The basic reproduction number for scrapie

Abstract

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.