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Table 4 Parameters and dependent variables and their interpretation

From: An immuno-epidemiological model for Johne’s disease in cattle

Parameter Meaning Value Range
b S Birth rate for susceptible cattle 100 0.1–1000
b S Per capita birth rate for susceptible cattle 100 0.01–100
b Constant in b I (τ) 0.1 0.0001–1
q Proportion of infected calves born to infected cows 0.25 0–0.25
Q Half saturation constant 100 0–100000
β C Susceptibility of calves to infection due to milk 0.0183333 0.001–1
μ C Natural death rate of healthy calves 1/(10 × 12) 1/(25 × 12)–1/(5 × 12)
μ A Natural death rate of healthy adults 1/(5 × 12) 1/(25 × 12)–1/(2 × 12)
μ Natural death rate of infected cattle 1/(3 × 12) 1/(5 × 12)–1/(2 × 12)
a Rate of progression of calves to adulthood 1/12 1/(2 × 12)–1/(0.5 × 12)
β A Susceptibility of adults to infection 0.00733333 0.001–1
γ C Proportion of newborns infected from environment 0.0001 0–1
γ A Rate of infection of healthy adults from environment 0.0000183333 0.0–3
κ T Half-saturation constant for κ (τ) 1000 10–10000
m Proportionality constant for ν (τ) 0.3 0.0001–1
v Proportionality constant for ν (τ) 0.01 0.0001–1
η E Shedding rate of infected individuals 0.01 0.001–0.1
d Clearance rate of MAP from the environment 1/5 1/15–1/3
K 1 Constant in f E 1 1–10000
K 2 Constant in f E 1 1–10000