Figure 1.
Schematic diagram of the model for the transmission dynamics of BTV within a farm.
The populations of infected hosts and vectors are subdivided into a number of stages to allow for more general distributions for the duration of viraemia and the extrinsic incubation period, respectively. A solid line indicates a flow from one compartment to another; a dotted line indicates that a compartment has an influence on a rate of transfer. Lines shown in red indicate a temperature-dependent rate.
Table 1.
Transitions, probabilities, and population sizes in the model for the transmission of BTV within farms†.
Table 2.
Parameters in the model for the within-farm transmission of BTV.
Table 3.
Summary of demographic factors included in models for the probability of transmission of BTV between farms.
Figure 2.
Models for the probability of transmission between farms.
(A) Comparison of model fit for different transmission kernels and demographic models (defined in Table 3) based on the Akaike information criterion (AIC). The cyan line indicates a difference of two in AIC between a model and that with the lowest AIC (i.e. Gaussian kernel and demographic model presented in Table 4), taken to represent a significant difference in model fit. (B) Transmission kernels, (8), using the maximum-likelihood estimates obtained by fitting the models to outbreak data from northern Europe in 2006 (Table 4). The FMD kernel is that estimated by Chis Ster and Ferguson [24] from the outbreak of foot-and-mouth disease (FMD) in the UK during 2001.
Table 4.
Maximum-likelihood estimates for the probability of transmission between farms when fitted to data on the spread of BTV in northern Europe during 2006.
Figure 3.
Temporal dynamics of BTV-8 in GB during 2007.
(A) Observed and expected number of farms reporting clinical disease each week. The figure shows the observed number of newly-identified holdings with confirmed clinical cases (bars) and the median (symbols) and 10th and 90th percentiles (error bars) for the simulated outbreaks. (B) Expected cumulative number of affected holdings over time. The figure shows the median (solid red line), 25th and 75th percentiles (red dashed lines), and 10th and 90th percentiles (dashed blue lines). Each figure shows the results for the simulated epidemics assuming a Gaussian transmission kernel and demographic model presented in Table 4 (i.e. the best-fit model to the northern European data), based on the results of 50 simulated outbreaks which took off (see Methods).
Figure 4.
Spatial dynamics of BTV-8 in GB during 2007.
Predicted spatial distribution of affected farms as of 31 December 2007 assuming: (A,B) a Gaussian kernel; (C,D) an exponential kernel; (E,F) a fat-tailed kernel; or (G,H) the FMD kernel. Transmission between farms is either (A,C,E,G) unrestricted or (B,D,F,H) restricted to the 2007 PZ. Each map shows the cumulative risk (see colour bars) expressed as the proportion of simulated outbreaks (out of 50 which took off; see Methods) for which at least one farm was affected by BTV within each 5 km grid square.
Figure 5.
Sensitivity of temporal dynamics of BTV-8 to different transmission kernels.
Comparison of (A) the median number of newly-identified holdings with confirmed clinical cases and (B) the cumulative number of affected holdings over time for different transmission kernels, where transmission between farms is either unrestricted or restricted to the 2007 protection zone. The figures are based on the results of 50 simulated outbreaks which took off (see Methods).