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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
J Infect Dis. Author manuscript; available in PMC May 15, 2011.
Published in final edited form as:
PMCID: PMC3060408
NIHMSID: NIHMS271334

Viral shedding and clinical illness in naturally acquired influenza virus infections

Abstract

Background

Volunteer challenge studies have provided detailed data on viral shedding from the respiratory tract before and through the course of experimental influenza virus infection. There are no comparable quantitative data on naturally-acquired infections.

Methods

In a community-based study in Hong Kong in 2008, we followed up initially well individuals to quantify trends in viral shedding based on culture and reverse transcription polymerase chain reaction (RT-PCR) through the course of illness associated with seasonal influenza A and B virus infection.

Results

Trends in symptom scores more closely matched changes in molecular viral loads measured by RT-PCR for influenza A than influenza B. For influenza A virus infections, replicating viral loads measured by culture declined to undetectable levels earlier after illness onset than molecular viral loads. Most viral shedding occurred during the first 2–3 days after illness onset and we estimated that 1–8% of infectiousness occurs prior to illness onset. Only 14% of infections with detectable shedding by RT-PCR were asymptomatic, and viral shedding was low in these cases.

Conclusions

Our results suggest that ‘silent spreaders’ (i.e. individuals who are infectious while asymptomatic or pre-symptomatic) may be less important in the spread of influenza epidemics than previously thought.

Keywords: influenza, viral shedding, infectiousness

INTRODUCTION

Influenza virus is associated with substantial mortality and morbidity worldwide through seasonal epidemics and occasional emergence of novel strains that lead to pandemics [1]. Volunteer challenge studies have provided detailed data on viral shedding from the respiratory tract through the course of experimental influenza virus infections, and the time lines and duration of illness after infection [2]. However, in volunteer challenge studies the participants are typically young adults who have been screened to ensure they have low levels of pre-existing immunity to the influenza strain of interest, and the findings may not generalize to the overall population annually at risk for naturally-acquired infections [2]. There are few data on viral shedding after naturally-acquired influenza virus infection in a community setting. The proportion of infections which are asymptomatic or subclinical and the degree to which these are contagious, as well as the proportion of shedding which occurs prior to onset of symptoms, affects the potential impact of control measures. We studied trends in clinical illness and viral shedding associated with naturally-acquired influenza virus infections in a community setting.

METHODS

We conducted a community-based study of the effectiveness of face masks and hand hygiene to prevent influenza transmission in households during 2008 [3]. As part of that study, index cases of all ages who presented with at least 2 of a range of signs and symptoms consistent with influenza virus infection were recruited from outpatient clinics and private hospital emergency rooms from January through September 2008. A positive result for influenza virus infection on a rapid antigen test was used to determine eligibility of the index cases’ households for further follow-up. Index cases and household contacts were eligible regardless of pre-existing conditions or treatment prescribed but index cases who had household members with concurrent influenza like illness were excluded [3, 4]. There was no recorded use of antiviral prophylaxis. Symptom diaries were provided to all household members at an initial home visit within 24–48 hours of index case recruitment to record respiratory and systemic symptoms daily. 82% of initial home visits were conducted within 12 hours of index case recruitment [3]. Compliance to symptom reporting was high, all symptom diaries were complete with the exception of 12/2170 (0.6%) entries. We provided each household with a digital tympanic thermometer and asked all household members to record their body temperature daily. Household members were followed up for approximately 7 days to observe secondary infections. Pooled nose and throat swab (NTS) specimens were collected from all household members regardless of illness at the initial home visit and at two follow-up visits 3(±1) and 6(±2) days later. Because index cases are likely to have higher viral loads given their positive result on a rapid test [5], and are less likely to have mild illness given that they sought outpatient care, all analyses here focus only on the household contacts to avoid selection bias.

Laboratory Methods

NTS specimens from household contacts were tested by quantitative reverse transcription polymerase chain reaction (RT-PCR) to detect influenza A or B virus infection and determine molecular viral loads. Total nucleic acid was extracted from specimens by using the NucliSens easyMAG extraction system (bioMérieux, Boxtel, the Netherlands) according to the manufacturer’s instructions. Twelve microliters of extracted nucleic acid was used to prepare complementary DNA (cDNA) by using an Invitrogen Superscript III kit (Invitrogen, San Diego, California) with random primer as described elsewhere [6].

For detection of influenza A virus, 2μL of cDNA was amplified in a LightCycler 2.0 (Roche Diagnostics, Penzberg, Germany) with a total reaction-mix volume of 20μL reaction containing FastStart DNA Master SYBR Green I Mix reagent kit (Roche Diagnostics), 4.0mM MgCl2 and 0.5mM of each primer. The forward primer (5′-CTTCTAACCGAGGTCGAAACG-3′) and the reverse primer (5′-GGCATTTTGGACAAAKCGTCTA-3′) were used for amplification of the matrix gene of influenza A virus [7]. Cycling conditions were as follows: initial denaturation at 95°C for 10 minutes, followed by 40 cycles of 95°C for 10 seconds, 60°C for 3 seconds, and 72°C for 12 seconds, with ramp rates of 20°C/s. At the end of the assay, PCR products were subjected to a melting-curve analysis to determine the specificity of the assay. The lower limit of detection of the RT-PCR assay was 23 virus gene copies per reaction, i.e. approximately 900 copies/ml.

For detection of influenza B virus, forward (5′-GCATCTTTTGTTTTTTATCCATTCC) and reverse (5′-CACAATTGCCTACCTGCTTTCA) primers and 5′ nuclease probe (Fam-TGCTAGTTCTGCTTTGCCTTCTCCATCTTCT-TAMRA) were used for amplification of the matrix gene [8]. Testing was performed by using the TagMan EZ RT-PCR. Core reagent kit (Applied Biosystems, Hammonton, New Jersey), with 0.8μmol/L of forward and reverse primers and 0.2μmol/L of probe in a total reaction volume of 25μL, comprising 4μL of nucleic acid extract. Amplification and detection was performed on an ABI StepOneTM Real-Time PCR System (Applied Biosystems) under the following conditions: initial hold at 50°C for 20 minutes and 95°C for 15 minutes, followed by 45 cycles at 95°C for 15 seconds and 60°C for 1 minute.

NTS specimens were additionally tested by quantitative viral dilutions to detect tissue culture infectious dose (TCID50) and determine replicating viral load. Madin-Darby canine kidney (MDCK) cells grown on microtitre plates. The cells were rinsed in serum-free minimum essential medium (MEM) (Gibco, New York). The NTS specimen was diluted initially by 1 in 5 and then in 10 fold steps in serum-free MEM containing tosylsulfonyl phenylalanyl chloromethyl ketone-treated trypsin (2μg/ml) (Sigma, St. Louis, Missouri). 100ul of the undiluted NTS specimen as well as each of the specimen dilutions was added in quadruplicate to the MDCK cell monolayers. Medium alone was added to control cells. An additional 100ul of serum free MEM with 2ug/ml trypsin was added to each well and the plates incubated at 33°C for 7 days. The plates were examined for cytopathic effect daily. The TCID50 was determined according to the Reed and Muench Method. The lower limit of detection was approximately 100.3 TCID50.

Statistical Analysis

We calculated daily scores grouped as systemic signs and symptoms (fever ≥37.8°C, headache, myalgia), upper respiratory symptoms (sore throat, runny nose), and lower respiratory symptoms (cough, phlegm), by summing the presence versus absence of each symptom or sign and dividing by three, two and two respectively [2]. We define acute respiratory illness (ARI) as at least 2 of the 7 symptoms listed above [9]. We plotted average symptom scores by time since ARI onset, which was defined as at the first day when the subject reported at least 2 of the 7 symptoms. We plotted quantitative viral loads by time since ARI onset, and calculated daily geometric means imputing half the lower limit of detection (i.e. 450 copies/ml and 0.15 log10 TCID50) for the undetectable values. As a sensitivity analysis we plotted viral shedding by time since onset of fever ≥37.8°C. We investigated the associations between tympanic temperature and viral shedding, and between symptom scores and viral shedding, by day since ARI onset.

We used a Bayesian approach to fit alternative parametric forms to the viral shedding trajectories and selected between models using the Bayesian information criterion [10]. We used the models to quantify the proportion of infectiousness remaining at ARI onset, and 1, 2 or 3 days after onset, assuming lognormal, Weibull or gamma-form associations between molecular viral shedding and infectiousness. Further technical details are provided in the Appendix. All analyses were conducted in R version 2.7.1 (R Development Core Team, Vienna, Austria) [11] and WinBUGS version 1.4 [12]. Further information about the study design, raw data from the study, and R syntax to permit reproducible statistical analyses are available on the authors’ website at http://www.hku.hk/bcowling/influenza/HK_NPI_study.htm.

RESULTS

We followed up 1,015 household contacts in 322 households. A total of 135 (13%) contacts were confirmed to have influenza virus infection by RT-PCR. Because we recorded symptoms prospectively and were particularly interested in patterns in viral shedding and symptoms around illness onset, for this analysis we excluded 59 contacts for whom the first NTS specimens collected were RT-PCR positive regardless of whether ARI was reported at the first home visit, and an additional 17 contacts who met the criteria for ARI onset at the first home visit with influenza virus infection subsequently confirmed by RT-PCR. Characteristics of the excluded 76 contacts were similar to the 59 retained contacts (Appendix Table 1). Of the 59 secondary infections analyzed here, 16 were influenza A/H1N1 viruses, 17 were influenza A/H3N2 viruses and 1 was an influenza A/H1N1 and A/H3N2 confection, with the remainder being influenza B virus. Forty-six (78%) were persons aged 16 years or older. At ARI onset, the most common symptoms were cough, nasal congestion/runny nose and sore throat (Table 1). Of the 34 subjects infected with influenza A viruses, 15 (44%) reported suffering from fever ≥37.8°C on at least one day over the course of illness while 21 (62%) reported either suffering from fever ≥37.8°C on at least one day or taking antipyretic medication or both. The corresponding proportions for influenza B virus infections were 8/25 (32%) and 13/25 (52%). 30/59 (51%) subjects reported seeking medical care.

Table 1
Initial symptoms and signs of naturally-acquired influenza A and B virus infections reported at ARI* onset.
Appendix Table 1
Comparison of characteristics of 59 secondary influenza virus infections our analysis with 76 excluded infections.*

Peak molecular viral shedding for influenza A virus infection as assessed by RT-PCR occurred on the day of ARI onset, followed by a steady decline in viral shedding through the following 7 days (Figure 1). The patterns of viral shedding for A/H1N1 and A/H3N2 subtypes were similar to each other (data not shown). Viral shedding was detected by RT-PCR in 4/15 (27%; 95% confidence interval: 8%, 55%) of the subjects with a specimen collected 1 day prior to ARI onset. Influenza B viral shedding was more variable over time and a clear peak was not observed; initial shedding was detected at 1–2 days prior to ARI onset in 4/14 (29%; 95% CI: 8%, 58%) cases and persisted for around 6 days before subsiding. We did not have sufficient sample size to explore differences in viral shedding between children and adults.

Figure 1
Patterns of viral shedding and symptoms and signs in naturally acquired influenza A and B virus infections by day relative to ARI onset* (day 0). Top row: viral shedding for children (crosses) and adults (open circles), and the geometric mean viral shedding ...

In influenza A virus infections the replicating viral load determined by viral culture peaked on the day of ARI onset and steadily declined over approximately 5 days (Figure 1). For influenza virus B infections the TCID50 levels initially peaked on the day of ARI onset and were more variable over time. Molecular viral shedding was most closely correlated with replicating viral load on the day after ARI onset. As replicating viral load declined more rapidly with time, the association between molecular viral shedding and replicating viral load became weaker later in the course of illness (Figure 2 and Appendix Figure 1). Replicating viral load determined by viral culture was detected in one adult for influenza A infection and two adults and three children for influenza B infection prior to ARI onset.

Figure 2
Association between replicating (by TCID50) and molecular (by RT-PCR) influenza A viral shedding by day since ARI onset for children (crosses) and adults (open circles).* Linear regression lines are plotted where there are 3 or more points.
Appendix Figure 1
Association between replicating (by TCID50) and molecular (by RT-PCR) influenza B viral shedding by day since ARI onset for children (crosses) and adults (open circles).* Linear regression lines are plotted where there are 3 or more points.

We found that a modified lognormal form provided a good fit to the molecular viral shedding patterns for influenza A virus infections. If infectiousness were proportional to molecular viral shedding, most infectiousness would occur within 2–3 days of ARI onset, whereas if infectiousness were proportional to log10 molecular viral shedding or presence of detectable viral RNA, infectiousness would persist for longer (Figure 3). We did not find any parametric forms which provided a good fit to the influenza B molecular viral shedding patterns, or replicating viral load for influenza A or B measured by TCID50.

Figure 3
Proportion of infectiousness remaining by time since ARI onset in the course of naturally-acquired influenza A virus infection. Infectiousness assumed proportional to (A) molecular viral shedding, (B) log10 molecular viral shedding, and (C) presence of ...

In both influenza A and B virus infections, mean tympanic temperature and trends in average scores for systemic signs and symptoms peaked at the day of ARI onset, and then steadily subsided to baseline after 3–5 days (Figure 1). On average upper respiratory and lower respiratory symptom scores peaked at ARI onset, however respiratory symptoms resolved less quickly than systemic symptoms and signs (Figure 1). For influenza A virus infections tympanic temperature was significantly positively correlated with viral RNA shedding on the day following ARI onset, although correlations were less clear later in the course of illness (Appendix Figure 2). There was also a positive correlation between number of symptoms and molecular viral shedding (data not shown). Data were insufficient to repeat these analyses for influenza B virus infections.

Appendix Figure 2
Association between tympanic temperature and molecular influenza A viral shedding by RT-PCR by day since ARI onset for children (crosses) and adults (open circles).* Linear regression lines are plotted where there are 3 or more points.

We detected viral shedding by RT-PCR in the absence of any reported signs or symptoms in 8/59 subjects (14%; 95% CI: 6.0%, 25%), 5 of them with influenza A virus. In 2 of the 8 subjects only NTS collected at the final home visit were positive by RT-PCR and we may have identified pre-symptomatic rather than asymptomatic shedding since these subjects may have subsequently developed symptoms. The geometric mean of peak viral titres in the NTS specimens of these 8 asymptomatic subjects was 3.2 × 103 copies/ml compared to 3.6 × 107 copies/ml in symptomatic subjects. Among 8 individuals with asymptomatic infections, 3 had specimens positive by quantitative viral culture with a geometric mean TCID50 of 100.7. Subclinical infections were identified in a further 7/59 subjects who reported at most 1 of 7 signs or symptoms on each day of the study period, and viral shedding in the NTS specimens of these 7 subjects had geometric mean 3.4 × 103 copies/ml. Three of 7 specimens from subjects with subclinical infection were positive by viral culture with a mean TCID50 of 100.5.

Viral shedding and replication trends assessed by RT-PCR and TCID50, respectively, were also assessed relative to time since fever resolution, along with symptom scores and tympanic body temperature time lines for influenza A (data not shown). Viral shedding measured by RT-PCR peaked 1 day prior to fever resolution. Shedding was detected in 4/9 subjects (44%; 95% CI: 14%, 79%) after fever resolution. Symptom trends, mean tympanic temperature and replicating viral load measured by TCID50 all followed a similar trend.

In a sensitivity analysis we investigated viral shedding relative to onset of fever ≥37.8°C in the subset of 22 subjects who reported a fever, and found that trends in viral shedding were generally consistent with the main analysis based on ARI onset (data not shown).

DISCUSSION

There are few data in the literature on the patterns in infectiousness over time in influenza virus infections, and how infectiousness may be related to viral shedding or symptoms. We investigated three alternative simple models for infectiousness in influenza A virus infections, and found that if infectiousness is proportional to viral RNA shedding (or log10 viral shedding or presence/absence of shedding), then the majority of infectiousness occurs within 1–2 days (or 3–4 days) after ARI onset (Figure 3). Given the more rapid decline in replicating viral load compared to molecular viral shedding (Figure 1), we may have overestimated the duration of infectiousness. In previous work, we estimated the mean serial interval of influenza to be 3.6 days [9], and given an incubation period of 1.5–2 days [13]. This implies the average time between ARI onset and onwards transmission to household contacts was around 2 days, which is consistent with infectiousness profiles in between a proportional relationship with log10 viral shedding and viral shedding. In a detailed model of influenza transmission in households from a French household study [14], Ferguson et al. estimated that infectiousness was highest around the time of illness onset, and that the infectiousness profile correlated closely with viral shedding [15] whereas in our data viral shedding peaked within 1–2 days of symptom onset (Figure 1). Similarly, Pitzer et al. [16] found that moderate increases in SARS transmissibility between 5 and 10 days after illness onset appeared more consistent with changes in log viral shedding rather than viral shedding over the same period [17]. Since the majority of viral shedding measured by RT-PCR or by TCID50 occurred within 2–3 days of ARI onset, isolation of cases or other interventions must be applied very soon after ARI onset otherwise they could not have any substantial effectiveness in reducing onwards transmission.

Our data are consistent with previous studies which documented the time lines of influenza viral shedding from volunteer challenge studies [2]. We found that influenza A viral shedding measured by RT-PCR peaked around the same day as ARI onset before declining. While some viral shedding was detectable by RT-PCR before ARI onset, this occurred in a minority of cases. Daily replicating viral shedding by TCID50 for influenza A virus infections declined faster than viral shedding by RT-PCR. Patterns in viral shedding associated with influenza B virus infections were more variable and followed a similar pattern to data observed in volunteer challenge studies, with shedding at substantial levels from ARI onset through to 5 days after ARI onset [2]. We found that levels of replicating virus measured by TCID50 had high correlation with molecular viral loads measured by RT-PCR soon after ARI onset but diverged as the infection progressed when TCID50 declined more rapidly (Figure 2 and Appendix Figure 1). A previous study also found that viral culture is less sensitive than RT-PCR later in the course of illness [18], perhaps because inactivated virus or viral DNA persist in the respiratory tract towards the end of illness.

In both influenza A and B virus infections, systemic symptoms and signs subsided more rapidly than respiratory symptoms [2]. The decline of systemic signs and symptoms, primarily fever, correlated closely with the decline in viral shedding most likely due to the subsiding of immune response with the gradual clearing of virus from the body [19]. Resolution of fever could also be affected by use of antipyretic medication. The correlation between higher tympanic temperature and higher viral shedding (Appendix Figure 2) implies that individuals with a higher fever could be more infectious in general.

Eight (14%; 95% CI: 6.0%, 25%) of the 59 individuals with RT-PCR-confirmed secondary infections did not report any clinical signs or symptoms, and in total 15/59 (25%; 95% CI: 15%, 38%) of infections were asymptomatic (reporting 0/7 sign or symptoms) or subclinical (reporting 1/7 sign or symptom). Our upper bound for the frequency of asymptomatic infection is somewhat lower than identified in volunteer challenge studies [2] or from longitudinal studies including pre- and post-season serology with illness recall [20]. It is possible that we failed to detect infections associated with lower levels of viral shedding or shedding for a shorter period, since swabs were only collected on average at 3 day intervals, and proportionally more such infections may be asymptomatic [2, 21]. Some individuals may have been infected without shedding virus. It is still unknown whether or to what degree asymptomatic individuals could transmit infection to others [22, 23], although mathematical models typically assume that 33% to 50% of infections are asymptomatic or subclinical, and these individuals are around half as infectious as symptomatic cases [24, 25]. Our results suggest the possibility that ‘silent spreaders’ (i.e. individuals who are infectious while asymptomatic or pre-symptomatic) may be less important in the spread of epidemics than previously thought.

US pandemic guidelines suggest sick individuals should remain home for a minimum of 24 hours after fever resolution in the absence of fever-reducing medication [26]. In our study of seasonal influenza predominantly among adults, viral shedding resolved within the recommended exclusion period for 10/12 (83%) individuals with febrile influenza A virus infection, suggesting that the exclusion period covers the majority of infectiousness for febrile infections if the patterns of fever and viral shedding are similar to pandemic influenza.

A strength of our study is that we analysed laboratory-confirmed naturally-acquired influenza virus infections in a community setting, which should allow broad generalizability. It is important to also note the limitations of our study. Due to sample size limitations, our study was underpowered to explore in detail differences by age and other characteristics. Secondly, because our study design tended to exclude households with more than one case at the recruitment stage, subjects in our study could be biased towards having a lower risk of infection or illness [3]. Thirdly, while we have investigated alternative models for the relationship between infectiousness and viral shedding, it is possible that specific symptoms also play an important role in infectiousness. Fourthly, we have a relatively small sample size and more data would be valuable to more precisely characterize patterns in viral shedding and illness, and particularly viral shedding associated with asymptomatic infections and before illness onset. Finally we did not record symptoms in household contacts retrospectively so we were unable to include in this analysis household contacts with evidence of influenza virus infection at the initial home visit, however the general characteristics of excluded contacts were similar to those included (Appendix Table 1).

One research gap highlighted by our work is the need for studies which collect paired serology as well as detailed viral shedding data. This would allow more accurate estimates of the proportion of infections which are asymptomatic or subclinical, and the characteristics of viral shedding in asymptomatic infections. Future studies of naturally acquired infections with increased frequency of clinical specimens and a longer follow up period would also contribute valuable knowledge on the shape of the peak and duration of viral shedding. If combined with data on transmission to contacts, these studies may be able to provide further information on the relations between viral shedding, illness and infectiousness, which would facilitate optimal application of interventions and control measures. Volunteer challenge studies can provide useful data, but large detailed studies of naturally-acquired infections are essential to inform differences in time lines and trends by age and other characteristics.

Supplementary Material

Acknowledgments

Sources of funding: This work received financial support from the US Centers for Disease Control and Prevention (grant no. 1 U01 CI000439-02), the Research Fund for the Control of Infectious Disease, Food and Health Bureau, Government of the Hong Kong SAR (grant no. 08070632), the Harvard Center for Communicable Disease Dynamics from the US National Institutes of Health Models of Infectious Disease Agent Study program (grant no. 1 U54 GM088558), and the Area of Excellence Scheme of the Hong Kong University Grants Committee (grant no. AoE/M-12/06). The funding agencies had no role in data collection and analysis, or the decision to publish, but the CDC was involved in study design and preparation of the manuscript. This work represents the views of the authors and not their institutions, including the Centers for Disease Control and Prevention.

We thank all the doctors, nurses, and staff of participating centers for facilitating recruitment; and Rita Fung, Lai-Ming Ho, Winnie Wai and Eileen Yeung for research support.

Viral shedding and clinical illness in naturally acquired influenza virus infections Technical Appendix: Additional details of curve-fitting methods

This appendix describes the methods used to fit smooth curves to trends in viral shedding in naturally-acquired influenza virus infections. We fitted and compared three different families of model (M1–M3).

We use the following notations in the specification of the models.

  • Viral loads are measured 3 times for each individual i, at times ti1, ti2 and ti3 respectively.
  • υi(tij) represents the observed viral load (or log10 viral load) of individual i observed at time tij, where tij = 0 refers to the symptom onset time.
  • ϕi(tij) represents the predicted viral load for the individual i at time tij under model M1–M3. The difference between υi(tij) and ϕi(tij) is the residual error εij.
  • t0 is the time interval from onset of viral shedding to ARI onset (assumed to be the same for each individual).
  • ci(tij) = 1 if the observation on i at time tij is censored below the lower limit of detection (i.e. viral load is less than 900 copies/ml) and ci(tij) = 0 otherwise.

The three models were given by:

M1:ϕi(t)=eb(t+t0)sexp{s2log2t+t0m}(similartoalognormaldistribution);M2:ϕi(t)=ebsm(t+t0m)s1exp{(t+t0m)s}(similartoaWeibulldistribution);M3:ϕi(t)=eb(t+t0)s1exp{t+t0m}msΓ(s)(similartoagammadistribution);

where b, s, m are the parameters to be estimated affecting the height and shape of the viral shedding patterns.

The residual error εij is assumed to be normal in each model. The likelihood contribution for a variable censored in (L, R) is F(R)-F(L) where F is the cumulative distribution function (CDF).

The likelihood contribution from the jth (j = 1,2,3) measurement on i is given by:

ij=(12πσ2exp{[υi(tij)ϕi(tij)2]2σ2})1ci(tij)(Φ{log10900ϕi(tij)σ})ci(tij),

where Φ is the CDF of the standard normal distribution. For uncensored observations the likelihood contribution is the density given by the first term and for censored observations the likelihood contribution is the cumulative distribution function given by the second term.

MCMC Implementation

We used MCMC to estimate posteriors for all parameters using non-informative priors which are given by:

bN(5,102)mN+(5,102)sN+(5,102)t0U(1,7)σN+(10,1002),

where N+ denotes a truncated positive normal distribution.

The process was coded in R version 2.8.0 (R Development Core Team, Vienna, Austria) which was linked to WinBUGS for MCMC implementation via the BRugs package. For each model, we ran the markov chains for 10,000 iterations with a thinning factor of 5, and discarded the first 1,000 iterations as a burn-in period. For each parameter we therefore obtained 1,800 simulations from the posterior distribution. Standard convergence statistics were checked to ensure estimates were reliable.

The best model was selected based on the Bayesian information criterion (BIC), where is given by BIC = 2 log(L) + k log(n), where 2log(L) is the log-likelihood function, and k is the number of free parameters estimated in the model. The estimated BIC for models M1–M3 were 203.0, 204.5 and 203.2 respectively. The lognormal-type model had the lowest AIC and was therefore selected, although the goodness-of-fit of all three models appeared fairly similar.

Results

Figure S1 shows the histogram of 1800 posterior estimates and the distribution of the corresponding non-informative priors, for each parameter. Figure S2 plots the log viral shedding (estimated from the best fitting model M1) along with time based on the MCMC estimates of the model parameters, where day 0 is the ARI onset day. ARI onset is defined as any 2 of the following 7 signs or symptoms – fever ≥37.8°C, headache, cough, sore throat, phlegm, runny nose, and pains in muscles or joints.

Appendix References

1. Cowling BJ, Chan KH, Fang VJ, et al. Facemasks and hand hygiene to prevent influenza transmission in households: a randomized trial. Ann Int Med. 2009;151:437–46. [PubMed]

Footnotes

Conflict of interest statement: The authors report no conflict of interest.

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