Deterministic model framework comprising most of the aspects that are of relevance (potentially or in reality) to the transmission dynamics of scrapie

Dependence of basic reproduction number (R ₀) and generation time on other parameters gives insight into the effects of these parameters

Simplified model yields insights into interplay of horizontal and vertical transmission, and the characteristics of endemic scrapie

Stochastic model of within-flock transmission

Analytical calculations using branching-process approximations and

Numerical calculation using stochastic model simulations

Disease extinction is most likely when late-stage infected animals are responsible for most of the transmission

Presence of an environmental reservoir reduces the probability of extinction

Mean incubation period for the outbreak is less than 1.5 years

Infectiousness of infected animals becomes appreciable at early stage of incubation

Difficult to quantify R ₀: the data are consistent with a broad range of values

Mathematical expression for R ₀ is derived based on a transmission model

Sensitivity of R ₀ to various parameters and genetic variation is studied

Reduction in the frequency of the susceptible allele reduces R ₀ most effectively when the allele is recessive

Inbreeding may increase R ₀ when the susceptible allele is recessive, increasing the chance of an outbreak

Point estimate of R ₀ for an outbreak in Cheviot sheep is given (R ₀ = 3.9)

Model reproduces observed allele frequencies and total numbers of susceptible animals remaining at the end of the outbreak

Indication that older animals have reduced susceptibility to scrapie

Three main observed patterns of outbreaks: sporadic, endemic and epidemic can be reproduced depending on parameter settings

Model results suggest that overall size of the outbreak is determined primarily by the initial genetic composition of the flock

Outbreak type is determined mainly by the herd management practices

Develop within-flock scrapie transmission model for assisting the interpretation of field data

Use model to explore properties of scrapie transmission dynamics

Scrapie outbreak is likely to be of long duration

Will lead to a reduction of scrapie susceptible allele frequency (but not to zero)

Partial-differential equation model of scrapie within-flock transmission dynamics

Applied to a natural outbreak in Romanov sheep

The observed patterns of seasonality in incidence cannot be accounted for by seasonality in demography alone

Provides support for the hypothesis of increased transmission during lambing

Partial-differential equation model of scrapie within-flock transmission dynamics

Parameter values consistent with available data

In a closed flock, scrapie outbreaks may have a duration of several decades, reduce the frequency of susceptible genotypes, and may become endemic if carrier genotypes are present

In an open flock, endemic scrapie is possible even in the absence of carriers

Control measures currently or likely to become available may reduce the incidence of cases but may be fully effective only over a period of several years

Model is able to reproduce key features of the outbreak, including its long duration and the ages of cases

Many infected sheep do not survive to show clinical signs

Most cases arise through horizontal transmission

Strong selection against susceptible genotypes