Table I.

Summary of models used to describe the transmission of scrapie within a sheep flock.

Author(s)	Aims	Modelling approach	Conclusions
Hagenaars et al. [37]a	Obtain general insights into the population-dynamical properties of possible scenarios of scrapie transmission in a sheep flock	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
Hagenaars et al. [38]a	Understand how persistence of scrapie in a flock depends on transmission and flock size	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
Hagenaars et al. [39]a	Estimate transmission parameters from a scrapie outbreak	Fitting stochastic transmission models to the outbreak data	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
Matthews et al. [57]b	Examine the role of a range of epidemiologically important parameters and the effects of genetic variation in susceptibility	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)
Matthews et al. [58]b	Analysis of a scrapie outbreak in a flock of Cheviot sheep	Fitting a deterministic model to outbreak data	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
Sabatier et al. [66]	Explore the impact of genetic resistance and flock management practices on scrapie outbreaks	Discrete-time deterministic mathematical model of the within-herd transmission dynamics of 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
Stringer et al. [71]b	Develop within-flock scrapie transmission model for assisting the interpretation of field data Use model to explore properties of scrapie transmission dynamics	Deterministic model defined using partial differential equations with respect to time, age and infection load	Scrapie outbreak is likely to be of long duration Will lead to a reduction of scrapie susceptible allele frequency (but not to zero)
Touzeau et al. [74]b	Explore hypothesis of increased scrapie transmission during lambing season	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
Woolhouse et al. [79]b	Explore the course of an outbreak in a sheep flock, and the potential impact of different control measures	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
Woolhouse et al. [80]b	Analysis of an outbreak of natural scrapie in a flock of Cheviot sheep	Partial-differential equation model of scrapie within-flock transmission dynamics	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

References with a common superscript use the same basic modelling approach: ^a Hagenaars et al. [37]; or ^b Stringer et al. [71].