Table A.1.
Parameters in the model for the transmission of bluetongue virus within a farm in Great Britain
| Description | Symbol | Estimatea or function | Comments and references | |
|---|---|---|---|---|
| Probability of transmission from vector to host | b | 0.82 (0.69, 0.95) | – | |
| Probability of transmission from host to vector | β | 0.02 (0.006, 0.05) | – | |
| Vectors to host ratio for species i | m i | γ(s V, μV/s V) | Sample drawn from gamma distribution for each farm | |
| Mean vector to host ratio | μV | 2,058 (763, 3683) | – | |
| Shape parameter for vector to host ratio | s V | 1.65 (0.47, 3.04) | – | |
| Number of animals of species i on farm | H i | – | Obtained from agricultural survey data | |
| Proportion of bites on species i | ϕi | – | For cattle ϕC = H C/(H C + σH S), while for sheep ϕS = σH S/(H C + σH S) | |
| Vector preference for sheep relative to cattle | σ | 0.15 (0.004, 0.65) | – | |
| Reciprocal of the time interval between blood meals | α | a(T) = 0.0002T(T − 3.7) (41.9 − T)1/2 . 7 | Depends on temperature (Mullens et al., 2004) | |
| Duration of viraemia (cattle) | Mean | 1/r C | 20.6 | Parameters estimated by fitting a gamma distribution to data on naturally infected cattle (Melville et al., 1996) |
| No. stages | n C | 5 | ||
| Disease‐associated mortality rate (cattle) | d C | 0.0015 (0.0001, 0.0037) | – | |
| Duration of viraemia (sheep) | Mean | 1/r S | 16.4 | Parameters estimated by fitting a gamma distribution to data on experimentally infected sheep (Goldsmit et al., 1975; Veronesi et al., 2005) |
| No. stages | n S | 14 | ||
| Disease‐associated mortality rate (sheep) | d S | 0.0078 (0.0006, 0.0020) | – | |
| Extrinsic incubation period (EIP) | Mean | 1/ν | ν(T) = α(T − T min) | Reciprocal of mean EIP depends on temperature (cf. Carpenter et al., 2011) |
| No. stages | k | 10 (2, 25) | ||
| Virus replication rate | α | 0.020 (0.016, 0.024) | ||
| Threshold temperature for virus replication | T min | 13.24 (12.75, 13.72) | ||
| Vector mortality rate | μ | μ(T) = 0.009 exp(0.16T) | Depends on temperature (Gerry and Mullens, 2000) | |
| Vector recruitment rate | ρ | – | For simplicity, assumed to be equal to equal to vector mortality rate | |
| Vector population size | N | – | For simplicity, assumed to be constant; given by N = m i H i | |
| Vector activity | sin, 12 month | b 11 | −1.59 (−1.80, −1.37) | – |
| cos, 12 month | b 21 | −3.81 (−4.40, −3.20) | ||
| sin, 6 month | b 12 | −1.46 (−1.59, −1.33) | ||
| cos, 6 month | b 22 | −0.99 (−1.41, −0.57) | ||
a
For those parameters estimated as part of the approximate Bayesian computation scheme, the mean and 95% credible interval (in brackets) for the marginal posterior distributions are reported.