Table 2 Parameters for infection and transmission used in a Mycobacterium avium subsp. paratuberculosis (Map) infection dynamics model within a structured dairy herd*

p _X

Probability of in utero transmission for cow in health state X

[24, 35]

p _L = 0.149

X = latently infected (L)

p _Is = 0.149

X = subclinically infected (I _S )

p _Ic = 0.65

X = clinically affected (I _C )

u

52

Maximal age in the susceptible compartment (weeks)

[15, 36]

h

0.1

Susceptibility follows an exponential decrease exp(-h(age-1)))

[14]

v _X

Mean time spent in health state X (weeks)

v _T = 25

X = transiently infectious (T)

[9]

v _L = 52

X = latently infected (L)

[2, 16]

v _Is = 104

X = subclinically infected (I _S )

[37]

v _Ic = 26

X = clinically affected (I _C )

a

sh _X

Probability of shedding in colostrum or milk for a cow in health state X

[38, 39]

sh _L = 0

X = latently infected (L)

sh _Is = 0.4

X = subclinically infected (I _S )

sh _Ic = 0.9

X = clinically affected (I _C )

α

10⁶

Map infectious dose

[40]

β _l

5 × 10^-4 × 7

Transmission rate if ingestion of an infectious dose (per week)

b

β _c

5 × 10^-5 × 7

Transmission rate if one infectious dose is present in the local environment (per week)

[9]

β _g

9.5 × 10^-7 × 7

Transmission rate if one infectious dose is present in the global environment (per week)

[9]

β _o

5 × 10^-6 × 7

Transmission rate if one infectious dose is present on pasture (per week)

b

g _X

Decrease in milk production for cattle in health state X (per week)

[41]

g _Is = 2.5 × 7

X = subclinically infected (I _S )

g _Ic = 4 × 7

X = clinically affected (I _C )

μ _k

Removal rate of Map from environment k

[7, 8]

μ _g = 0.4

   all the environments (per week)

μ _ip = 0.67

   individual pens (when empty)

μ _cp = 0.17

   collective pens (when empty)