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Infectious Disease: Brief Report

The Effective Reproduction Number of Pandemic Influenza

Prospective Estimation

Cowling, Benjamin J.a; Lau, Max S. Y.a; Ho, Lai-Minga; Chuang, Shuk-Kwanb; Tsang, Thomasb; Liu, Shao-Haeic; Leung, Pak-Yinc; Lo, Su-Vuic,d; Lau, Eric H. Y.a

Author Information
doi: 10.1097/EDE.0b013e3181f20977


When pandemic (H1N1) 2009 virus emerged, an urgent priority for international and national public health authorities was to establish the transmissibility and virulence of the pandemic strain. The effective reproduction number, R (defined as the average number of secondary cases that 1 index case generates over the course of its infectious period), is a useful measure of transmissibility and can be estimated over time (ie, Rt) through the course of an epidemic.1 Cauchemez et al2 developed methodology to permit prospective estimation of Rt. In this paper, we extend the method for prospective estimation to account for repeated importations and reporting delays. We apply the method to prospective surveillance of laboratory-confirmed pandemic H1N1 notifications and pandemic H1N1-associated hospitalizations in Hong Kong.


We obtained individual patient data on all laboratory-confirmed pandemic H1N1 cases reported between 1 May and 15 November 2009 and collected by the Hong Kong Hospital Authority and Centre for Health Protection (the “e-flu” database). The database includes demographic information on age and sex, clinical information including illness-onset date, laboratory-confirmation date and hospital-admission date, and an indicator for recent overseas travel to an affected area (collected until 16 June 2009). In Hong Kong, pandemic H1N1 infection was a reportable disease throughout our study period.

We estimated delays between illness onset and case notification, and for the subset that were hospitalized, the joint distribution of delays from illness onset and hospitalization to notification. We extended the methodology proposed by Cauchemez et al2 to allow for these reporting delays. Cases classified as imported infections were incorporated into the analysis as infectors but not infectees, to avoid overestimation of Rt. Illness-onset dates were not available for some confirmed cases, and we used multiple imputation to incorporate these in the analysis.3 We estimated Rt assuming that the serial interval followed a Weibull distribution with mean 3.2 days and standard deviation 1.3 days.4 In a sensitivity analysis, we used serial intervals with mean 2.6 days5–7 and 3.6 days.8 All statistical analyses were conducted in R version 2.9.2 (R Development Core Team, Vienna, Austria). Further technical details of the statistical methods used and R syntax are given in the eAppendix (


Following the World Health Organization global alert on 27 April 2009, Hong Kong implemented “containment phase” protocols that included entry screening at airports, ports, and border crossings, and enhanced surveillance of outpatients and inpatients with influenza-like illness. Laboratory-confirmed pandemic H1N1 cases were medically isolated and usually prescribed oseltamivir treatment. Their close contacts were quarantined for 7 days and usually prescribed oseltamivir chemoprophylaxis. Imported pandemic H1N1 cases were sporadically identified from late April to June. On 11 June 2009, following identification of the first untraceable local pandemic H1N1 case, the Hong Kong government initiated a “mitigation phase” and announced immediate class dismissal in primary schools, kindergartens and childcare centers for 14 days starting from 12 June 2009. The school closures were subsequently extended to summer vacation in early July. Some containment phase policies, such as medical isolation of confirmed cases and contact tracing of airplane passengers, continued through June. On 13 June 2009, 8 public outpatient clinics were converted to designated flu clinics across the territory to provide low-cost high-throughput outpatient medical consultation, free laboratory testing for pandemic H1N1, and antiviral treatment. These public outpatient clinics resumed some chronic disease services in mid-August.

Figure 1A shows the epidemic curve of notified pandemic H1N1 cases and associated hospitalizations from May through October 2009. Under containment-phase protocols, all laboratory-confirmed cases until 28 June were medically isolated in hospitals, and recorded as hospitalizations in the e-flu database. We therefore analyzed only the 5553 hospital admissions from 29 June to 31 October. The cumulative proportion of laboratory-confirmed cases that were hospitalized fluctuated around 15% during the early stages of the epidemic (Fig. 1B). After the designated flu clinics resumed chronic disease services and laboratory testing was focused on more severe cases, the cumulative proportion of cases hospitalized gradually increased to around 18% by the end of the study period.

A, Number of cases of laboratory-confirmed cases of pandemic influenza A (H1N1) virus infection (gray) and hospitalizations (black) by date of illness onset and dates of important control measures, Hong Kong, from April through October 2009. B, The cumulative proportion of hospitalized cases among all pandemic H1N1 notifications with 95% point-wise confidence intervals. C, Daily estimates of the effective reproduction number R t based on pandemic H1N1 notifications with 95% confidence intervals, where the dashed line represents the threshold of R t = 1. D, Daily estimates of the effective reproduction number R t based on pandemic H1N1-associated hospitalizations with 95% confidence intervals, where the dashed line represents the threshold of R t = 1.

Figure 1C shows the estimated Rt based on pandemic H1N1 notifications from late May through October. The estimated Rt reached an initial peak of 1.5 on 12 June and fell below 1 between 20 June and 3 July. Subsequently, Rt fluctuated between 0.8 and 1.3 through the school vacations in July and August. Rt briefly increased to around 1.2–1.3 after schools reopened in September until the epidemic peaked in late September, and subsequently fluctuated below 1 as the epidemic declined. The trends in Rt based on H1N1-associated hospitalizations were broadly consistent with the estimates based on case notifications, with wider confidence intervals (Fig. 1D).

The real-time estimates of Rt based on data to the end of July, August, September, and October were consistent with the final estimates for the period (Fig. 2), with some divergence only in the last few days of each analysis. In a sensitivity analysis using alternative serial intervals, real-time estimates of Rt were similar to our main results and slightly closer to 1 with a shorter serial interval (eAppendix,

The epidemic curves of pandemic H1N1 notifications (gray bars) and pandemic H1N1-associated hospitalizations (black bars) up to different time points and corresponding real-time estimates of R t (gray lines based on notifications, black lines based on hospitalizations) for the periods. A, up to 31 July; B, up to 31 August; C, up to 30 September 2009; D, up to 31 October 2009.


Situational awareness of the transmissibility and epidemic growth rate of pandemic influenza was a priority for national and international health authorities in 2009. Much early attention focused on counts of laboratory-confirmed cases, but in affected regions laboratory capacity was typically focused on more severe cases, and changes in laboratory testing and notification rates meant that case counts did not necessarily reflect the underlying epidemic.9 An example of this in our data is the apparent peak in cases in mid-June and the subsequent decline through to the end of June. This pattern was probably an artifact of changes in testing priorities (as Hong Kong switched from containment to mitigation phase) rather than a real decline in epidemic growth.10 Substantial declines have been seen previously in Rt during SARS outbreaks, in response to implementation of government control measures.1,11 In contrast, there were no apparent substantial changes in Rt through the first wave of H1N1pdm in Hong Kong, other than the suppression of Rt during school holidays.

A useful alternative to case-based surveillance is surveillance of the subset of severe infections, such as hospital admissions or intensive-care-unit admissions.9 Our results lend support to this approach, although changes in the hospitalization rate over a shorter time period (as for example occurred in Hong Kong at the end of June 2009) could lead to problems in estimation of Rt based on hospitalizations.

The estimated reproduction number of pandemic H1N1 appeared to be lower in Hong Kong during our study period than in other countries. For example, other studies estimated that R was around 1.5–2.0 in the initial phases of epidemics in the United States,12 Peru,13 Australia,14 and New Zealand.15 Lower transmissibility may be associated with the summer vacations from July through August16 or interventions during the mitigation phase such as widespread use of antiviral treatment. Seasonality may also be a factor, because influenza virus does not usually circulate in Hong Kong after July or August.17 Finally, Hong Kong has an ageing population and some older people may have pre-existing immunity to pandemic H1N1.18

Around 20% of notified cases were admitted to hospital during the mitigation phase in Hong Kong. This is a higher hospitalization rate than observed in other countries such as Australia (13%)19 and Canada (10%).20 However, among the cases hospitalized in Hong Kong between July and October, only 1.9% were admitted to ICU and only 0.8% died. These rates among hospitalized cases are much lower than in other countries such as Australia (13% admitted to ICU and 4% died),19 Canada (18% admitted to ICU and 4% died),20 and California (31% admitted to ICU and 11% died),21 suggesting that the clinical threshold for hospitalization may have been lower in Hong Kong. The admission rate would also have been higher due to broader admission criteria, with young children and pregnant women routinely admitted for testing and investigation.

In addition to the potential changes in rates of case identification, notification, and hospitalization discussed above, there are other limitations to our work. First, Rt was estimated based on aggregate data and did not take into account variation in transmissibility, for example, due to age. Our estimates of transmissibility provide information about the overall trends in the epidemic, and local data on within- and between-age group contact patterns are limited. Second, while we allowed for imported cases to be infectors but not infectees, we did not allow for cases infected in Hong Kong and exported to other countries; this may have underestimated the total Rt. However, the number of exported cases should be fewer than imported cases during the early stage of the epidemic, and exported cases are less relevant to the local epidemic growth rate. Third, interventions are not the only factors associated with decrease in the effective reproduction number. Particular care must be taken when interpreting estimates of effective reproduction numbers through time since depletion of susceptibles can lead to a decline in the effective reproduction number.22


We acknowledge the Hospital Authority Strategy and Planning Division, Quality and Safety Division, and Information Technology Division and the Center for Health Protection for the collation of the e-flu database. We thank Steven Riley and Joseph Wu for helpful discussions. We thank 2 anonymous referees for comments that helped us to improve the manuscript.


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