Multiscale modelling of scrapie epidemiology: I. Herd level: a discrete model of disease transmission in a sheep flock

A mathematical model of the within-herd transmission dynamics of scrapie is used to explore the phenomenology of the epidemic process in a sheep flock and the potential impact of an outbreak, according to several biological hypotheses and flock management practices. The model incorporates both infectious (horizontal and vertical) transmission and genetic predisposition to infection. It involves three main processes: epidemic dynamics; physiological aging (and reproduction stages), and genetic evolution. Numerical experimentation is performed to explore several biological hypotheses about the genetic resistance mechanisms against scrapie. It also allows us to reproduce the three main observed patterns of outbreaks: sporadic (short outbreaks), endemic (long outbreaks, with clinical cases mainly in young animals), and epidemic (long outbreaks, with clinical cases in all the age classes). The results suggest that the global size of an outbreak is mainly based upon the initial genetic composition of the flock whereas the herd management practices rather influence the outbreak type.