Table 1. Parameters and associated ranges.
| Parameter name | Description | Minimum | Maximum | References |
|---|---|---|---|---|
| β | Effective contact rate, average number of cases caused by one case in a fully susceptible population (per year per infectious case)a | 2 | 20 | (Blower et al., 1995; Aparicio & Castillo-Chavez, 2009) |
| p | Proportion of new infections that develop disease within a year, for susceptible and latent individuals (post-famine)b | 0 | 0.30 | (Blower et al., 1995; Gomes et al., 2004). |
| f | Probability of developing infectious TB for individuals who develop active disease | 0.5 | 0.85 | (Blower et al., 1995; Aparicio & Castillo-Chavez, 2009) |
| ζ | Fractional protection conferred by latent infection to reinfection (post-famine)b | 0.0 | 0.8 | (Ferguson, 1928; Gomes et al., 2004) |
| ν | Rate of progression from latent to active disease (post-famine) (per year)b | 0.00256 | 0.00527 | (Blower et al., 1995; Gomes et al., 2004) |
| μ | Background mortality rate (post-famine) (per year)b | 0.015 | 0.03 | (Blower et al., 1995) |
| μ TB | TB mortality rate (post-famine) (per year)b | 0.2 | 0.7 | (Blower et al., 1995; Gomes et al., 2004; Tiemersma et al., 2011) |
| c | Self-cure rate (per year) | 0.021 | 0.086 | (Blower et al., 1995; Tiemersma et al., 2011) |
| ω | Relapse rate (per year) | 0.01 | 0.03 | (Blower et al., 1995) |
| σ | Factor by which susceptibility to infection among more susceptible individuals is increased | 1 | 1,000 | |
| γ | Factor by which risk of progression among more susceptible individuals is increased | 1 | 1,000 | |
| 1-s | Fraction of individuals with increased susceptibility to TB infection at the start of the epidemic or with increased risk of progression at the start of the epidemic | 0 | 1 | |
| Λ | Birth rate (post-famine) (births per 1,000 population per year) | 30 | 50 | (Lux, 2001) |
| δp | Factor by which famine conditions increased p | 1 | 3 | |
| δ μTB | Factor by which famine conditions increased μTB | 1 | 3 | |
| δ μ | Factor by which famine conditions increased μ | 1 | 3 | |
| δ ν | Factor by which famine conditions increased ν | 1 | 3 | |
| δ ζ | Factor by which famine conditions decreased ζ | 0.3 | 1 | |
| δ β | Percent increase in β per year following 1880 | 0% | 2% | (Milloy, 1999; Lux, 2001) |
| δ Λ | Factor by which famine conditions decreased the birth rate | 0.3 | 1 | |
| t 1 | Start time of epidemic for cluster 1 | 1870 | 1883 | (Lux, 2001), census data |
| t 2 | Start time of epidemic for cluster 2 | 1870 | 1883 | (Lux, 2001), census data |
| p 1 | Starting population of cluster 1 | 800 | 1,600 | Census data |
| p 2 | Starting population of cluster 2 | 400 | 1,200 | Census data |
| ϵ | Time when famine conditions improved | 1895 | 1905 | (Lux, 2001), census data |
Notes.
a
See associated δ parameter since this quantity described by this parameter changes over time.
b
See associated δ parameter and ϵ since the quantity described by this parameter changes pre-/post- famine.