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Am J Epidemiol. 2013 June 15; 177(12): 1443–1451.

Published online 2013 April 28. doi: 10.1093/aje/kws402

PMCID: PMC3676150

Contributed by

Abbreviations: CI, confidence interval; SD, standard deviation; SI, serial interval.

Received 2012 April 3; Accepted 2012 October 2.

Copyright Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health 2013.

This article has been cited by other articles in PMC.

The serial interval (SI) of human influenza virus infections is often described by a single distribution. Understanding sources of variation in the SI could provide valuable information for understanding influenza transmission dynamics. Using data from a randomized household study of nonpharmaceutical interventions to prevent influenza transmission in Bangkok, Thailand, over 34 months between 2008 and 2011, we estimated the influence of influenza virus type/subtype and other characteristics of 251 pediatric index cases and their 315 infected household contacts on estimates of household SI. The mean SI for all households was 3.3 days. Relative to influenza A(H1N1)pdm09 (3.1 days), the SI for influenza B (3.7 days) was 22% longer (95% confidence interval: 4, 43), or about half a day. The SIs for influenza viruses A(H1N1) and A(H3N2) were similar to that for A(H1N1)pdm09. SIs were shortest for older index cases (age 11–14 years) and for younger infected household contacts (age ≤15 years). Greater time spent in proximity to the index child was associated with shorter SIs. Differences in the SI might reflect differences in incubation period, viral shedding, contact, or susceptibility. These findings could improve parameterization of mathematical models to better predict the impact of epidemic or pandemic influenza mitigation strategies.

Understanding the basic epidemiologic parameters related to infection dynamics in populations is vital to the design of interventions and mitigation strategies for both seasonal influenza epidemics and pandemics (1). Mathematical models that are used to study these dynamics as well as the impact of vaccinations or other interventions use 2 interrelated statistical parameters that ground these models in the underlying infection process of individuals. One is the serial interval (SI), defined as the time between onset of specific signs and symptoms in a primary case and onset in a secondary case (2, 3). It is the observable surrogate measure of the generation time—the time between successive infections. The other parameter is the basic reproductive number (*R*_{0}). Together, these parameters characterize the infectiousness profile and determine the rate at which an epidemic grows.

The SI can be estimated in 2 ways. One is to impute it from models that use surveillance data and rely on various assumptions. Modeled estimates of the SI for the 1918 epidemic suggest that it varied between 3.3 days in confined spaces and 2.8–8.3 days in communities (4). The second way is to estimate the SI directly from observed data in closed populations for which chains of transmission are tractable, such as can be found in households and schools or with direct contact tracing. Observed estimates of the mean household SI for interpandemic influenza in households include 3.4 (standard deviation (SD), 1.2), 3.6 (SD, 1.6), and 2.4 (no SD reported) days (3, 5, 6). Estimates of the observed mean household SIs from the 2009 pandemic varied between 2.6 and 4.4 days (5, 7–9). An observed estimate of the mean household or close-contact SI from a meta-analysis of studies of the 2009 pandemic was 3 days (95% confidence interval (CI): 2.4, 3.6), after accounting for tertiary transmission (10). In 2 additional studies with large sample sizes from the United States and Canada, the SIs for the 2009 pandemic were estimated to be 2.9 (mean) (*n* = 261) and 3.4 (median) (*n* = 262) days, respectively (11, 12).

The SI, although reported in the literature as a single distribution with a mean and variance, could vary because of the biology of the virus (related to antigenic characteristics of the virus and the amount and timing of viral shedding), immunity (of the infected person and his/her contacts), and behavior (the contact patterns leading to infection). Some of these characteristics cannot be measured directly but are correlated with other variables. Understanding the sources of variability in the SI can help in specifying parameters of mathematical models to describe infection dynamics, predicting the impact of interventions, and quantifying the uncertainty of these predictions (13).

To our knowledge, there have been no detailed comparisons among the SIs of different influenza virus types and subtypes, with the exception of 1 small study in Hong Kong (5). In the present analysis, we use data from a randomized controlled trial of nonpharmaceutical interventions conducted between 2008 and 2010 in Bangkok, Thailand, to estimate and compare the SIs of influenza A(H1N1) virus, influenza A(H3N2) virus, A(H1N1)pdm09 virus, and influenza B virus (14).

A randomized controlled trial was designed to study the effect of hand-washing education with and without the use of a face mask, compared with a control arm, on secondary influenza transmission in Bangkok, Thailand (14). Pediatric index cases were identified from the pediatric outpatient clinic of Queen Sirikit National Institute of Child Health, the largest public referral hospital in Bangkok. Index cases were eligible for enrollment if 1) they presented in the outpatient clinic with influenza-like illness (documented fever with cough or sore throat); 2) the initial symptoms had occurred within the previous 48 hours; and 3) no household members had had influenza-like illness in the previous 2 weeks. After enrollment of the child, an initial household visit included the collection of nasal swabs and blood from household members. Two subsequent household visits at days 3 and 7 (relative to the enrollment day) were conducted, and nasal and throat swabs were collected from both the index case and household members. At day 21, a final home visit was made to collect blood from the household members. At enrollment, the symptom history of the index case was collected. During the 7 days of follow-up, household members kept a daily symptom diary.

All diagnostic laboratory tests were performed at the US Armed Forces Research Institute of Medical Sciences in Bangkok. Nasal and throat swabs were tested for influenza viruses by using real-time reverse-transcription polymerase chain reaction according to the US Centers for Disease Control and Prevention protocol (15).

In evaluating the relation between variables and influenza category, we used the Student's *t* test (2 categories) or 1-way analysis of variance (all categories) to evaluate age; we used χ^{2} tests to evaluate sex; we used the Fisher's exact test on the number of infections in a household to account for cells expected to contain small numbers; and we used the “row mean scores differ” Mantel-Haenszel statistic to evaluate the ordinal categorical variables for age and quartile of time spent in proximity to the index patient. The SI was calculated as the time (in days) between symptom onset in the index case and symptom onset in the household contacts with an influenza virus confirmed in the laboratory by real-time reverse-transcription polymerase chain reaction (2). We chose to base the SI on a single discrete symptom—reported fever—for 2 reasons: 1) Fever is the only symptom common to all index cases because of the inclusion criteria for the index case, and therefore using fever as the symptom included the greatest number of households; and 2) during the first year of the study, there were unintentional differences in the reporting of initial symptoms in the index case and the household members (sore throat was not included on the list of individual symptoms of the index cases). Therefore, the primary outcome we investigated was the interval between the reported onset of fever in the index case and onset of fever in the household contact.

We estimated SIs by using methods to account for left-truncation resulting from the study design (16–19). Briefly, in our study, index cases were recruited within 48 hours of illness onset and were eligible only if no other recent or concurrent illnesses had occurred in the subject's household. This could have led to the exclusion of some short SIs from our analyses. We used a nonparametric generalization of the Kaplan-Meier estimator that accounts for left-truncation (17) and made a visual comparison between it and fitted parametric models (i.e., Weibull, gamma, and lognormal) for the overall SI distribution. The median value for Kaplan-Meier type method was calculated as the value corresponding to the proportionate difference between 2 time intervals with cumulative proportions on either side of 50%. A comparison among the parametric models was performed with the Akaike Information Criterion to determine the one with the best fit. Having established the parametric model with the best fit, we also estimated the mean SI and the standard deviation from the fitted model for each influenza virus stratum separately. We performed a sensitivity analysis by using mixture models, which allow for multivariate distributions, to estimate the SI that incorporated the probability that some of the infections among household members actually could be tertiary infections. The mixture models, however, were found to be a poor fit to the data, and the mixture parameters were not identifiable when we fitted the model.

We performed multivariable analysis by using accelerated failure time models to evaluate the contribution of covariates to the SI. The transformed regression coefficients derived from these models were interpreted as the acceleration factor—that is, the proportional increase (if >0) or decrease (if <0) of the median SI relative to the referent category. We first fitted a univariable accelerated failure time model that used only influenza virus type and subtype categories (influenza A(H1N1), A(H3N2), A(H1N1)pdm09, and B) to examine the differences in SIs, with the influenza category with the shortest estimated SI used as the referent category. We subsequently included index patient age category (0–2, 3–5, 6–10, and 11–15 years), household member age category (0–15, 16–49, and ≥50 years), and category of average time spent within 2 m of the index child (expressed by quartile among all members enrolled after 1 week) to examine other factors potentially affecting the SI in our study. As a sensitivity analysis to explore how the SI differed when a syndromic definition of influenza was used, we repeated the analysis with an SI based on acute respiratory illness, defined as having 2 or more of the following symptoms: fever, cough, sore throat, or rhinorrhea. Categorical data analysis was performed in SAS 9.2 (SAS Institute Inc., Cary, North Carolina), and all modeling analyses were performed in R, version 2.10.1 (R Development Core Team, Vienna, Austria).

Between April 9, 2008, and February 20, 2011, we enrolled 832 index patients and their household members (Table 1). Of these, 44 dropped out (*n* = 9), moved (*n* = 4), were hospitalized (index cases) (*n* = 7), were negative for influenza virus by real-time reverse-transcription polymerase chain reaction (*n* = 16), or were otherwise found ineligible (*n* = 8). The remaining 788 households with 1,995 enrolled members were followed up for 3 visits over the subsequent week. We excluded 20 households in which the reported onset of the first symptom was more than 2 days before enrollment. Of the remaining 1,946 members in 768 households, influenza virus was confirmed by real-time reverse-transcription polymerase chain reaction in 549 members in 378 households (secondary attack rate = 28.2%). Of these, 475 (86.5%) members in 342 (90.5%) households had at least 1 symptom during the week of follow-up. Of these, 315 (66.3%) household members in 251 (73.4%) households reported a fever during the week of follow-up, from which we could calculate an SI. Fifty-nine households (23.5%) had more than 1 member contributing SI information (54 with 2 members and 5 with 3 members). Among the other members of the 251 households were 82 members with laboratory-confirmed influenza virus who did not report a fever. The distribution of influenza type and subtype in households with a secondary case reporting fever was not different from that in those not reporting fever (χ^{2} test: *P* = 0.31).

Enrollment Cascade Leading to Analytical Data Set With Subset Distribution of Influenza Type and Subtype, Bangkok, Thailand, 2008–2011

The age of the index cases differed by influenza virus (1-way analysis of variance: *P* < 0.0001) (Table 2). The mean ages of the index cases were similar for influenza A(H1N1) and influenza A(H3N2): 4.6 and 4.3 years, respectively (*P* = 0.66). The mean ages of the index cases were also similar for influenza A(H1N1)pdm09 and influenza B virus: 6.4 and 6.8 years, respectively (*P* = 0.47). Compared with influenza A(H1N1)pdm09, however, the mean ages for influenza A(H1N1) and influenza A(H3N2) virus were significantly lower (6.4 vs. 4.6 years, *P* = 0.01; 6.4 vs. 4.3 years, *P* ≤ 0.0001). The proportions of index cases who were male were similar among influenza virus categories (χ^{2} test: *P* = 0.84). The total number of infected contacts with fever in a household did not vary by influenza virus (Table 2; Fisher's exact test: *P* = 0.93).

Characteristics of Households With at Least 1 Secondary Case of Influenza With Fever, Bangkok, Thailand, 2008–2011

The secondary attack rate among household members varied little by the influenza virus type/subtype of the index case: influenza A(H1N1)pdm2009 = 27.1%; A(H3N2) = 31.6%; A(H1N1) = 25.9%; and influenza B = 25.9% (data not shown). Among the household members with secondary influenza infection, the mean age was 29 years, and the age structure did not differ by influenza virus category (χ^{2}
*P* = 0.46; Table 3). Similarly, the proportions who were male were similar across influenza categories (χ^{2}
*P* = 0.222). Also, there was no significant difference among influenza virus types with regard to the distribution of time spent within 1 m of the index case (χ^{2}
*P* = 0.15).

Characteristics of Febrile Household Contacts With Laboratory-Confirmed Influenza Virus, Bangkok, Thailand, 2008–2011

The nonparametric estimate closely approximated the parametric models for the SI (Figure 1). The median value for the SI with the nonparametric method was 2.7 days. The median values for the lognormal, gamma, and Weibull parametric models were the same, 3.0 days. The mean values were estimated to be 3.3 (SD, 1.7), 3.3 (SD, 1.6), and 3.2 (SD, 1.7) days, respectively. The lognormal model had the lowest Akaike Information Criterion value and hence was considered the best parametric fit. In a stratified analysis in which the lognormal distribution was used, we compared the SI estimates of the influenza virus category (Table 4, column 1). The SIs for influenza A(H1N1)pdm09, influenza A(H1N1), influenza A(H3N2), and influenza B were 3.1 (SD, 1.4), 3.3 (SD, 1.9), 3.5 (SD, 1.9), and 3.7 (SD, 2.0) days, respectively (Figure 2).

Crude and Adjusted Serial Intervals for Influenza Virus Infection in 251 Households in Bangkok, Thailand, 2008–2011

Estimated cumulative distribution of the serial interval for all categories of influenza from households in Bangkok, Thailand, 2008–2011, with the parametric models (Weibull, gamma, and lognormal) compared with the nonparametric method.

Fitted lognormal distributions for the household serial interval by influenza type and subtype, Bangkok, Thailand, 2008–2011.

In the univariable model that included only influenza virus type and subtype, the estimated acceleration factors (and standard deviations) were relative to the shortest estimated SI, influenza A(H1N1)pdm09 (Table 4, column 2). Only the SI for influenza virus type B was significantly longer (*P* = 0.03). The model parameters correspond to SIs for influenza A(H1N1)pdm09, influenza A(H1N1), influenza A(H3N2), and influenza B of 3.2 (SD, 1.55), 3.2 (SD, 1.6), 3.5 (SD, 1.7), and 3.8 (SD, 1.9) days, respectively (data not shown). The inclusion of household contact age group, time spent in proximity to the index case, and age of the index case in a multivariable model changed the relative difference of the influenza virus categories in relation to A(H1N1)pdm09 very little (Table 4, column 3). Among household contacts, the shortest SIs were associated with the oldest index cases (age 11–14 years). The longest SIs were associated with index cases aged ≤2 years, which were 28% longer than those associated with the oldest index cases (95% CI: 1.02, 1.60). Household contacts under 16 years of age had the shortest SI. The estimated SI was 17% longer for adults 16–49 years of age (*P* < 0.01) and 16% longer for adults 50 years of age and older (*P* = 0.16). Time spent in proximity to the index case, as measured by quartile of time spent within 1 m of the index case, was related to the SI in a dose-dependent fashion, with those in the highest quartile having the shortest SI. It is noteworthy that relative to the control arm of the study, there was no difference in the estimated SI for the hand-washing (*P* = 0.64) and hand-washing–plus–face mask (*P* = 0.76) arms. This is consistent with the null association observed between the intervention arms and the overall household transmission in the larger study (14). The variables corresponding to the intervention arms were therefore left out of the multivariable model.

On repeating the SI analysis in a sensitivity analysis, we found the SI based on acute respiratory illness was 3.1 (SD, 1.5) days, shorter than that based on fever alone (*n* = 414; data not shown). To explain this, we found that cough and sore throat occurred earlier than fever among the infected household members. The results of the multivariable analysis based on acute respiratory illness were similar, with the exception that the SI for influenza A(H1N1) was significantly shorter than that for influenza A(H1N1)pdm09 (acceleration factor = 0.73, 95% CI: 0.64, 0.85). The SI for influenza B remained significantly longer than that for influenza A(H1N1)pdm09 (acceleration factor = 1.08, 95% CI: 1.03, 1.34).

We estimated the overall household SI for all influenza viruses combined to be 3.3 days, which is similar to the 3- to 4-day estimate from similar studies conducted in Hong Kong (3, 5). Households in which the index case was infected with A(H1N1)pdm09 had the shortest SI, estimated to be 3.1 days, which is very similar to the estimate of 3.0 days from the meta-analysis of A(H1N1)pdm SIs and the other studies (10–12). Relative to influenza A(H1N1)pdm09, SIs in households of index cases infected with influenza B virus were significantly longer by approximately half a day. The estimated SIs for the other viruses, influenza A(H1N1) and A(H3N2), were similar to that for A(H1N1)pdm09 virus. Adjustment for household index patient age and contact characteristics changed the results very little.

The SI will vary on the basis of the timing of infection (relative to the onset of symptoms in the index case) as well as the incubation period of the secondary case (2). The minimum SI therefore is as long as the incubation period, estimated to be between 1.4 days for seasonal influenza A and 0.6 days for influenza B (20). The incubation period for influenza A(H1N1)pdm2009 is estimated to be 1.4–1.6 days (21–23). Therefore, SIs of 1 day or less that were unobserved because of ineligibility were likely few and limited to those infected with influenza B. SIs of 2 days or less that were left-truncated would be slightly more common. However, we did account for left-truncation in our nonparametric analysis and found the estimate to be slightly reduced (median, 2.7 days) compared with the parametric analysis (3.0 days).

Another bias in estimating the SI can arise from high attack rates that result in a depletion of susceptible household members. The result would be a shorter observed SI. Differences in attack rates between the influenza types/subtypes might explain differences in SIs, with the higher attack rate associated with a shorter SI. The attack rate in this study was slightly higher in the influenza A subtypes (28.7%) than in influenza B (25.9%). It is possible that the higher attack rate in influenza A subtypes might account for shorter SIs relative to influenza B. Nevertheless, influenza A(H3N2) had the highest secondary attack rate of all influenza types/subtypes (31.6%) and yet had the longest SI (3.5 days) after influenza B (3.7 days). Other factors, such as length of viral shedding and incubation periods, could also play a role. Our findings of a longer SI for influenza B virus than for influenza A virus are interesting, given that a few reports suggest that children shed influenza B virus longer than influenza A(H3N2), thereby extending the infectious period (24, 25). However, at least 1 report indicated that influenza B virus has a shorter incubation period than influenza A virus (20). The implications are perhaps most important for influenza A viruses, which have pandemic potential, and shorter SIs translate into less time to implement interventions.

Our multivariate model includes time spent in proximity to the index patient, and this is an important contribution over other published studies. Given the assumption that the mechanisms of infection are mediated by distance, proximity to the index case represents an increased frequency of exposure to an influenza virus by the household contact. We previously published data from this study demonstrating that proximity was associated with the probability of infection, and the finding here that close proximity to the index case is associated with shorter SIs is consistent and supports the validity of the model. Proximity is therefore also an important adjustment affecting the interpretation of the age variables—age of the index case and age of those with secondary infection—that would otherwise be confounded by their correlation with behavior that relates to intimate contact. In our model, we found a shorter SI associated with infected household contacts less than 15 years old (adults had 20% longer SIs), which perhaps suggests that incubation periods in children are shorter than those in adults, although we are not aware of any literature on this. We previously reported that the odds of infection tended to be highest among the children relative to adults (14). This suggests that, rather than a shorter incubation period, children might have more intimate contact with the index cases who are other children, in spite of the inclusion of the time-spent-in-proximity variable in the model.

Age, as a characteristic of the index case, is more likely relevant to the amount or duration of viral shedding of the index case than to the incubation period of the secondary case. In our study, pediatric index cases between the ages of 11 and 14 years (i.e., older) had the shortest intervals relative to the younger index cases, and we previously reported little difference in the odds of infection between age groups (14). Another explanation for this difference, therefore, is that younger cases shed the virus longer than the older adolescents (24, 26, 27).

The present study has several limitations. By design, we excluded households if any other household members had symptoms of influenza-like illness up to 1 week before the date of the visit of the child to the outpatient department. We cannot, however, adjust for the possibility that some index cases actually might have been secondary cases because a subclinical infection of another member of the household preceded that of the presumed index child. This could result in underestimation of the SI. Another possibility is that the secondary infections actually are mixed with tertiary infections, a bias we were unable to account for by using mixture models. The result of such mixing would be an overestimate of the SI. This possibility is made more likely by the fact that up to 25% of household members were not enrolled in the study.

We calculated SI on the basis of fever alone, thus excluding 26% of the secondary cases of influenza infection. SIs on average will have a similar mean regardless of the choice of symptom/syndrome used, and that mean should be similar to the mean generation time (2). However, our sensitivity analysis showed that the SI based on acute respiratory illness was shorter (3.1 days, vs. 3.3 days for fever alone). The study enrollment criteria (exclusion of an index case if initial symptoms occurred more than 48 hours before presentation with influenza-like illness) naturally restricted the distribution of symptoms surrounding the onset of illness. Index cases with symptoms such as cough or sore throat, which in the household members occurred earlier than the onset of fever, were more likely to have been excluded from our study. Therefore, in an analysis of SI, we believe use of fever alone is less biased. Systematic differences also could exist in the reporting of symptoms between index cases and household contacts. Initial symptoms were reported up to 2 days after onset among index children and were reported by proxy among the youngest children, whereas among the largely adult secondary cases, data on symptoms were collected prospectively in symptom diaries.

The data could have limited external validity because index cases in the present study came from a single outpatient department setting. Our estimated household SIs might not be generalizable to households with index patients who are adults (who are likely to have less viral shedding than children) or have more severe illness (28). Some other environmental components of infectiousness in the present study, such as climate or humidity, also might not be generalizable. Furthermore, households in urban Bangkok are likely to experience more crowding than the average household in more developed parts of the world. These circumstances likely result in shorter estimated SIs. Finally, we estimated the household SI, and SIs could differ in other settings, such as schools and the general community (29).

Despite these limitations, our study has notable strengths. Index and secondary cases were confirmed by laboratory testing. Also, our study is one of the largest studies of SIs and permitted multivariable analysis, including a direct comparison between pandemic and seasonal influenza A, which revealed a notable similarity between the two. However, even small differences of up to half a day could have meaningful differences in the overall transmission dynamics in populations, as estimated by mathematical/simulation models that are sensitive to the specification of SIs (30, 31). Parameter estimates such as those provided in the present study could contribute to more realistic and appropriately complex models to guide influenza intervention and mitigation strategies (13).

Author affiliations: Influenza Program and International Emerging Infections Program, Thailand Ministry of Public Health–US Centers for Disease Control and Prevention Collaboration, Nonthaburi, Thailand (Jens W. Levy, James M. Simmerman, Sonja J. Olsen); Department of Community Medicine, School of Public Health, The University of Hong Kong, Hong Kong Special Administrative Region, China (Benjamin J. Cowling, Vicky J. Fang, Brendan Klick); Influenza Division, Centers for Disease Control and Prevention, Atlanta, Georgia (James M. Simmerman, Sonja J. Olsen); Department of Pediatrics, Queen Sirikit National Institute of Child Health, Bangkok, Thailand (Piyarat Suntarattiwong, Tawee Chotipitayasunondh); and Department of Virology, US Armed Forces Research Institute of Medical Sciences, Bangkok, Thailand (Richard G. Jarman).

This work was supported by funding from the Department of Medical Sciences, Thailand Ministry of Public Health, and the US Centers for Disease Control and Prevention (Cooperative Agreement 5U51IP000345). Benjamin J. Cowling was supported by the Harvard Center for Communicable Disease Dynamics from the National Institute of General Medical Sciences (grant U54 GM088558). Richard G. Jarman received funding from the Global Emerging Infections Surveillance and Response System, a Division of the Armed Forces Health Surveillance Center, for a portion of the laboratory work.

The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the Centers for Disease Control and Prevention, the US Army, or the US Department of Defense.

Conflict of interest: none declared.

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