The basic reproduction number for scrapie

The basic reproduction number R-0 provides a quantitative assessment of the ability of an infectious agent to invade a susceptible host population. A mathematical expression for R-0 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 R-0 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 R-0 most effectively when the allele is recessive, whereas inbreeding may increase R-0 when the allele is recessive, increasing the chance of an outbreak. Using this formulation, R-0 is calculated for an outbreak of scrapie in a flock of Cheviot sheep.