The basic reproduction number RR0; population genetics; control; epidemiology; inbreeding;transmissible spongiform encephalopathy provides a quantitative assessment of the ability of an infectious agent to invade a susceptible host population. A mathematical expression for R0 is derived based on a recently developed model for the spread of scrapie through a flock of sheep. The model incorporates sheep demography, a long and variable incubation period, genetic variation in susceptibility to scrapie, and horizontal and vertical routes of transmission. The sensitivity of R0 to a range of epidemiologically important parameters is assessed and the effects of genetic variation in susceptibility are examined. A reduction in the frequency of the susceptibility allele reduces R0 most effectively when the allele is recessive, whereas inbreeding may increase R0 when the allele is recessive, increasing the chance of an outbreak. Using this formulation, R0 is calculated for an outbreak of scrapie in a flock of Cheviot sheep.