Investigation of a Simple Model for Within-Flock Transmission of Scrapie

Abstract

Genetic control programs for scrapie in sheep build on solid knowledge of how susceptibility to scrapie is modulated by the prion protein genotype at the level of an individual sheep. In order to satisfactorily analyze the effectivity of control programs at the population level, insight is needed at the flock level, i.e., how the grouping of sheep in flocks affects the population-level transmission risk. In particular, one would like to understand how this risk is affected by between-flock differences in genotype frequency distribution. A first step is to model the scrapie transmission risk within a flock as a function of the flock genotype profile. Here we do so by estimating parameters for a model of within-flock transmission using genotyping data on Dutch flocks affected by scrapie. We show that the data are consistent with a relatively simple transmission model assuming horizontal transmission and homogeneous mixing between animals. The model expresses the basic reproduction number for within-flock scrapie as a weighted average of genotype-specific susceptibilities, multiplied by a single overall transmission parameter. The value of the overall transmission parameter may vary between flocks to account for random between-flock variation in non-genetic determinants such as management practice. Here we provide an estimate of its mean value and variation for Dutch flocks.

Modelling of strategies for genetic control of scrapie in sheep: The importance of population structure

“…As the rate of propagation to the brainstem is also genotype dependent, test sensitivity may therefore also be expected to depend on genotype. Detected scrapie prevalence in Dutch culled flocks gives an indication of the minimum value of the sensitivity [ 13 ].…”

“…This is based on a model developed in Ref. [ 13 ], which is parameterized using genotyping and case data from Dutch flocks culled under EU statutory control measures [ 13 ]. An initial frequency distribution of within-flock values is based on both a farm genotyping survey [ 10 ] and a genotyping sample from the active surveillance [ 11 ].…”

“…We use an SI-type within-flock transmission model with homogeneous mixing between sheep of different genotype, in which we assume that genotypes differ both in susceptibility and in infectiousness; this model was developed in Ref. [ 13 ]. We denote by f γ the proportion of animals in the flock that has genotype γ , by g γ the relative susceptibility of genotype γ , and by h γ the relative infectiousness of genotype γ .…”

“…[ 11 ] (the values of g γ used are given in Table 1 of Ref. [ 13 ]) and on setting the parameters h γ equal to one for all genotypes except for those with at least one ARR allele, for which h γ is set to zero. This approximation is based on the assumption motivated in [ 13 ] that the contribution of ARR/VRQ and ARR/ARQ animals to is negligible.…”

“…We will use a within-flock transmission model developed in Ref. [ 13 ] to translate the distribution of within-flock genotype frequencies into a distribution of within-flock R 0 values which in turn serves as a basis for the modelling of between-flock transmission. The second important between-flock heterogeneity is of contact rates (mixing) between sheep flocks.…”