### Data and data handling

In the framework of the European FP6 Network of Excellence of Diagnostics and Control of Epizootic Diseases EPIZONE [9], National Reference Laboratories from Germany (FLI), the Netherlands (CVI) and Belgium (CODA-CERVA), together with the Centre de Coopération Internationale en Recherche Agronomique pour le Développement (CIRAD), Montpellier, France collaborated on an epidemiological analysis of the BTV-8 epidemic in ruminant herds in 2006 and 2007.

The epidemiological data we used were the following: the geographical coordinates for each outbreak farm (in total the datasets include 40 927 reported farms) and the date when clinical suspicion was reported to veterinary authorities. Furthermore, we used information on the number of all farms housing cattle, sheep and goats per municipality as administrative unit. FLI provided a secure database platform and server making these and some further background data on the 2007 BTV-8 epidemic available to all group members. The number of non-outbreak farms per administrative unit has a mean of 16, a standard deviation of 41, a minimum of 0, a maximum of 1668, while the quartiles are: Q_{1} = 3, Q_{2} = 7, and Q_{3} = 15. The nearest-neighbour distance between administrative units has a mean of 3.1 km, a standard deviation of 1.4 km, a minimum of 0 km, a maximum of 48.6 km, while the quartiles are: Q_{1} = 2.2 km, Q_{2} = 2.8 km, and Q_{3} = 3.7 km.

The daily mean temperature data during the epidemic period was obtained from four weather stations, with a central location in the affected area per country; De Bilt (Netherlands), Kassel (Germany), Ukkel (Belgium) and Aulnois-SO (France). We restricted ourselves to those four centrally located stations, which are used as temperature reference for the whole country (see Figure 1). The method of analysis does not allow for each farm to be linked to the nearest weather station, since the force of infection links susceptible farms to all farms that are infectious (at the time considered). Thus, the temperature is assessed at country level, without further spatial detail.

### Transmission modelling

The above mentioned data were used to quantify the transmission between herds (1) in terms of a reproduction ratio (only temporal information on the affected herds was used) and (2) in terms of a spatial transmission kernel (both spatial and temporal information required). The first analysis was carried out to evaluate the impact of seasonality and temperature on transmission, while the second analysis aimed at determining the spatial scale of BTV-8 transmission.

A complicating factor in both analyses as compared to the analysis of the 2006 BTV-8 epidemic [2] was that the 2007 epidemic was not a newly arising epidemic, but one advancing from whereto it had already spread in 2006.

### Estimation of reproduction ratio between herds

We estimate the so-called effective reproduction ratio (*R*) between herds, defined as the number of newly infected (herds) initiated by one typical infected (herd), for a given prevalence of immune herds in the population. The effective reproduction ratio equals the basic reproduction ratio multiplied with the susceptible fraction of the population (of herds). In a starting and expanding epidemic, the fraction of susceptibles is close to one, and the effective reproduction ratio is to a good approximation equal to the *basic* reproduction ratio, *R*_{
0
}.

The effective reproduction ratio is estimated from the number and chronology of reported case farms, as described by de Koeijer et al. and Bouma et al. [2],[10]. In essence, the calculation determines the estimated number of offspring infections for each source farm by determining for each candidate offspring infection the number of possible source herds, and assigning a corresponding proportion of the farm to the source farm in question. We assume that a herd becomes infectious two weeks after introduction of the infection, when the infection has spread substantially in a herd. We assume that the reporting date equals the time at which a herd becomes infectious. From the available data it is not possible to determine in detail when an outbreak farm ceases to be infectious, i.e. when the infection would have died out in both the livestock and surrounding vector population. Since the infection can spread and persist in the livestock and in vectors in and on the farm for several months [11], we therefore assume that all infected farms remain infectious during the whole remainder of the vector-active season.

We analysed the full data set of the 2007 epidemic under these assumptions. To assess if there was a regional effect on transmission we also analysed the data from Belgium, Germany and the Netherlands separately. Furthermore, we tested the impact of the assumption concerning the infectious period by assuming shorter infectious periods.

### Kernel estimation

For the spatial-temporal analysis of the 2006 BTV-8 outbreak [2], we applied the method published by Boender et al. [12],[13]. In this method, the inter-farm transmission of a livestock disease is described in terms of a probability as a function of the inter-farm distance. For the formulation of this transmission probability, the transmission kernel is a central component, which is described as a transmission rate *λ*(*r*) across the straight-line inter-farm distance *r*. The estimation of the transmission kernel thus involves calculation of the inter-farm distances between infectious and susceptible farms. In order to calculate these, the location coordinates of non-outbreak farms were set equal to the centre coordinates of their administrative unit. As this approximation to the farm locations was only applied to the non-outbreak farms and not to the outbreak farms, the errors in the calculated distances of susceptible to infectious farms average out, thus having a negligible influence on the estimated distance-dependent transmission risk.

To be as general as possible, while limiting the number of possibilities, we used the following model parameterization for the transmission kernel:

\lambda \left(r\right)=\frac{{\lambda}_{0}}{1+{\left({\scriptscriptstyle \frac{r}{{r}_{0}}}\right)}^{\alpha}}

(1)

in which *r* is the inter-farm distance, α the power, *λ*_{0} the rate of transmission for small distances and *r*_{0} the half-value distance (\lambda \left({r}_{0}\right)={\scriptscriptstyle \frac{1}{2}}{\lambda}_{0}). The parameterization shown in equation (1) is flexible enough to encompass a range of possible distance dependencies of transmission. In particular, the value of the power α controls whether the transmission is in essence global (α < 2), local (α > 3), or intermediate (2 < α < 3) [2]. In addition, this parameterization has been shown to be preferable to other possibilities, as it produces the best model fit for both the FMD outbreak in the Netherlands in 2001 as well as for the Dutch Avian Influenza epidemic in 2003 [12],[14]. In this approach it is assumed that transmission is isotropic (independent of direction), homogeneous (independent of location of the farm) and constant (time independent during the infectious period of the farm). In order to limit the number of estimable model parameters so as to keep the analysis tractable, we make the simplifying approximation that the transmission between farms is farm-size and species independent. Based on these assumptions and on the model parameterization of the transmission kernel, the inter-farm transmission probability can be formulated. The probability of transmission occurring in the infectious period *T* of the source farm to a susceptible farm a distance *r* away equals:

p\left(r,T\right)=1-exp\left(-\lambda \left(r\right)T\right).

We used the same assumptions as in the estimation of the reproduction ratio between herds and motivated above, namely that a herd becomes infectious at the time when the first clinical symptoms were observed, that it has a latent period of 14 days before that date, and that all infected farms remain infectious for the whole remainder of the vector-active season. The same assumptions have been employed previously by de Koeijer et al. [2]. The parameters are estimated using Maximum-Likelihood (ML), following the same approach as used in [12]. We calculate 95% confidence intervals for the parameters using the likelihood-ratio test. The likelihood is given by the following expression:

L={\displaystyle \prod _{k\in {\mathrm{\Lambda}}^{\mathrm{s}}}}{p}_{\mathrm{esc},k}\left({t}_{\mathrm{end}}\right){\displaystyle \prod _{m\in {\mathrm{\Lambda}}^{\mathrm{i}}}}{p}_{\mathrm{esc},m}\left({t}_{inf,m}\right){p}_{inf,m}\left({t}_{inf,m}\right).

Here the total number of farms is subdivided in two sets: Λ^{i} is the set of all farms that are infected during the epidemic, and Λ^{s} is the set of all farms remaining susceptible. Any farm *m* from the set Λ^{i} escapes from infection until it is infected at time *t*_{inf,m} , and any farm *k* from the set Λ^{s} escapes until the end of the vector-active season *t*_{end}. The quantity *p*_{esc,m}(*t*) is the probability that farm *m* is escaping from infection by all infectious farms up to time *t*; which is given by

{p}_{\mathrm{esc},m}\left(t\right)={\displaystyle \prod _{s=1}^{t-1}}{\displaystyle \prod _{j\in {\mathrm{\Lambda}}^{\mathrm{i}}}}\mathit{exp}\left(-\lambda \left({r}_{\mathit{mj}}\right){\mathbb{I}}_{inf,j}\left(s\right)\right)\phantom{\rule{0.25em}{0ex}}.

Here \lambda \left({r}_{\mathit{mj}}\right){\mathbb{I}}_{inf,j}\left(t\right) is the probability per day that an infectious farm *j* infects a susceptible farm *m* at time *t*, where *r*_{
mj
} is the distance between farms *m* and *j*, and {\mathbb{I}}_{inf,j}\left(t\right) denotes the indicator function which is 1 when farm *j* is infectious at time *t*, and 0 otherwise. The quantity *p*_{inf,m}(*t*) is the probability that farm *m* is infected by any of the infectious farms at time *t*:

{p}_{inf,m}\left(t\right)=1-{\displaystyle \prod _{j\in {\mathrm{\Lambda}}^{\mathrm{i}}}}\mathit{exp}\left(-\lambda \left({r}_{\mathit{mj}}\right){\mathbb{I}}_{inf,j}\left(t\right)\right)\phantom{\rule{0.25em}{0ex}}.

We note that the interpretation of the data in terms of infection events is complicated by the fact that the starting point of the epidemic in 2007 was not a population of naïve herds (in which the virus was introduced), but rather a population in which in one area many herds were affected by BTV already in the previous year (2006). About 80% of the farms in Belgium had already been affected by Bluetongue in 2006, while the within-herd prevalence was 24% [15]. Therefore, detected outbreak farms in the 2006 infected area are most probable re-emerging infected, while detected outbreak farms outside this area are most probably susceptible herds becoming infected by means of transmission. In order to assess the importance of local re-emergence, we used the estimation of a spatial transmission kernel as a diagnostic tool. In this analysis (and also in the other analyses performed in this paper) farms are treated as uninfected initially in 2007 even if they were affected before in 2006. If the re-emergence effect dominates, we would expect to find a kernel that shows only a very weak distance-dependence, because the random local re-emergence would in this analysis be interpreted as transmission over random distances. After carrying out this diagnostic procedure we moved on to quantify the between-farm transmission. We correct for the presence of re-emergence by excising the 2006 infected area from the data. To approximate the infected area, a two-step approach was used. In a first step, to study the effect of an approximate excision on the analysis, the infected area was approximated by a single geometric shape. As proxy for the infected area we used the first six months (220 days) of the 2007 epidemic. We approximated the infected area by a circle with a radius of 200 km around the centre of this part of the epidemic. This radius was chosen because 94% of cases was situated inside this circle. All the farms inside this circle were removed from the dataset and the modified dataset was used in the likelihood estimation. The outcome of this first step shows the direction in which the transmission kernel is changing by modifying the dataset. This step justifies the application of a more refined strategy in the next step. In this second step, a more refined approximation of the infected are is used. We assumed that each case farm in 2006 gave rise to an infected area at the start of the 2007 epidemic. Therefore, we removed all farms in a (varying) circle around each farm infected in the 2006 epidemic. With this modified dataset the transmission kernel is re-estimated for excision radii varying from 20 to 160 km.