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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