Table 1 Description and values of model parameters

r _s

Rate at which patients complete treatment

0.125 (0.111, 0.1667)

[14]

μ _b

Natural birth rate

0.001

[27]

μ _d

Natural death rate

0.00059

[27]

α

Proportion of patients infected with non-MDR-TB

0.898 (0.878–0.9164)

[16]

q ₁

Cure rate of patients infected with non-MDR-TB

94%

[1]

q ₂

Cure rate of patients infected with MDR-TB

57%

[28]

θ

Rate at which an infected person develops disease due to reduced immunity and subsequent proliferation of M. tuberculosis already in the body

0.00026 (0.00013, 0.00039)

[4, 27]

δ

Rate of spontaneous recovery in patients with primary pulmonary tuberculosis

0.5

[1]

r ₁

Rate of treatment completion in patients infected with non-MDR-TB

0.1667

[17]

τ

Rate at which an infected person in the incubation period converts to primary pulmonary tuberculosis

0.206 (0.1542, 0.2765)

[15]

r ₂

Rate of treatment completion in patients infected with MDR-TB

0.05

[17]

λ

Proportion of susceptible individuals who have been infected with M. tuberculosis, but show no symptoms

0.19

[15]

ν

Proportion of pulmonary tuberculosis patients seeking treatment

0.472

[4]

κ _s

Rate of M. tuberculosis is completely eliminated

0.939 (0.928, 0.947)

[29]

κ _f

Rate of M. tuberculosis is not completely eliminated

0.014 (0.011, 0.019)

[29]

d _f

Rate of death from pulmonary tuberculosis without treatment

0.019 (0.015, 0.024)

[30]

d _h

Rate of spontaneous recovery in patients with secondary pulmonary tuberculosis

0.0069

[14]

d _t

Rate of death of pulmonary tuberculosis patients after treatment

0.013 (0.011–0.016)

[29]

p(t)

Proportion of patients with infectious pulmonary tuberculosis at time t

Table a1

[13]

f()

Probability density distribution function of the average infectious period

Gamma distribution

shape = 6.612; scale = 2.755

Weibull distribution

shape = 2.782; scale = 2.696

log-normal distribution

mean = 0.805; SD = 0.375

[18]