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

From: Predicting fadeout versus persistence of paratuberculosis in a dairy cattle herd for management and control purposes: a modelling study

Notation Value Definition Source
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)  
  1. *The values of the parameters in the epidemiological model (Table 2) are estimates based on experimental data reported in the literature.
  2. a Expert opinions
  3. b Parameters' values are assumed