Table 1 Parameters coding for the phenotypic traits of resistance: definition and values

u

Susceptibility period duration

52 weeks

[1–52]

–

[51,52,53]

h

Decay in susceptibility with age (coefficient)

0.1

[0.1–1]

0.2

0.3

0.4

0.5

[54]

α

Required infectious dose to be infected

10⁶ bacteria

[10⁶–10¹²]

1.5 × 10⁶

2 × 10⁶

2.5 × 10⁶

3 × 10⁶

[55]

ν _L

Duration of latent state

52 weeks

[52–208]

–

[10, 11]

ν _L  + ν _Is

Duration before high shedding and clinically affected state

156 weeks

[156–468]

234

312

390

468

[10,11,12]

v _T with ν _T  + ν _L = constant

Duration of transiently infectious state with constant duration before moderate shedding state

νT = 25 weeks

(νT + νL = 77)

[1–25]

–

[8,9,10,11]

ν _Is with ν _L  +  ν _Is  = constant

Duration of moderate shedding state with constant duration before high shedding or clinically affected state

νIs = 104 weeks

(νL + νIs = 156 weeks )

[60–104]

95

86

77

68

[8,9,10,11,12]

φMilk _X

Factor of decrease of Map shed in milk by animals in health state X

 φMilk _Is

 Moderate shedding state (Is)

100%

[0–100]

50%

10%

5%

0%

[56]

 φMilk _Ic

 High shedding and clinically affected state (Ic)

100%

[0–100]

[57]

φFeces _X

Factor of decrease of Map shed in faeces by animals in health state X

 φFeces _T

 Transient state (T)

100%

[0–100]

50%

10%

5%

0%

[9]

 φFeces _Is

 Moderate shedding state (Is)

100%

[0–100]

[58]

 φFeces _Ic

 High shedding or clinically affected state (Ic)

100%

[0–100]

66%

50%

40%

33%

[59, 60]

φP _X

Factor of decrease of probability of in utero transmission for cows in health state X

[2, 61]

 φP _LIs

 Latent and moderate shedding states (LIs)

100%

[0–100]

50%

10%

5%

0%

 φP _Ic

 High shedding or clinically affected state (Ic)

100%

[0–100]