Table A.2.

Transitions, probabilities and population sizes in the model for the transmission of bluetongue virus within a farm

Description	Transition	Probability	Population size
Hosts
Infection	$\left\{\begin{array}{c}{X}^{(i)}\to X^{(i)}-1\\ Y_1^{(i)}\to Y_1^{(i)}+1\end{array}\right.$	λiδt	X (i)
Completion of infection stage j (j = 1,…, n i−1)	$\left\{\begin{array}{c}{Y}_j^{(i)}\to Y_j^{(i)}-1\\ Y_{j+1}^{(i)}\to Y_{j+1}^{(i)}+1\end{array}\right.$	n i r iδt	$Y_j^{(i)}$
Mortality during infection stage j (j = 1,…, n i)	$Y_j^{(i)}\to Y_j^{(i)}-1$	d iδt	$Y_j^{(i)}$
Recovery	$\left\{\begin{array}{c}{Y}_{n_i}^{(i)}\to Y_{n_i}^{(i)}-1\\ Z^{(i)}\to Z^{(i)}+1\end{array}\right.$	n i r iδt	$Y_{n_i}^{(i)}$
Vectors
Infection	$\left\{\begin{array}{c}S\to S-1\\ L_1\to L_1+1\end{array}\right.$	λVδt	S
Completion of extrinsic incubation period (EIP), stage j (j = 1,…,k−1)	$\left\{\begin{array}{c}{L}_j\to L_j-1\\ L_{j+1}\to L_{j+1}+1\end{array}\right.$	kvδt	L j
Vector mortality during EIP (j = 1,…, k) (and compensatory recruitment)	$\left\{\begin{array}{c}{L}_j\to L_j-1\\ S\to S+1\end{array}\right.$	μδt	L j
Completion of EIP	$\left\{\begin{array}{c}{L}_k\to L_k-1\\ I\to I+1\end{array}\right.$	kvδt	L k
Mortality of infectious vectors (and compensatory recruitment)	$\left\{\begin{array}{c}I\to I-1\\ S\to S+1\end{array}\right.$	μδt	I