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 |