A mathematical model of the dynamics of scrapie in a sheep flock

A mathematical model is developed for the dynamics of an outbreak of scrapie in a single sheep flock with the aim of assisting the interpretation of field data. The model incorporates age structure of the sheep population, both horizontal and vertical transmission, genetic predisposition to infection, variable initial load of the infectious agent, and increasing infection load during an incubation period of the same order as sheep life expectancy. This leads to system of partial differential equations with respect to time, age and infection load. Numerical analyses using this model demonstrate that a scrapie outbreak is likely to be of long duration (several decades), will lead to reduction of scrapie susceptible allele frequency (but not to zero), and has different dynamics in homozygous and heterozygous susceptible sheep, even if these genotypes are equally susceptible, due to the different contributions of vertical infection to transmission to genotypes.