Table 3 Parameters and dependent variables and their interpretation
From: An immuno-epidemiological model for Johne’s disease in cattle
Variable or parameter | Meaning |
|---|---|
S C (t) | Number of healthy calves at time t |
S A (t) | Number of healthy adults at time t |
i (τ, t) | Density of infected cattle with age-post-infection τ at time t |
B (t) | Number of bacteria in the environment at time t |
b S | Birth rate for susceptible cattle |
q (τ) | Proportion of births of infected calves from infected cows |
β C | Susceptibility of calves to infection due to milk |
μ C | Natural death rate of healthy calves |
μ A | Natural death rate of healthy adults |
μ | Natural death rate of infected cattle |
a | Rate of progression of calves to adulthood |
β A | Susceptibility of adults to infection |
γ C | Proportion of newborn calves getting infected from the environment |
γ A | Rate of infection of healthy adults from the environment |
b I (τ) | Birth rate of infected adults τ units post infection |
κ (τ) | Infectivity of infectious cattle τ units post infection |