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Analyzed the data: TG. Other: Initiated the research, obtained the datasets and wrote the outline of the paper: AG. Programmed and performed the data analysis and wrote the first draft of the paper: TG. Developed the statistical methods for calculating the confidence intervals: PC.

The authors have declared that no competing interests exist.

With the increased occurrence of outbreaks of H5N1 worldwide there is concern that the virus could enter commercial poultry farms with severe economic consequences.

We analyse data from four recent outbreaks of highly pathogenic avian influenza (HPAI) in commercial poultry to estimate the farm-to-farm reproductive number for HPAI. The reproductive number is a key measure of the transmissibility of HPAI at the farm level because it can be used to evaluate the effectiveness of the control measures. In these outbreaks the mean farm-to-farm reproductive number prior to controls ranged from 1.1 to 2.4, with the maximum farm-based reproductive number in the range 2.2 to 3.2. Enhanced bio-security, movement restrictions and prompt isolation of the infected farms in all four outbreaks substantially reduced the reproductive number, but it remained close to the threshold value 1 necessary to ensure the disease will be eradicated.

Our results show that depending on the particular situation in which an outbreak of avian influenza occurs, current controls might not be enough to eradicate the disease, and therefore a close monitoring of the outbreak is required. The method we used for estimating the reproductive number is straightforward to implement and can be used in real-time. It therefore can be a useful tool to inform policy decisions.

A new highly pathogenic strain of avian influenza, H5N1, emerged in the poultry markets of Hong Kong in 1997 and subsequently re-emerged in Vietnam in 2003. From this time onwards it has rapidly spread across the globe and is likely to be endemic in poultry in many parts of the world. Although onward transmission to humans at present remains limited, the high case fatality rate in those people that are infected has raised concerns about the impact of a potential human pandemic

Avian influenza occurs naturally in wild water fowl, usually in a low-pathogenic version (LPAI) causing no symptoms or only mild disease. However, in poultry some strains also occur in a highly-pathogenic form (HPAI) and result in a devastating disease which can kill up to 100% of infected birds within 48 hours, and is highly transmissible between individual birds

The reproductive number for infected poultry farms, defined as the average number of farms that each original infected farm infects at the start of an outbreak (i.e., when most farms are susceptible), is an important measure of the overall transmissibility of the virus in a population. It determines whether a self-sustaining epidemic will occur and, more importantly, yields a tool to assess the effectiveness of control measures. If, on average, at any point in time, each infected farm infects more than one further farm, the epidemic will continue. However, if on average, each infected farm infects less than one further farm, the epidemic will decline and the intervention measures applied at that point can be interpreted as being sufficient to control the outbreak.

In this paper, we analyse published data from four outbreaks of HPAI in commercial poultry in industrialised countries to estimate the farm-to-farm reproductive number of HPAI to explore the extent to which different intervention measures implemented during these outbreaks reduce the reproductive number. The results from our analyses can be used to inform current planning for an outbreak of HPAI in similar commercial poultry sectors.

We analyse data from three different outbreaks of HPAI that occurred in the past 8 years in industrialised countries: an outbreak of H7N1 in Italy in 1999/2000, an outbreak of H7N7 in the Netherlands in 2003, that will be treated as two distinct outbreaks due to geographic separation, and an outbreak of H7N3 in Canada in 2004.

Number of infected farms detected daily for the four distinct epidemics. The data is given in

Northern Italy has experienced a number of avian influenza outbreaks from 1997 onwards ^{2}) and involved a significant number of farms keeping turkeys, a species known from experimental studies to be highly susceptible to avian influenza

In March 1999, H7N1 LPAI was detected in a farm keeping turkeys

The H7N7 epidemic in the Netherlands in 2003 affected a total of 255 commercial flocks in two distinct geographical and temporal clusters. The outbreak was situated in the Gelderse Vallei, the densest poultry production area in the Netherlands, in which over 10 million birds are kept in 984 flocks with a density of 4 flocks/km^{2}

In the Gelderse Vallei, HPAI was confirmed on 28^{th} February, 6 days after clinical signs appeared in the first infected farm, and between March and early April, a total of 212 farms were infected. In Limburg, a further 43 farms were infected between April and early May.

A number of control policies were enforced in several stages. From 1^{st} March all movement of poultry and poultry products was banned, the tracing of dangerous contacts was initiated and reinforcement of strict bio-security measures was implemented. Two days later, from 3^{rd} March, culling of infected farms was initiated. On 5^{th} March the additional pre-emptive culling of farms within a 1 km radius of any infected farms was put in place. This was further extended to a 10 km radius for turkey flocks and 3 km radius for all other flocks on 7^{th} April

During this epidemic, 89 human infections were also reported, most of whom presented with conjunctivitis or mild influenza-like illness. One person died from their infection. There was also evidence of limited human-to-human transmission

The H7N3 outbreak in the Fraser Valley, British Columbia in Canada

Following detection of the index case, a broiler breeder farm, a surveillance program was initiated, which led to the detection of the second case on 11^{th} March. The Fraser Valley south of the River Fraser was declared a Control Area, restricting movements of birds, bird products and equipment. Furthermore, active surveillance was undertaken in a High Risk Region (HRR, 5 km around the index case) and in flocks deemed dangerous contacts in a Surveillance Region (SR, 10km around index case).

After the identification of 7 infected farms, all birds within the HRR were slaughtered from 24^{th} March onwards, but as this failed to stop transmission, on 5^{th} April it was decided to depopulate the whole Control Area, containing approximately 19 million birds.

Infected farms were located mainly in three distinct local clusters within the Control Area. It is hypothesized that long distance spread between these clusters was due to bird, equipment or people movement, whereas once a farm in a densely populated area became infected, where sheds are sometimes within a few hundred metres from each other, the virus spread via dust or feather debris.

Assuming homogeneous mixing, that all farms are equally infectious, and that the time-dependence of infectiousness from the point of infection is identical, we can estimate both the distribution of generation time intervals and the reproductive numbers of individual farms from the time-course of an epidemic using the following method

Suppose there are _{1},…,_{N}_{1} = … = _{k}

Now denote the ‘infection tree’ by _{k}_{+1},…,_{N}_{j}

But as _{j}

The maximum likelihood (ML) estimate

More details on how ML estimation is performed are given in _{j}_{i}

We further investigated whether the generation time distribution changed after control measures were introduced. To do this, we extended the above model to allow for distinct parameters for the generation times before and after controls, _{pre}_{post}

Given

To calculate confidence intervals for the reproductive number we use an approximation of the parametric bootstrap percentile interval method

This first stage can be loosely thought of as sampling the mean behaviour for a subgroup of possible outbreaks. To allow for variability within each subgroup, stage two involves fixing (^{*},^{*})and independently generating reproductive numbers for each farm according to model (2). Steps one and two together give ^{*}^{*}_{i}_{i}^{th} and 97.5^{th} percentiles of the bootstrap distribution. The second stage of the calculation of the approximate CIs was done using

The generation time is defined as the time between the infection of a farm and the time at which the farm passes on infection to another farm. We have assumed the generation time distribution is Weibull. While this is a biologically plausible choice, we cannot verify it empirically. As such, we assessed robustness to this choice using other plausible choices such as the gamma distribution (results not shown). However, the following results under these alternatives did not differ substantively from those shown below.

Parameters of these distributions are shown in

Dataset | mean | variance | ||

Italy | 2.2 (1.7–3.0) | 0.18 (0.14–0.22) | 5.0 (4.0–6.3) | 5.9 (3.5–11.7) |

British Columbia | 1.6 (1.1–2.5) | 0.11 (0.07–0.16) | 8.4 (5.7–12.1) | 29 (12–84) |

Gelderse Vallei | 2.9 (1.9–4.1) | 0.46 (0.29–0.59) | 1.9 (1.5–3.1) | 0.51 (0.23–2.2) |

Limburg | 3.3 (1.6–8.3) | 0.26 (0.19–0.38) | 3.4 (2.3–4.9) | 1.3 (0.37–5.1) |

The estimates are obtained with the MLE for the generation time distribution parameters. The light blue area shows the 95% confidence intervals. The vertical orange line marks the date of reinforced controls. For British Columbia, this was the date the decision to cull the HRR region was taken, for the other datasets it is the date of detection of HPAI within the area.

Dataset | Maximum | mean |

Italy | 2.3 | 1.9 (1.2–2.7) |

British Columbia | 3.2 | 2.4 (1.4–3.6) |

Gelderse Vallei | 2.9 | 1.1 (0.9–1.5) |

Limburg | 2.2 | 1.9 (1.0–3.0) |

Maximum reproductive numbers estimated for any farm during the course of each outbreak and mean reproductive numbers

The impact of control measures on the effective reproductive number can be clearly seen in all four outbreaks. For the outbreak in Italy (^{th} March when the decision was taken to cull the whole high risk region. Our estimates show that the control activities following this decision were effective in reducing the reproductive number to below one.

Our results show that the situation in the Gelderse Vallei, The Netherlands (

Our estimates of the farm-to-farm reproductive number prior to interventions for HPAI are in the range 1.1 to 2.4 and were remarkably consistent across the four datasets. However, these estimates are substantially lower than those previously reported for the Dutch epidemic. Prior to the implementation of control measures we obtained estimates of 1.1 (95% CI 0.9–1.5) in the Gelderse Vallei and 1.9, (95% CI 1.0–3.0) in Limburg which are significantly lower than those previously reported for the same outbreak prior to notification (6.5 (95% CI 3.1–9.9) for the epidemic in the Gelderse Vallei). However, as demonstrated in

Our results showed substantial differences between the estimated generation time distributions for the different outbreaks. Whilst much is known from experimental studies on the course of infection in individual birds

All of the outbreaks investigated here occurred within dense poultry farming areas and hence were difficult to control. The control policies implemented in the different outbreaks were similar, comprising strict bio-security measures for movement of poultry and poultry products, swift culling of infected flocks, and if these failed to control the epidemics, additional pre-emptive culling of flocks in the neighbourhood of any infected farms. Our results demonstrate that the bio-security measures, movement restrictions and culling of infected farms, all of which were initiated early on in the outbreaks, did have an effect but for all four outbreaks only reduced the reproductive number to close to the threshold value of 1. The additional pre-emptive culling of flocks and de-population of the areas was needed to fully control the outbreaks. Current contingency plans for HPAI outbreaks in Europe focus on the former set of control measures to contain any outbreak

The method used here to estimate the reproductive number and generation time parameters is an extension of that developed by Wallinga and Teunis

The Transmissiblity of Highly Pathogenic Avian Influenza in Commercial Poultry in Industrialised Countries: Technical Appendix

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Time Series of the Epidemics

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Source code for the maximum likelihood estimation of the parameters of the generation time distribution, shown in

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header file for

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Source code for the maximum likelihood estimation of the parameters of the generation time distribution, assuming two different distributions (i.e., different parameters), pre- and post-intervention.

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header file for

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Source code for generating the bootstrap samples for the parameters of the generation time distribution, used in the calculation of the confidence intervals.

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Source code for estimating R0 and the confidence intervals based on the uncertainties inherent in the estimation procedure and the uncertainty of the generation time distribution, shown in

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Source code for calculating the mean R0 prior to interventions and its confidence intervals shown in

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We would like to thank Jamie Griffin for insightful comments and helpful discussions.