Table 2 Definitions of model parameters and symbols. We estimated the model parameters R ₀ (0), $S\left(a\right),{\tilde{S}}_{\gamma }\left(a\right)$ and g _γ (a) for each flock individually

R ₀ (0)

The basic reproduction number in the flock just before the start of the breeding programme

S(a)

Survival function for non-infected animals

${\tilde{S}}_{\gamma }\left(a\right)$

Survival function for infected animals of genotype γ

g _γ (a)

Relative susceptibility to infection of an animal of age a and genotype γ. It is determined by the parameters p _γ and α below.

β(τ)

Level of infectiousness of an animal that acquired scrapie infection a time τ ago (τ = incubation stage of time since infection)

f_γ(t,a)

Genotype distribution in the flock as a function of time

R ₀ (t)

The basic reproduction number in the flock as a function of time. It is determined by all parameters listed in the rows above.

p _γ

Probability of becoming infected in a certain year conditional on not having become infected before.

α

Age-dependency parameter

λ

Force of infection

Q _γ (a)

The uninfected proportion of animals of age a and genotype γ