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MCMdJ, GJB, MvB, and TJH conceived the ideas underlying the analyses. AB, GN, and ARWE collected the data. GJB, TJH, and MvB analyzed the data and wrote the paper. AB, GN, ARWE, and MCMdJ commented on the text.

¤ Current address: Department of Virology, Central Institute for Animal Disease Control, Wageningen University and Research Centre, Lelystad, The Netherlands

The authors have declared that no competing interests exist.

Devastating epidemics of highly contagious animal diseases such as avian influenza, classical swine fever, and foot-and-mouth disease underline the need for improved understanding of the factors promoting the spread of these pathogens. Here the authors present a spatial analysis of the between-farm transmission of a highly pathogenic H7N7 avian influenza virus that caused a large epidemic in The Netherlands in 2003. The authors developed a method to estimate key parameters determining the spread of highly transmissible animal diseases between farms based on outbreak data. The method allows for the identification of high-risk areas for propagating spread in an epidemiologically underpinned manner. A central concept is the transmission kernel, which determines the probability of pathogen transmission from infected to uninfected farms as a function of interfarm distance. The authors show how an estimate of the transmission kernel naturally provides estimates of the critical farm density and local reproduction numbers, which allows one to evaluate the effectiveness of control strategies. For avian influenza, the analyses show that there are two poultry-dense areas in The Netherlands where epidemic spread is possible, and in which local control measures are unlikely to be able to halt an unfolding epidemic. In these regions an epidemic can only be brought to an end by the depletion of susceptible farms by infection or massive culling. The analyses provide an estimate of the spatial range over which highly pathogenic avian influenza viruses spread between farms, and emphasize that control measures aimed at controlling such outbreaks need to take into account the local density of farms.

Outbreaks of highly contagious animal infections such as foot-and-mouth disease, classical swine fever, and highly pathogenic avian influenza traditionally have been and continue to be important loss factors in production animals throughout the world. In recent years, several large epidemics have occurred with serious socioeconomic consequences [

To explain the observed patterns of infection of highly pathogenic avian influenza virus between farms, and to be able to evaluate the potential effectiveness of control measures, we adopt a phenomenological modelling approach. Similar approaches have been used in modelling studies of the interfarm spread and the effectiveness of control measures during the foot-and-mouth epidemic in the United Kingdom in 2001 [

For estimation of the model parameters, we use an extensive dataset that was collected during an outbreak of a highly pathogenic H7N7 avian influenza virus in The Netherlands in 2003. Shortly after the detection of virus circulation, the Dutch authorities undertook an aggressive control strategy that consisted of an animal movement ban and enhanced biosecurity measures in the affected regions, tracing and screening of suspected flocks, and culling of infected and contiguous flocks. In all, 241 commercial flocks became infected during a period of 9 wk, and more than 30 million birds died by infection and culling.

A striking characteristic of the 2003 epidemic was that most of the infected farms were confined to two areas with a high density of poultry farms. In fact, it was noted that proximity to an infected herd was a significant risk factor for acquiring infection [

Farms that were infected during the 2003 epidemic of avian influenza are represented by black dots, and farms that were not infected are represented by yellow dots.

As a first step to gain further insight into the spatial transmission characteristics of the 2003 epidemic, we plot in

(A) The frequency distribution of the distances of potential infection events. Notice that the majority of potential infections occur within a radius of 25 km around an infected farm.

(B) The proportion of farms infected within different distance categories from a potential source farm, averaged over all possible source farms (i.e., over all farms confirmed positive during the 2003 epidemic).

Our more detailed analyses below confirm that the probability of infection decreases strongly as the distance between farms increases. In fact, the probability that a farm that is close to an infected farm (0–2 km) will be infected by that farm is 1%–2%, while farms that are further away from an infected farm (>10 km) have a probability of less than 0.05% of being infected by that farm. Our analyses also reveal that there are two high-risk poultry-dense areas in The Netherlands in which an introduction of highly pathogenic avian influenza virus is likely to cause a major epidemic. In these areas, targeted control strategies such as vaccination or culling of farms within a ring of 1–2 km around affected premises are unlikely to be effective in containing an epidemic. On the other hand, culling in a wider ring of 3–5 km may be effective, although the number of farms that has to be culled around each infected farm may become very large (>100 per infected farm).

The analyses rely on the availability of two pieces of information. The first is the spatial locations of all farms that are at risk of infection and subsequent transmission to uninfected farms. The second is an assessment of the infection status (uninfected, infected but not yet infectious, infected and infectious, removed) of each farm during the epidemic. While the former data are relatively easy to retrieve and can be collected before or after an epidemic, the latter require a considerable effort of data collection during the epidemic. In short, as the epidemic unfolded, an attempt was undertaken to record for all infected farms the key demographic characteristics (number of barns, number of animals, type of animals, age of the animals) and data of epidemiological interest (number of dead animals per day, number of sick animals per day, food and water intake per day). By no means could all of the above information be collected for all farms, although the day at which mortality first increased and the moment of culling were reported for all farms. In our analyses, farms were assumed to be infected 6 d before the day on which mortality first increased. Upon infection, each farm then remained latently infected for 2 d, after which it was assumed to be infectious until culling. For a more detailed description of the epidemic, including detailed case reports of the first five infected premises, we refer to [

Technically, the infection data are collected in an _{max} infection matrix C = (_{ij}_{max} days of the epidemic. For the Dutch outbreak we have _{max} = 78 [_{ij}_{ij}

The farm location data take the form of a list of _{i}_{i}_{i}

The model is defined on a farm level (i.e., farms are the individual units). These individual units differ by their location and infection status, and are considered identical in all other respects. This simplification (in particular, ignoring differences in farm size) is made because more detailed modelling introduces additional parameters that cannot be estimated with sufficient precision to add further insight into the spatial transmission risk. The infection matrix C discussed above specifies how each farm's status (_{ij}_{i}_{ij}_{i}_{j}_{ij}_{ij}_{i}_{ij}_{ij}

With estimates of the transmission kernel at hand, a risk map can be constructed in the following way. At every farm location we calculate the (basic) reproduction number _{i}_{i}_{c}

The above theoretical considerations assume that farm density is constant. This is hardly ever true in practice, and we need to take into account the actual distribution of farms. For a specific distribution of farms and assuming a stochastic infectious period _{i}

_{i}

If the infectious periods are drawn from a parametric distribution, an explicit expression for _{i}

Below, we obtain a risk map for epidemic spread by drawing a map in which all commercial poultry farms are indicated by a dot, representing those farms with _{i}

To obtain quantitative estimates for the local reproduction numbers, we need estimates of both the transmission kernel _{ij}_{i}

The infectious periods at the farm level were obtained from the infection matrix C. The mean infectious period of the 241 farms that were infected was 7.47 d (95% CI = (7.2–7.8). On the basis of these data we took

We estimate the transmission kernel _{ij}

To evaluate the performance of the transmission kernel specified by

To derive the likelihood function, we define the force of infection _{i}_{i}_{i}

Using _{cul,l}_{inf,m}

The maximum likelihood estimates of the parameters of interest (_{0}, _{0}, and

Maximum Likelihood Estimates of the Model Parameters

Mathematica 5.2 (Wolfram,

The 95% confidence areas of the transmission kernel are represented by the shaded area.

See _{i}_{i}_{i}_{i}_{i}

^{−3} (d^{−1}) in the direct neighbourhood of an infected farm to 1.6 × 10^{−3} (d^{−1}) at 1 km, and to 6.1 × 10^{−3} (d^{−1}) at 10 km distance. This implies that the probability that a given farm will be infected if it is at 0 km, 1 km, or 10 km from an infected farm is approximately 0.016, 0.012, and 4.6 × 10^{−4} if the infectious period is 7.5 d.

_{i}_{i}_{i}_{i}

The analysis shows that there are two areas in The Netherlands that are at risk of a locally propagating epidemic after a virus introduction: one large area in the central part of the country comprising 913 farms (95% confidence bounds of the high-risk area: 685–1,065) and one small area in the south of 61 farms (95% confidence bounds of the high-risk area: 0–206). In those two areas the local density of poultry farms is such that an infected farm is expected to produce a substantial number of subsequent infections.

A comparison of

At this point we would like to note that, in order not to miss or underestimate the size of high-risk areas close to the Dutch border, we have incorporated the poultry farms in the Belgian provinces and German administrative areas (NUTS2 administrative levels) bordering The Netherlands in our calculations (both in the kernel estimation and in the risk-map calculation). As we do not have access to location data for the farms in these regions, we have approximated the farm structure of these regions by generating random model locations on the surface of these regions according to a homogeneous Poisson point process. The total number of model locations per region was matched to Eurostat data (

To investigate the robustness the above results, we performed a suite of sensitivity analyses. We paid particular attention to the functional form of the transmission kernel, the range of farms included in the estimation procedure, the assumptions leading to the infection data matrix, and the assumed constancy of the transmission level over time. Below, we discuss each of these aspects in turn.

As a first step to investigate the sensitivity of the above results we considered a number of different functions of varying complexity for the transmission kernel. The performance of the different kernels was evaluated on the basis of the support received by AIC [

Evaluation of the Performance of Different Transmission Kernels

(A) Results for the default scenario (no culling).

(B) Results for a scenario with immediate culling of all farms within a range of 1 km around an infected farm.

(C,D) Culling is carried out in a range of 3 km and 5 km around infected farms, respectively. Farms in yellow pose no risk of epidemic spread for the chosen control strategy, while farms in red constitute a risk of epidemic spread even with the control strategy in place.

_{0}) gives by far the worst fit to the data and has negligible support in comparison with models that do include some form of negative distance dependence. These results imply that the risk of transmission is not constant but decreases with interfarm distance. In particular, the results of ^{α}

To further investigate the sensitivity of our results, we considered alternative transmission models in which the transmission kernel does not depend on the Euclidean distance between farms, but on the distance rank of infected farms to susceptible farms, or the distance rank of susceptible farms to infected farms (see [

Our kernel estimates are based on all commercial farms in The Netherlands. Since The Netherlands is a small country (35,000 km^{2}), this implies that the kernel parameter estimates are based mainly on pairs of farms that are less than 150 km apart. To investigate the sensitivity of the results to the range of distances for which information is available, we have repeated the kernel estimation using an extended dataset in which the distribution of poultry farms outside The Netherlands was taken into account. Specifically, we approximated Europe by one-half of an annular area of inner radius of 200 km and an outer radius of 1,600 km with a uniform poultry farm density equal to the mean poultry farm density of the 24 non-Dutch European Union member states (

The results show that the inclusion of farms outside of The Netherlands (and the information that these had not been infected) only marginally affects the estimated local reproduction numbers, yielding risk maps that are indistinguishable from those in

In the above analyses, we assumed perfect knowledge of the course of the epidemic in The Netherlands in 2003. There is, however, some uncertainty in the data with regard to the infection matrix C, in particular with respect to the precise moment of infection of infected farms. To investigate the sensitivity of the results to assumptions underlying the infection matrix, we carried out additional analyses in which the moment of introduction was placed 2 d later than in our default analyses (see [_{0} increases from an estimated 0.0020 d^{−1} in our default scenario to 0.0028 d^{−1} in the additional analyses. Hence, the sensitivity analysis indicates that although the estimates of the parameters of the transmission kernel (in particular the baseline infection hazard _{0}) are sensitive to the moment of introduction and length of the infectious period, the risk map of

The above analyses assume that both the infectious period at the farm level as well as the transmission kernel remained constant throughout the epidemic. This, however, is only approximately the case. Especially during the first week of the epidemic there were no or hardly any control measures in place, and the detection of infected farms was still imperfect and slow. In line with our earlier nonspatial analyses [

Besides a movement ban and biosecurity measures, there are two potentially attractive local control measures: culling of farms in the proximity of infected premises that have a heightened risk of infection, and vaccination. We first investigate the effectiveness of rapid culling of all farms in a ring around infected farms. The effect of this measure can be described by reducing the height of the transmission kernel of the infected farm and/or the length of the infectious period of potential contact farms within the culling radius. Here, we assume that culling occurs before any infected farm in the culling ring starts spreading the infection to other farms, so that the intervention can be described by setting the transmission kernel of the infected farm to zero at distances within the culling radius. Thus, the analyses below correspond to a best-case scenario, and assume in effect that no transmission takes place from farms within the culling radius. This can probably only be achieved if ring culling is carried out within a couple of days after infection of a focal farm.

^{2} so that a 5-km ring culling strategy would imply that for each infected farm more than 300 farms have to be culled within a couple of days (^{2} ×

As far as emergency vaccination around infected farms is concerned, we note the following. On the one hand, it is highly unlikely that vaccination can be effective once a highly pathogenic virus has successfully been introduced in a densely populated poultry region. The reason is that it takes at least a week to vaccinate all susceptible poultry and an additional 7–14 d before a vaccine provides effective protection against infection and subsequent transmission [

In this paper we have presented an analysis of the spatial transmission dynamics of highly pathogenic avian influenza virus spread between farms by using an extensive dataset of a major epidemic of H7N7 avian influenza virus in The Netherlands in 2003. As the specific transmission route responsible for infection is unknown for all of the infected farms, we have adopted a phenomenological modelling approach in which we do not distinguish between different specific routes contributing to between-farm virus transmission. This allows us to obtain quantitative estimates of model transmission rate parameters that describe the transmission risk between pairs of farms as a function of distance.

We have shown how the estimation of the transmission kernel naturally leads to estimates of a local reproduction number, which allows one to map out the transmission risk geographically. In this way, two poultry-dense areas at risk of local epidemic spread are identified in The Netherlands. The local reproduction number can be interpreted as a measure of the local farm density or, more precisely, as a measure of the density of farms surrounding a farm at a given location. As a result, we may view the geographic risk map as a farm density map. In particular, the critical farm density above which epidemic spread is possible corresponds to a situation where the local reproduction number equals the threshold value 1.

The density of poultry farms happens to differ quite strongly between the high-risk areas and elsewhere in The Netherlands. For instance, while the average farm density in the two areas that were classified in our analyses as high-risk (913 farms) is about 3.8 farms/km^{2}, the average density in the remainder of The Netherlands (4,447 farms) was only about 0.5 farms/km^{2}. This corresponds well with ^{2}. As a result of the large differences in poultry densities in The Netherlands, moderate changes in the transmission kernel have very little effect on the important features of the risk map, in particular the location and the size of the high-risk areas. Due to this insensitivity, our results are robust under variation of uncertain parameters.

By adjusting the transmission kernel, we have also produced risk maps that evaluate the effectiveness of pre-emptive ring culling around infected farms. These risk maps show that pre-emptive culling within 3 km or less is unlikely to be able to halt an unfolding epidemic in the high-risk areas. In these areas, an epidemic can only be brought to an end by the depletion of susceptible farms by infection or massive culling. Our analyses indicate that in the high-density areas in The Netherlands, ring culling is only effective (in the sense that it can halt an unfolding epidemic) if the culling radius is more than 3 km. On the other hand, our analyses also show that in the remainder of The Netherlands (i.e., the large low-density areas of

An important open problem is whether culling or vaccination programmes are able to reduce the total number of animals that would die during an epidemic (by infection or culling) compared with a strategy in which only a movement ban and biosecurity measures are put in place. During the epidemic of the highly pathogenic H7N7 avian influenza virus that wreaked havoc in The Netherlands in 2003, it was decided, on the basis of the then-available epidemiological and economic information and legislative constraints, to put in place an aggressive control strategy in which culling around infected premises was an integral part. Based on the present analyses, we would expect that an introduction of a highly pathogenic avian influenza virus in one of the poultry-dense areas in The Netherlands cannot easily be contained, and probably would affect a large fraction of the farms in such a region. However, some form of preventive culling around infected premises would still pay off, as it would decrease the length and severity of the epidemic in this region, and thereby also reduce the risk of spread of the disease to other (high-density) areas.

Each line gives the infection status (

(72 KB TXT)

We thank Don Klinkenberg and Pieter Trapman for helpful discussions. The constructive comments of three anonymous reviewers are highly appreciated.

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