Table 1 Parameter values and their meanings

Λ

Rate of recruitment (Λ × N)

0.0100

Yes

\(\mu _{1}\)

Natural death rate

0.0222

[28]

\(\mu _{2}\)

Mortality rate linked to TB

0.040

[2]

γ

Recovered rate after treatment (I to \(R_{1}\))

0.840

[2]

σ

Spontaneously recovered rate (I to \(R_{2}\))

0.250

[29]

α

Contact rate

0.0010

Yes

λ

Rate of transmission

0.100

[30]

1 − p

Fraction of fast-developing active TB

0.05

[31, 32]

β

Rate of transfer to a hospital

0.010

Yes

v

Rate of lost to follow-up

0.030

[2]

q

Progression rate (\(L_{e}\) to I)

0.129

[33]

h

Rate of progression of TB (\(L_{e}\) to \(L_{f}\))

0.821

[33]

r

Reinfection rate (\(R_{i}\) to \(L_{e}\)) with i=1,2

0.030

[31]

\(r_{1}\)

Rate of re-infection (I to \(L_{e}\))

0.63

[33]

\(r_{2}\)

Rate of re-infection (T to \(L_{e}\))

0.63

[33]

\(r_{3}\)

Rate of re-infection (K to \(L_{e}\))

0.63

[33]

\(g_{1}\)

Rate of recovered (\(L_{e}\) to \(R_{1}\))

0.840

[2]

\(g_{2}\)

Rate of spontaneously recovered (\(L_{e}\) to \(R_{2}\))

0.250

[29]

\(k_{1}\)

Rate of recovered (\(L_{f}\) to \(R_{1}\))

0.840

[2]

\(k_{2}\)

Rate of spontaneously recovered (\(L_{f}\) to \(R_{2}\))

0.250

[29]

w

Rate of progression (\(L_{f}\) to I)

0.075

[33]