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Table 1 Parameters and dependent variables and their interpretation

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

Variable or parameter Meaning
M u (τ) Number of uninfected macrophages at time τ
M i (τ) Number of infected macrophages at time τ
C (τ) Number of immune cells at time τ
r Total recruitment rate for uninfected cells
α Infection rate of uninfected macrophages by infected macrophages
d 1 Natural death rate for uninfected macrophages
δ Death rate of infected macrophages
d 2 Clearance rate for immune cells
k Stimulation rate of immune response from infected cells
ε 1 Reciprocal of half saturation constant for killing of infected macrophages
ε 2 Reciprocal of half saturation constant for immune response stimulation rate
ε 3 Reciprocal of half saturation constant for killing of infected macrophages
c Reciprocal of half saturation constant for macrophages infection rate
p Killing rate of infected macrophages by immune response.