Open Access

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].