probability of transmission from vector to host |
|
b |
beta (7.38,2.12) |
based on an analysis of data on the transmission of BTV to sheep presented in [26] (cf. [27]); full details are presented in the electronic supplementary material |
probability of transmission from host to vector |
|
β |
beta (1.05,39.6) |
based on experimental infection of field-caught Culicoides imicola with a number of different strains of AHSV [28]; full details are presented in the electronic supplementary material |
reciprocal of the time interval between blood meals |
|
a |
— |
depends on temperature, T, such that: a = 0.0002T (T − 3.7)(41.9 − T)1/2.7 [29] |
duration of viraemia |
mean |
1/rH
|
uniform (4,8) |
assumed to follow a gamma distribution with mean (1/rH) and variance (1/nHrH2 ); estimates for the mean were obtained from [30] |
scale parameter |
nH
|
uniform (7,15) |
disease-associated mortality rate |
|
dH
|
uniform (0.28,0.52) |
based on a case fatality of 75–90% [30]; full details are presented in the electronic supplementary material |
maximum vector-to-host ratio |
only horses |
m |
uniform (0,10 000) |
based on a maximum host biting rate (ma) of 2500 bites per host per day [31], and light trap catches of up to 10 000 individuals per night [32]; the vector-to-host ratio varies seasonally as mδ(t), where δ(t) is the seasonal vector activity (see below). In general, the ratio is rescaled by a factor f depending on the density of other non-susceptible hosts. Other regimens (table 2) are also considered |
horses and non-susceptible hosts |
m |
uniform (0,10 000)f
|
extrinsic incubation period (EIP) |
mean |
1/ν
|
— |
follows a gamma distribution with mean (1/ν) and variance (1/nν
ν
2 ); the mean EIP depends on temperature, T, so that: [25] |
scale parameter |
nν
|
17 |
vector mortality rate |
|
μ |
— |
depends on temperature: μ = 0.009exp(0.16T) [33] |
seasonal vector activity |
|
δ |
— |
given by ; note that this function was normalized, so that the maximum value is equal to 1; parameters are: b0 =−1.71, a1 =−1.56, a2 =−1.49, b1 =−3.74, b2 =−1.00 [34] |