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Table 2 The definition and value range of parameters for the model (1)

From: The prevention and control of tuberculosis: an analysis based on a tuberculosis dynamic model derived from the cases of Americans

Parameter

Definition

μ

Natural mortality of human

Λ

New individuals coming into the system

α in [0.1,0.4]

The rate for incompletely treated going to diagnosed infectious

β1 in [2,6]

The transmission rate of diagnosed infectious

β2 in [0.1,0.4]

The transmission rate of undiagnosed infectious

β3 in [4,6]

The transmission rate of incompletely treated

χ in [0.08,0.3]

The natural vaccination ratio of the newborn babies

d1 in [0.05,0.1]

TB-related mortality of diagnosed infectious

d2 in [0.5,0.8]

TB-related mortality of undiagnosed infectious

d3 in [0.09,0.3]

TB-related mortality of incompletely treated

δ in [0.5,0.8]

Rate for diagnosed infectious coming into the incompletely treated

ε in [0,0.3]

Indicate the reduction in risk of infection due to vaccination

g in [0.4,0.8]

Recovery rate of the diagnosed infectious

γ in [0.125,0.6]

Reactivated rate of recovered individuals

h in [0.2,0.6]

Detection ratio of active TB

k in [0.033,0.333]

Rate of progression to infectious

p1 in [0.02,0.08]

The proportion of susceptible individuals who become diagnosed infectious

p2 in [0,0.5]

The proportion of susceptible individuals who become undiagnosed infectious

ψ in [0.05,0.2]

Loss of vaccination rate

ϕ in [0.05,0.1]

Vaccine coverage rate

q1 in [0,0.4]

The ratio of recovered relapsing into the infectious

q2 in [0.15,0.6]

The ratio of recovered reinfected into the exposure

r in [0.7,0.9]

Chemoprophylaxis of the exposed

ρ in [0.15,0.25]

Rate of progression from undiagnosed infectious to exposed

θ in [0.6,0.9]

Rate of progression from undiagnosed infectious to diagnosed infectious

ω in [0.15,0.25]

Recovery rate of the incompletely treated