Table 1 Parameters of the intra-herd infection dynamics for a dairy cattle herd (adapted from [23]).

m

Transition probability I ⁻ ⇒ S

0.7

q

Transition probability I ⁻ ⇒ I ⁺

0.02

pIp

Proportion of cows going from I ⁻ to I ⁺ and becoming I ^{milk pers}

0.5

r1

Transition probability I ⁻ ⇒ C ⁺

0.2

r2

Transition probability I ^{milk pers} ⇒ C ⁺

0.02

s

Transition probability C ⁺ ⇒ I ⁺

0.15

τ

Transition probability C ⁺ ⇒ C ⁻

0.0096

μ

Proportion of bacteria eliminated due to death and plume generation (can be written as \(\mu_{death} + \mu_{plume source}\))

0.2

p

Infection probability

1−e ^−E

ρ ^m/f

Proportion of bacteria shed through mucus/faeces filling the environment compartment

0.28

ρ ^m

Proportion of bacteria shed through milk filling the environment compartment

0.125ρ ^m/f