A MATHEMATICAL-MODEL OF THE DYNAMICS OF SCRAPIE IN A SHEEP FLOCK

A mathematical model is developed for the dynamics of an outbreak of s crapie in a single sheep flock with the aim of assisting the interpret ation of held data. The model incorporates age structure of the sheep population, both horizontal and vertical transmission, genetic predisp osition to infection, variable initial load of the infectious agent, a nd increasing infection load during an incubation period of the same o rder as sheep life expectancy. This leads to system of partial differe ntial equations with respect to time, age and infection load. Numerica l analyses using this model demonstrate that a scrapie outbreak is lik ely to be of long duration (several decades), will lead to a reduction of scrapie susceptible allele frequency (but not to zero), and has di fferent dynamics in homozygous and heterozygous susceptible sheep, eve n if these genotypes are equally susceptible, due to the different con tributions of vertical infection to transmission to genotypes. (C) 199 8 Elsevier Science Inc. All rights reserved.