Table 2. Summary table of mathematical symbols used.

Symbol	Description	Notes
λj(t)	Infectious pressure on susceptible farm j at time t
βij	Contribution to total infectious pressure from infectious farms.
${\beta }_{ij}^{*}$	Contribution to total infectious pressure from notified farms.	${\beta }_{ij}^{*}={\gamma }_2{\beta }_{ij}$
$\mathcal{S}\left(t\right),\mathcal{I}\left(t\right)$, $\mathcal{N}\left(t\right)$, $\mathcal{R}\left(t\right)$	Set of susceptible, infected, notified, and removed farms (respectively) at time t.
${\mathbb{S}}_t$	Complete state of the outbreak at time t.	${\mathbb{S}}_t=⟨\mathcal{S}\left(t\right),\mathcal{I}\left(t\right),\mathcal{N}\left(t\right),\mathcal{R}\left(t\right)⟩$
h(t)	Function for modeling disease latency.	$h\left(t\right)=\{\begin{array}{l}1t<4\\ 0otherwise.\end{array}$
Ik, Nk, Rk	Infection, notification and removal times of farm k (respectively).	Notification time is time of laboratory confirmation of FMD; removal time is mean date when the farm is both culled and disposed of.
ϵ(t)	Baseline infectious pressure at time t.	$ϵ\left(t\right)=\{\begin{array}{l}{ϵ}_{1}t<movementban\\ {ϵ}_1{ϵ}_{2}otherwise\end{array}$
q(i;ξ)	Contribution to infectious pressure from characteristics of the infectious farm.	ξ = {ξ2,ξ3}
w(j;ζ)	Contribution to infectious pressure from characteristics of the susceptible farm.	ζ = {ζ2,ζ3}
ξ = {ξ2,ξ3}	Parameters for determining the transmissibility of pigs (2) and sheep (3) relative to cattle.
ζ = {ζ2,ζ3}	Parameters for determining the susceptibility of pigs (2) and sheep (3) relative to cattle.
ψ1,ψ2,ψ3	Exponential terms for calculating infectious pressure from an infectious farm for cattle(1), pigs(2), and sheep(3) respectively.
ϕ1,ϕ2,ϕ3	Exponential terms for calculating infectious pressure for a susceptible farm for cattle (1), pigs (2), and sheep (3) respectively.
γ1,γ2	Multiplicative factor for contribution to infectious pressure from infected (1) and notified (2) farms respectively.
δ	Decay of the transmission rate with distance between premises.
ρij	Euclidean distance between premises i and j.
ω	Exponential parameter associated with the distance kernel.	Fixed at 1.3 in all outbreaks.
θt	Vector of all transmission parameters.	θ = {ϵ1,ϵ2,γ1,γ2,ξ,ζ,ψ,ϕ,δ,b}
ck, pk, sk	Number of cattle, pigs and sheep (respectively) on premises k.
$\overline{c},\overline{p},\overline{s}$	Mean numbers of cattle, pigs, and sheep (respectively) across all farms in the outbreak.
di	Infection to notification time.	di ~ Gamma (4, b)
b	Scale parameter of a gamma distribution governing infection to notification time.	Set at 0.5.
$X_{t^{-}}$	Demographic and event history data observed to time t.
Yt	Demographic and event data of the ongoing epidemic from time t onwards.
${\pi }_t\left({\theta }_t,I_t\right|X_{t^{-}})$	Joint posterior distribution of model parameters and infection times at time t, conditional on the demographic and event history data.
$I_j^{-}$	The time immediately before the infection time of the jth premises.
P	Set of all individuals in the population.
κ	The initial infective.
a	Control intervention a.
U(Yt|a)	Expected total number of animals culled (utility function) in the ongoing outbreak from time t onwards under intervention a.
$a_t^{\star }$	Optimal control strategy at time t.