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

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.