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

From: Which phenotypic traits of resistance should be improved in cattle to control paratuberculosis dynamics in a dairy herd: a modelling approach

Parameters Definition Reference value Univariate simulations: [min–max] Multivariate simulations: tested values Source
#1 #2 #3 #4
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]