Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, 31 Center Dr, MSC 2220, Bethesda 20892-2220, Maryland, USA

Mathematical, Computational & Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, 900 S. Cady Mall, Tempe 85287-2402, Arizona, USA

Department of Global Health, School of Public Health and Health Services, George Washington University, 2175 K Street, Washington, DC 20037, USA

Abstract

Background

On 31 March 2013, the first human infections with the novel influenza A/H7N9 virus were reported in Eastern China. The outbreak expanded rapidly in geographic scope and size, with a total of 132 laboratory-confirmed cases reported by 3 June 2013, in 10 Chinese provinces and Taiwan. The incidence of A/H7N9 cases has stalled in recent weeks, presumably as a consequence of live bird market closures in the most heavily affected areas. Here we compare the transmission potential of influenza A/H7N9 with that of other emerging pathogens and evaluate the impact of intervention measures in an effort to guide pandemic preparedness.

Methods

We used a Bayesian approach combined with a SEIR (Susceptible-Exposed-Infectious-Removed) transmission model fitted to daily case data to assess the reproduction number (R) of A/H7N9 by province and to evaluate the impact of live bird market closures in April and May 2013. Simulation studies helped quantify the performance of our approach in the context of an emerging pathogen, where human-to-human transmission is limited and most cases arise from spillover events. We also used alternative approaches to estimate R based on individual-level information on prior exposure and compared the transmission potential of influenza A/H7N9 with that of other recent zoonoses.

Results

Estimates of

Conclusion

Although uncertainty remains high in R estimates for H7N9 due to limited epidemiological information, all available evidence points to a low transmission potential. Continued monitoring of the transmission potential of A/H7N9 is critical in the coming months as intervention measures may be relaxed and seasonal factors could promote disease transmission in colder months.

Background

An outbreak of novel A/H7N9 influenza virus infections rapidly unfolded in Eastern China, with the first laboratory-confirmed case identified in Shanghai on 31 March 2013 and a total of 132 laboratory-confirmed cases and 38 fatalities reported as of 3 June 2013

A particular cause for concern is the fact that poultry infected with the A/H7N9 virus seem to exhibit relatively mild symptoms

Preliminary studies suggest a low incidence of A/H7N9 infection in chickens and pigeons in affected areas

The reproduction number, R, is a key epidemiological tool for assessing the transmission potential of an emerging infection and monitoring the likelihood of large-scale outbreaks. Estimates of R >1 signal the potential for an emerging pathogen to generate a major epidemic while R <1 indicates that transmission chains cannot be sustained in the population.

In the case of an emerging infection, obtaining near real time estimates of R is essential to guide intervention strategies. Bayesian estimation approaches

In this report, we estimate the transmission potential of the influenza A/H7N9 virus by relying on daily official notifications of laboratory-confirmed cases in mainland China. In particular, we focus on assessing whether the progression of the outbreak is consistent with unsustained human-to-human transmission dynamics in line with R <1 and whether intervention measures may have reduced transmission. Further, we compare R estimates for A/H7N9 with those for other zoonotic pathogens that have recently caused pandemic concern.

Methods

Data sources

We used official notifications of laboratory-confirmed A/H7N9 influenza cases reported in mainland China from 1 March to 20 May 2013 to the Chinese Center for Disease Control and Prevention (China CDC) through a national surveillance system. For each of the 130 cases, we obtained the exact date of symptoms onset, the province of residence and whether the patient had recent exposure to poultry or live bird markets. None of the records had missing information on residence location or onset date. We focused our analysis on Zhejiang and Shanghai provinces, where the majority (60%) of cases have been reported to date. A plot of the daily A/H7N9 epidemic curve is provided in Figure

Temporal incidence of laboratory-confirmed A/H7N9 influenza in the provinces of Shanghai and Zhejiang according to date of symptoms onset (n = 78)

**Temporal incidence of laboratory-confirmed A/H7N9 influenza in the provinces of Shanghai and Zhejiang according to date of symptoms onset (n = 78).** Vertical dashed lines indicate the timing of the preemptive live bird market closure in Shanghai (6 April) and Zhejiang (15 April), respectively. Cases are color coded by exposure history.

Ethics

The dataset of laboratory-confirmed cases of avian influenza A H7N9 infection was part of a continuing public health investigation of an emerging outbreak and was, therefore, exempt from institutional review board assessment.

Estimation of the reproduction number

We adopted a sequential Bayesian framework combined with a susceptible-exposed-infectious-removed (SEIR) transmission model to estimate R for influenza A/H7N9 ^{-1} days. Exposed individuals (E) then progress to the infectious stage (I), with an average infectious period of γ^{-1} days. Both the latent and infectious periods are assumed to be exponentially distributed.

This model assumes that all A/H7N9 cases originate from human-to-human transmission and, hence, provides an upper bound on the transmissibility of A/H7N9. We also conducted simulation studies to assess the performance of this approach in the situation of an emerging pathogen, where most human cases are due to spillover events originating from exposure to an animal reservoir or the environment, and human-to-human transmission is limited [See Additional file

**Supplementary information.**

Click here for file

In the Bayesian SEIR approach, we use a relationship that is directly applicable to time series data as it expresses the expected number of new cases over the time period τ (for example, τ = 1 day) as a function of the number of cases in the previous time period, given with prior epidemiological information. The relation follows from a standard SEIR model

where E[C(t + τ)] is the expected number of new cases at time t + τ, b(R, γ, κ) defines the progression of cases, γ^{-1} and κ^{-1} are the infectious and latent periods, respectively, and C(t) is the observed number of new cases at time t. The progression operator is given by:

Where λ_{+} is the dominant eigenvalue derived from linearization of the SEIR model around disease-free equilibrium, following

In this approach, both the latent and infectious periods (1/γ, 1/κ) are fixed and, hence, the only parameter to be estimated is R. We made two different assumptions for the latent and infectious periods to illustrate a short infection process consistent with seasonal influenza ^{-1} = 1.5 days and γ-^{1} = 1.5 days, so that the generation interval is 3.0 days) and a longer infection process in line with descriptions of the prolonged course of A/H7N9 infections in humans (k^{-1} = 3 days, γ-^{1} = 3 days, so that the generation interval is 6.0 days)

Bayesian inference of the reproduction number

We formulate the model in discrete time probabilistic form to account for the discrete nature of the influenza case data and estimate the distribution of R using Bayes’ theorem.

The distribution of new incident cases

which states that

where the denominator is a normalization factor. Hence, Equation (5) defines the sequential Bayesian estimation scheme, where the posterior probability distribution of

We have to set an initial prior on R to initialize the sequential approach at

To compute numerically the posterior of R at each daily iteration, we use Equation 5, relying on the posterior from the previous day as the new prior, following

Simulation studies

We carried out simulation studies to evaluate the performances of the Bayesian sequential estimation method in the context of an emerging pathogen. Specifically, we simulated A/H7N9 influenza outbreaks using a modified SEIR transmission process including different levels of human-to-human transmission (as measured by R) together with spillover events originating from a hypothetical reservoir. We varied the true R in the range 0.1 to 2.0 and modeled spillover events as a constant daily rate of new infections arising from exposure to the reservoir (α, in the range 1 to 10 infections per day). We used the model to simulate daily outbreak data, applied the Bayesian estimation method to these data, and confronted the estimated

These simulations were designed to gauge the level of error associated with neglecting transmission from environmental or animal sources in our main Bayesian estimation approach, and also to assess the sensitivity of R estimates to prior distribution assumptions, under different epidemiological scenarios.

Variance on case series of A/H7N9 influenza

The SEIR transmission model imposes a requirement on the mean of A/H7N9 cases, but variance can be modeled in a more flexible manner. Because we are dealing with disease count data, the most general choice is the Poisson distribution, where the mean equals the variance. As sensitivity analysis we considered a Negative Binomial distribution which allows for greater variance and better accounts for over-dispersed data, and assumed the variance to be twice the mean.

Estimating the impact of live bird market closures

To estimate the impact of live bird market closures in the most affected provinces of Shanghai and Zhejiang, we fit an exponential curve with intrinsic growth rate

Reproduction number estimates based on individual-level exposure data

As a complementary method to estimate the R for influenza A/H7N9, we used an approach recently developed by Cauchemez

An alternative approach to estimate R relies on the average size of chains of human-to-human transmission, as R can be estimated by dividing the number of secondary infections occurring within clusters by the number of primary cases with a direct link to the reservoir

Finally, we provide a comparative review of the transmission potential of emerging zoonoses using both individual-level contact tracing and exposure data and transmission model fitting approaches, with a focus on avian influenza A/H5N1, swine influenza A/H3N2v, seasonal and pandemic influenza, Nipah virus and severe acute respiratory syndrome (SARS).

Results

Influenza A/H7N9 epidemic curves

Figure

Epidemic curve and sequential Bayesian estimation of the distribution of

**Epidemic curve and sequential Bayesian estimation of the distribution of ****for the A/H7N9 influenza outbreak in Shanghai, China. A)** Daily number of laboratory-confirmed A/H7N9 influenza cases by date of symptoms onset. Vertical dashed lines indicate the timing of the preemptive live bird market closures in Shanghai (6 April). **B)** Evolution of R estimates as data accumulate over time, assuming a prolonged serial interval of six days (latent period, k^{-1} = 3 days and infectious period, γ-^{1} = 3 days). Median

Epidemic curve and sequential Bayesian estimation of the distribution of

**Epidemic curve and sequential Bayesian estimation of the distribution of ****for the A/H7N9 influenza outbreak in Zhejiang province, China. A)** Daily number of laboratory-confirmed A/H7N9 influenza cases by date of symptoms onset. Vertical dashed lines indicate the timing of the preemptive live bird market closures in Zhejiang (15 April). **B)** Evolution of R estimates as data accumulate over time, assuming a prolonged serial interval of six days (latent period, k^{-1} = 3 days and infectious period, γ-^{1} = 3 days). Median R (solid red line) and 95% credible intervals (dashed red lines) are shown. Horizontal dotted line indicates the threshold at R = 1, above which large epidemics are expected to occur. R, reproduction number.

Reproduction number estimates based on the Bayesian sequential approach

The Bayesian sequential estimation approach revealed that the Shanghai and Zhejiang A/H7N9 data were most consistent with a R around 0.1, with broad 95% credible intervals (0.01 to 0.49) excluding 1 (Table

**Parameters**

**R estimate (95% CI)**

**Zhejiang**

**Shanghai**

R estimates based on the sequential Bayesian estimation SEIR method, prior to the start of control interventions on 6 April 2013.

(k^{-1} = 3 days and γ-^{1} = 3 days)

0.13 (0.01 to 0.46)

0.15 (0.01 to 0.47)

(k^{-1} = 1.5 days and γ-^{1} = 1.5 days)

0.11 (0.003 to 0.42)

0.17 (0.01 to 0.49)

Comparison of prior and posterior distributions for the reproduction number, R, associated with the A/H7N9 outbreak in Zhejiang (top) and Shanghai (bottom), using the sequential Bayesian SEIR estimation method

**Comparison of prior and posterior distributions for the reproduction number, R, associated with the A/H7N9 outbreak in Zhejiang (top) and Shanghai (bottom), using the sequential Bayesian SEIR estimation method.** Sequentially obtained posterior distributions are based on data up to 15 April, immediately prior to the first closure of live bird markets, and up to 20 April, two weeks into the intervention period. We assume a serial interval of six days (latent period k^{-1} = 3 days and infectious period γ-^{1} = 3 days). The initial prior for R is a normal distribution left-truncated at 0 and centered at 0.2 (SD = 0.2). SEIR, susceptible-exposed-infectious-removed.

Sensitivity analyses and simulation studies

A sensitivity analysis on the prior distribution for

Next, we simulated outbreak data illustrating the spread of an emerging infection, where human cases originate from both human-to-human transmission and direct contact with a hypothetical reservoir. Simulations indicate that the Bayesian estimation approach tends to overestimate R, especially when the true R is low and spillover events are frequent [see Additional file

Importantly, simulations show a substantial change between prior R distribution (centered at 0.2, as in our main analysis) and posterior R distributions, when the true R is above 0.6 [see Additional file

Additional sensitivity analyses considering longer latent and infectious periods did significantly change

Impact of intervention measures

To gauge the impact of preemptive bird market closures, we analyzed temporal trends in cumulative daily A/H7N9 incidence by fitting an exponential curve to data for the combined provinces of Shanghai and Zhejiang, in the pre-intervention period 1 March to 6 April (Figure

Predicted progression of cumulative laboratory-confirmed A/H7N9 cases in the provinces of Shanghai and Zhejiang (n = 73 cases) according to dates of symptoms onset, in the absence of interventions (solid blue line)

**Predicted progression of cumulative laboratory-confirmed A/H7N9 cases in the provinces of Shanghai and Zhejiang (n = 73 cases) according to dates of symptoms onset, in the absence of interventions (solid blue line).** Dashed blue lines represent 95% confidence intervals. Predictions are based on an exponential model fit to the progression of reported cases from the end of February to 6 April, prior to live bird market closures, and using a negative binomial distribution to account for over-dispersion in case counts. Shown in red is the prediction of the model fit past 6 April. Black dots indicate the progression of reported A/H7N9 cases. Vertical dashed lines indicate the timing of the preemptive live bird market closures in Shanghai (6 April) and Zhejiang (15 April), respectively.

Estimates of the reproduction number for A/H7N9 using alternative approaches

As a complementary analysis, we present R estimates for A/H7N9 based on alternative approaches relying on individual-level information on prior exposure and contacts with infected patients

Among the 130 A/H7N9 patients reported by 26 May 2013, in mainland China, three family clusters ranging in size from two to three were identified, with onset dates between 11 February and 21 March [see Additional file

**Outbreak**

**R estimate**

**Source and method**

SARS, severe acute respiratory syndrome.

A/H7N9 outbreak

Avian influenza A/H7N9- 2013, China

0.1 (95% CrI: 0.01 to 0.49)

This study; Bayesian approach from

Avian influenza A/H7N9- 2013, China

0.03 to 0.05

This study; exposure-based approach from

Avian influenza A/H7N9- 2013, China

0.28 (95% CI: 0.11 to 0.45)

Analysis of cluster size distribution from

Other zoonotic influenza viruses

Avian influenza H5N1 -2003 to 2006, SE Asia and Egypt/Turkey

0.29

Cluster size distribution approach

Avian influenza H5N1 – 2004 to 2006; SE Asia and Egypt/Turkey

0.52 to 0.54

Swine influenza H3N2v - 2011, USA

0.5 to 0.74

Exposure-based approach

Human influenza viruses

1918 A/H1N1 influenza pandemic

1.8 to 5.4

1957 A/H2N2 influenza pandemic

1.5

1968 A/H3N2 influenza pandemic

1.5

2009 A/H1N1 influenza pandemic

1.2 to 3.1

Seasonal influenza

1.3

Other zoonotic viruses

Nipah virus, Malaysia, 1990s

0.05 to 0.08

Exposure-based approach

Nipah virus, Bangladesh, 2000s

0.48 to 0.51

Exposure-based and cluster size distribution approaches

SARS virus, Singapore, Hong Kong, 2003

2.2 to 3.6

An alternative R estimate is provided by the average distribution of secondary chains of transmission. If we assume that all three A/H7N9 clusters represents one spillover event (primary case) followed by one to two serial transmission events, we obtain R = 4/126 = 0.03. Inclusion of one additional suspected cluster of size two identified by contact tracing [see Additional file

Comparison of transmissibility estimates between influenza A/H7N9 and other zoonotic viruses

Table

We compiled R estimates for zoonotic influenza viruses that episodically cause human infections, in particular for avian-origin A/H5N1 and swine-origin A/H3N2v. Estimates in the range 0.52 to 0.54 have been proposed for A/H5N1 in Thailand and Indonesia, based on a Bayesian approach similar to that used here

The H3N2v swine-origin influenza virus has recently become a cause of concern in the US, especially in the context of agricultural fairs in 2011 and 2012. Information on the proportion of patients with direct exposure to swine

In the case of seasonal and pandemic influenza outbreaks, model-fitting approaches reveal that R is 1.3 on average for seasonal outbreaks

Nipah virus is another emerging viral zoonosis worth comparing to influenza A/H7N9 (Table

Table

Discussion

We have provided near real-time estimates of the transmission potential of the emerging A/H7N9 influenza outbreak in China by applying different methodological approaches to official notifications of laboratory-confirmed cases. Although there is relatively limited information in the A/H7N9 case data at this point, all available evidence points to R estimates well below 1.0 in Shanghai and Zhejiang provinces, where the majority of cases have been reported. Instead, a deceleration in growth rate in mid April is consistent with the effectiveness of preemptive live bird market closures initiated in early April. Comparison between A/H7N9 and other zoonotic threats suggests a relatively low transmission potential relative to that of other avian or swine influenza viruses and recent Nipah viruses, although further data are necessary to confirm this result.

Our Bayesian SEIR estimation approach assumes that all infections originate from human-to-human transmission and, hence, yields 'worst-case scenario’ R estimates. Our estimation framework was robust to assumptions about the duration of the infectious and latent periods, whether we considered a short serial interval characteristic of seasonal influenza

Alternative estimation approaches based on individual level contact tracing and prior exposure suggest a range of R of 0.03 to 0.53, in line with a recent modeling study analyzing the cluster size distribution of A/H7N9 cases

We observed a reduction in the growth rate of H7N9 cases in mid to late April, coinciding with the closure of live bird markets in Shanghai, Zhejiang and large Chinese cities in response to the evolving outbreak. The deceleration in the growth rate was significant in our data as early as 18 April, a period when the effectiveness of these measures was still being debated

We have provided transmissibility estimates for influenza A/H7N9 and other zoonoses using several approaches, which rely on very different assumptions. The Bayesian SEIR model-fitting approach is based on the progression of case incidence; our analyses suggest that currently available A/H7N9 data provide relatively limited information, so that the inference process is heavily dependent on the prior (see also more extreme priors in Additional file

In the context of subcritical outbreaks (R <1), alternative methods based on contact tracing and exposure information are attractive, although they depend heavily on prior knowledge of the ecology of the disease. These methods rely on estimates of the proportions of cases arising from human-to-human transmission versus direct exposure to the reservoir

Information regarding the reservoir of A/H7N9 and the natural history of this disease is still limited, as would be the case for any emerging zoonosis with limited prior experience. It is intriguing that 23% of A/H7N9 cases do not report any prior contact with poultry (suggesting R is approximately 0.23), and yet clusters are extremely infrequent (suggesting R closer to 0). These conflicting findings could be reconciled with additional information on the prevalence of asymptomatic infections; unfortunately, recent serological information is currently lacking. Overall, all R estimation methods tend to produce high uncertain ranges for A/H7N9. In a similar context, early estimates of the transmissibility of the MERS-CoV virus using a related approach were relatively broad, with confidence intervals ranging between 0.5 and 1.1

This study is subject to limitations. First, A/H7N9 incidence could be underreported. However, serological surveys conducted at the end of 2012 in China and Vietnam revealed low levels of prior infections

Second, we have used a simple model to estimate R, relying on a SEIR transmission model typically used for human diseases, while in fact there is likely very little transmission between humans. Our simulations suggest that in the context of frequent spillover events arising from a reservoir, our estimates of R are inflated (consistent with providing worst-case scenarios of the true human-to-human transmission potential of A/H7N9). However, our approach accurately predicts whether an emerging pathogen remains below the critical epidemic threshold (R <1). A more refined approach could integrate more information regarding the hypothetical reservoir and the probability of contacts with humans, and could estimate the relative contribution of each component to overall disease transmission. The yet unresolved nature of the reservoir of A/H7N9 and its ecology hampers the calibration of such models.

Third, our model assumes homogeneous mixing, which may not be valid. We have focused on province-specific data, which provides a better approximation of well-mixed populations than nationally-aggregated data, especially as most cases arose from large cities (especially Shanghai). Still, there could be residual spatial heterogeneity, which may artificially decrease the estimated R. Overall, our very generic model only requires information on the date of symptoms onset and could be applicable to a variety of emerging infections that include spillovers from a putative reservoir and human-to-human transmission.

Conclusion

In conclusion, we have shown that the available epidemiological data on influenza A/H7N9 are consistent with subcritical transmission potential below R = 0.6 in the first three months of virus circulation in Shanghai and Zhejiang provinces, suggesting infrequent human-to-human transmission events. A decline in the growth rate of influenza A/H7N9 cases in April 2013 highlights the beneficial impact of live bird market closures. The estimated transmission potential of A/H7N9 appears lower than that of other zoonotic threats, although uncertainty remains important due to limited statistical information in the available data. Our proposed approach could be useful to quantify the progression of the outbreak and the impact of control measures in the coming months and help monitor the pandemic potential of this emerging pathogen in near real-time.

Abbreviations

R: Reproduction number; SARS: Severe acute respiratory syndrome; SEIR: Susceptible-exposed-infectious-removed.

Competing interests

The authors declare they have no competing interests.

Authors’ contributions

GC and CV designed the experiments/the study. GC, LS, ST, MM and CV analyzed the data. GC and CV wrote the first draft of the paper. GC, LS, ST, MM and CV contributed to the writing of the paper. All authors read and approved the final manuscript.

Acknowledgments

We are thankful to Drs Hongjie Yu and Liao Qiaohong, China CDC for providing access to official notifications of influenza A/H7N9 cases in China and information on exposure history. We thank Aimee Mead, Fogarty International Center, NIH, for editorial assistance.

This research was conducted in the context of the Multinational Influenza Seasonal Mortality Study (MISMS), an on-going international collaborative effort to understand influenza epidemiological and evolutionary patterns, led by the Fogarty International Center, National Institutes of Health (

Pre-publication history

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