Scrapie is a transmissible spongiform encephalopathy in sheep and an example of a disease that may be controlled through breeding for disease resistance. Member states of the European Union have introduced strategies for breeding against scrapie based on the selection of genetically resistant breeding rams. An ambitious strategy adopted in The Netherlands consisted of selecting resistant rams for breeding throughout both breeding and production sectors. Mathematical modelling of the effect of a breeding program on the spreading capacity of scrapie in a national flock is needed for making assessments on how long a breeding strategy needs to be maintained to achieve disease control. Here we describe such a model applied to the Dutch situation, with the use of data on the genetic content of the Dutch sheep population as well as on scrapie occurrence in this population. We show that the time needed for obtaining scrapie control depends crucially on two parameters measuring sheep population structure: the between-flock heterogeneity in genotype frequencies, and the heterogeneity of mixing (contact rates) between sheep flocks. Estimating the first parameter from Dutch genetic survey data and assuming scenario values for the second one, enables model prediction of the time needed to achieve scrapie control in The Netherlands.