The influence of between-farm distance and farm size on the spread of classical swine fever during the 1997-1998 epidemic in The Netherlands

Abstract

As the size of livestock farms in The Netherlands is on the increase for economic reasons, an important question is how disease introduction risks and risks of onward transmission scale with farm size (i.e. with the number of animals on the farm). Here we use the epidemic data of the 1997-1998 epidemic of Classical Swine Fever (CSF) Virus in The Netherlands to address this question for CSF risks. This dataset is one of the most powerful ones statistically as in this epidemic a total of 428 pig farms where infected, with the majority of farm sizes ranging between 27 and 1750 pigs, including piglets. We have extended the earlier models for the transmission risk as a function of between-farm distance, by adding two factors. These factors describe the effect of farm size on the susceptibility of a 'receiving' farm and on the infectivity of a 'sending' farm (or 'source' farm), respectively. Using the best-fitting model, we show that the size of a farm has a significant influence on both farm-level susceptibility and infectivity for CSF. Although larger farms are both more susceptible to CSF and, when infected, more infectious to other farms than smaller farms, the increase is less than linear. The higher the farm size, the smaller the effect of increments of farm size on the susceptibility and infectivity of a farm. Because of changes in the Dutch pig farming characteristics, a straightforward extrapolation of the observed farm size dependencies from 1997/1998 to present times would not be justified. However, based on our results one may expect that also for the current pig farming characteristics in The Netherlands, farm susceptibility and infectivity depend non-linearly on farm size, with some saturation effect for relatively large farm sizes.

Figure 1. Map with the Outbreak Area (OA, black circle) in The Netherlands.

This includes the infected farms (red dots) and the high-risk areas (blue). The high-risk areas for transmission of CSF (blue) were calculated using the basic kernel (without farm-size dependence), using the method of Boender et al. , .

Figure 2. Estimated transmission kernels λ^c and their confidence bounds.

The basic kernel parameterization is given by c = 0 in Equation (1) and (2) without farm-size dependence (dashed blue line) and the best-fit kernel c = 5 (solid red line), where N_S is set equal to the average size of the farms in the OA (1038.3) and N_I to the average size of the infected farms in the OA (1515.7), with their confidence bounds (thinner lines).

Figure 3. The relative susceptibility or infectivity of a farm as a function of its size, according to the best-fit parameterization c = 5 (maximum susceptibility or infectivity equals 1).

Full line: point estimate (d = 1.76), short-dashed line: lower bound (d = 1.21), long-dashed line: upper bound (d = 2.66).

Figure 4. Comparison of the best-fit model prediction to the observed epidemic in 1997/1998.

Number of newly infected farms per 28-day period: as derived directly from the 1997/1998 CSF epidemic data (bars) and as predicted by the fitted c = 5 model for the between-farm transmission risk (line with symbols). Here time t = 0 corresponds to 24 December 1996.