Table 2. Parameter estimates.
Parameter estimates for the baseline model, famine model, intrinsic immunity model, and adaptive immunity model, respectively, to two significant figures (or the nearest year). Discrepancies are given to the nearest tenth. Best parameter estimates were obtained from optimization. Intervals were estimated from the 2.5%ile and 97.5%ile of the fits to the bootstrap data sets.
| Parameter | Description | Model 0 | Model 1 | Model 2 | Model 3 |
|---|---|---|---|---|---|
| Best estimate (interval) | Best estimate (interval) | Best estimate (interval) | Best estimate (interval) | ||
| p | Proportion of new infections or new reinfections that develop disease within a year, for susceptible, latent, and recovered individuals (post-famine) | 0.30 (0.30, 0.30) | 0.26 (0.19, 0.27) | 0.042 (0.028, 0.054) | 0.18 (0.10, 0.23) |
| β | Effective contact rate, average number of cases caused by one case in a fully susceptible population (per year per infectious case) | 10 (9.5, 18) | 3.4 (2.0, 4.1) | 2.7 (2.2, 4.1) | 2.43 (2.2, 3.2) |
| s | Fraction of individuals with normal (lower) susceptibility to TB infection at the start of the epidemic | – | – | 0.20 (0.18, 0.26) | 0.40 (0.30, 0.50) |
| t 1 | Start time of epidemic for cluster 1 | 1870 (1870, 1875) | 1872 (1870, 1875) | 1873 (1872, 1877) | 1873 (1871, 1878) |
| δp | Factor by which famine conditions increased p | – | 2.3 (2.3, 3.0) | – | – |
| t 2 | Start time of epidemic for cluster 2 | 1870 (1870, 1870) | 1872 (1870, 1872) | 1872 (1870, 1875) | 1872 (1870, 1876) |
| ζ | Fractional protection conferred by latent infection to reinfection (post-famine) | 0.80 (0.80, 0.80) | 0.80 (0.78, 0.80) | 0.74 (0.67, 0.78) | 0.51 (0.00, 0.78) |
| f | Probability of developing infectious TB for individuals who develop active disease | 0.85 (0.50, 0.85) | 0.56 (0.50, 0.85) | –a | –a |
| μ TB | TB mortality rate (post-famine) (per year) | 0.70 (0.59, 0.70) | –a | –a | –a |
| σ | Relative susceptibility to infection among more susceptible individuals compared with normally susceptible individuals | – | – | 46 (32, 71) | – |
| γ | Factor by which risk of progression among more susceptible individuals is increased | – | – | – | 5.43 (4.42, 9.23) |
| Lowest discrepancy | 186.7 (136.5, 241.5) | 65.1 (45.5, 81.4) | 62.4 (44.7, 75.8) | 66.9 (46.4, 85.0) |
Notes.
a
For each model, the seven most important parameters relevant to that model were fit to the data. For models 2 and 3, f and μTB were dropped in order to include s and σ and s and γ, respectively. For model 1, μTB was dropped in order to include δp.