AE3 and 2AE5 in 1918 (using estimates obtained with GTs approximately 3 days), 8, 11, 12, [52] [53] [54] lower than 2 in 1957, 10, [55] [56] [57] and in the range of 1-2 in 1968. 9, 57 A large number of studies have documented transmission parameters for the A ⁄ H1N1 (2009) pandemic almost in real time. Short generation times and low reproduction number were characteristic in the first year of introduction of the virus. The A ⁄ H1N1 (2009) pandemic led to less mortality than previous pandemics, compared with past flu pandemics regarding transmission.

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Partial support by FP7 project FLUMODCONT (n°20160).

