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We formulate and investigate the properties of a model framework to mimic the transmission dynamics of the aetiological agent of scrapie in a sheep flock. We derive expressions for summary parameters that characterize transmission scenarios, notably the basic reproduction number R(0) and the mean generation time T(g). The timescale of epidemic outbreaks is expressed in terms of R(0) and cumulants of the generation time distribution. We discuss the relative contributions to the overall rate of transmission of horizontal and vertical routes during invasion and in endemicity. Simplified models are used to obtain analytical insight into the characteristics of the endemic state.

Original publication




Journal article


Mathematical biosciences

Publication Date





117 - 135


Wellcome Trust Centre for the Epidemiology of Infectious Disease, Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3FY, UK.


Animals, Sheep, Scrapie, Disease Susceptibility, Disease Outbreaks, Disease Reservoirs, Models, Biological, Infectious Disease Transmission, Vertical, Disease Transmission, Infectious, United Kingdom