A modeling framework to describe the transmission of bluetongue virus within and between farms in Great Britain

Abstract

Background: Recently much attention has been given to developing national-scale micro-simulation models for livestock diseases that can be used to predict spread and assess the impact of control measures. The focus of these models has been on directly transmitted infections with little attention given to vector-borne diseases such as bluetongue, a viral disease of ruminants transmitted by Culicoides biting midges. Yet BT has emerged over the past decade as one of the most important diseases of livestock.

Methodology/principal findings: We developed a stochastic, spatially-explicit, farm-level model to describe the spread of bluetongue virus (BTV) within and between farms. Transmission between farms was modeled by a generic kernel, which includes both animal and vector movements. Once a farm acquired infection, the within-farm dynamics were simulated based on the number of cattle and sheep kept on the farm and on local temperatures. Parameter estimates were derived from the published literature and using data from the outbreak of bluetongue in northern Europe in 2006. The model was validated using data on the spread of BTV in Great Britain during 2007. The sensitivity of model predictions to the shape of the transmission kernel was assessed.

Conclusions/significance: The model is able to replicate the dynamics of BTV in Great Britain. Although uncertainty remains over the precise shape of the transmission kernel and certain aspects of the vector, the modeling approach we develop constitutes an ideal framework in which to incorporate these aspects as more and better data become available. Moreover, the model provides a tool with which to examine scenarios for the spread and control of BTV in Great Britain.

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.

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 from the outbreak of foot-and-mouth disease (FMD) in the UK during 2001.

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).