Persistence patterns of scrapie in a sheep flock

The epidemiology and transmission dynamics of sheep scrapie is as yet poorl y understood. Here we present a theoretical analysis of the transmission dy namics within a sheep flock, concentrating on how persistence properties de pend on transmission scenario and flock size. Patterns of disease persisten ce and extinction are studied analytically using branching-process approxim ations and numerically using stochastic model simulations. For a given basi c reproduction number, disease extinction is most likely when late-stage in fected animals are responsible for most of the transmission. This effect ca n be understood in terms of aggregation in the distribution of the number o f secondary infections arising from a single primary infection. The presenc e of an environmental reservoir reduces the probability of extinction.