In recent years, the control or eradication of scrapie and any other transmissible spongiform encephalopathies (TSEs) possibly circulating in the sheep population has become a priority in Britain and elsewhere in Europe. A better understanding of the epidemiology of scrapie would greatly aid the development and evaluation of control and eradication strategies. Here we bound the range of key epidemiological parameters using a combination of relatively detailed pathogenesis and demography data, more limited data on susceptibility and incubation times, and recent survey data on scrapie incidence in Great Britain. These data are simultaneously analysed using mathematical models describing scrapie transmission between sheep and between flocks. Our analysis suggests that occurrence of scrapie in a flock typically provokes changes in flock management that promote termination of the outbreak, such as the adoption of selective breeding, and that a large fraction of cases (possibly over 80%) goes undetected. We show that the data analysed are consistent with the within-flock reproduction number of scrapie lying in the range 1·5–6, consistent with previous epidemiological studies.