Table 1.
Summary of parameters used in the models.
| Parameter | Definition | Assumptions | Sensitivity analysis assumptions |
|---|---|---|---|
| N t a | Population size of a-th age group at time t | Varied by years19 | — |
| δ t | Number of new births at time t | Varied by years20 | — |
| μ t a | Net rate of natural mortality and migration of a-th age group at time t | Varied by years4,20. The ratio of mortality between older to younger groups were assumed at 7:1, 9:1, 12:1, 16:1, and 20:1 for year <1981, 1981–1990, 1991–2000, 2001–2010, and >2010 respectively. | — |
| φ t | BCG vaccination proportion on new births at time t | Varied by years50 | Uniform (99%, 99.9%) |
| ρ | BCG efficacy | 74%, an estimate based on 4 randomized-controlled trials26 | Uniform (62%, 83%)26 |
| λ t a | Force of infection for age group a at time t | — | — |
| β ak | Age-specified transmission rate from age group k-th to a-th | Estimated by MCMC using the TB notification data50 | Follow posterior distributions |
| τ | Transition rate from youngers to elders | — | — |
| α | Proportion developing recent latent infection stage from remote latent and recovered stages | 0.0133 | Uniform (0.011, 0.015)3 |
| υ s | Progression rate from recent latent infection to remote latent | 0.2 per year | — |
| υ i | Progression rate from recent latent infection to infectious or non-infectious stage | 0.03 per year22,51,52 | Uniform (0.02, 0.04)22,51,52 |
| σ a | Progression rate from remote latent infection to infectious or non-infectious stage | 0.0005 per year for younger adults. A multiplier K to this value was assumed for elders and estimated by the MCMC approach2,22,51,52 | Follow the posterior distribution |
| γ | Proportion of infectious TB from either fast or slow latent TB | 0.853 | Uniform (0.75, 0.95)3 |
| q | Proportion of infectious and non-infectious individuals being detected and treated | 0.93,53–55 | Uniform (0.80, 0.99)3,53–55 |
| p | Proportion of treated individuals able to complete TB treatments | 0.25 for years before 1970; 0.6 for years 1970–1978; 0.87 after year 197853–55 | Uniform (0.80, 0.95) |
| κ c | Efficacy for treatment completion | 0.9353–55 | Uniform(0.85, 0.99) |
| κ d | Efficacy for treatment defaulted | 0.8453–55 | Uniform(0.65, 0.90) |
| ξ | Progression rate from treatment to recovered stage | Reciprocal for 6 months | — |
| ϕ | Natural annual recovery rate | 0.23,22,51,52 | Uniform (0.1, 0.3)3,22,51,52 |
| ω | Relapse rate | 0.04550 | Uniform (0.017, 0.17)2,22,50 |
| m | Screened proportion (acceptability) of LTBI in elders | Test for different proportions | — |
| r | Detection rate of LTBI | 77%, an average sensitivity of the tuberculin skin test16. Enhancing sensitivity of 90% (T-spot TB test) was also tested. | — |
| h j | LTBI treatment adherence level for duration j | Duration j can be 52, 24, and 12 weeks; the current adherence levels were respectively assumed to be 65% (complete treatment), 15%, and 5%16,29,30. We varied the treatment completion rate from 0–80% to assess the changes (24- and 12-weeks completion rate was unchanged). | |
| η j | Progression rate from LTBI treatment with duration j to recovered stage | Reciprocal for 52, 24, and 12 weeks of isoniazid therapy16,27,28 | — |
| κ l j | Efficacy for different durations of LTBI treatment | 75%, 65%, and 21% for 52, 24, and 12 weeks of treatments, respectively17,29 | — |