Table 1. Expected parameter values derived from the literature.
Parameter | Description | Expected value [Range: min, max] | Distribution | Reference(s) |
---|---|---|---|---|
rh | Human birth rate | 1/(25·365) = 0.00011 [1/(30·365) = 0.000091, 1/(20·365) = 0.00013] days-1 | Uniform | [23]; also, consistent with 0.04 yr-1 [26] |
dh | Natural human death rate | 1/(25·365) = 0.00011 [1/(30·365) = 0.000091, 1/(20·365) = 0.00013] days-1 | Uniform | [23]; also, consistent with 0.04 yr-1 [26] |
βp | Pneumonic plague transmission rate in humans | 0.08 [0.01, 1] days-1 | Uniform | 0.0734 (SE = 0.00005) [27]; 0.08 [28]; 0.084 [19];0.42–0.48 [16]; |
σp−1 | Duration of pneumonic incubation rate in humans | 4.3 [2.5–6.1] days | Normal | [27]; 2–4 days [18] |
γp−1 | Duration of pneumonic infection period in humans | 2.5 [1.3–3.7] days | Normal | [27] |
βr | Transmission rate from fleas to rats | 1.248 [0–3.67] fleas-1 days-1 | Triangle | 0.04–0.14 days-1 [16]; 0–3.67 days-1 *calculated from percent per flea transmission efficiency/days post infection at 23°C [29] |
α | Flea searching efficiency | 3/Sr(t = 0) [0.39 < αKr< 20] rats-1 | Uniform | [26,30] |
rr | Reproductive rate in rats | 0.014 [0.011, 0.016] rats days-1 | Uniform | 5/365 days [25,26] |
Kr | Carrying capacity of rats |
Nr(t = 0) [0.5Nr(t = 0), 1.5Nr(t = 0)] rats |
Uniform | Varied in conjunction with sensitivity analysis on initial condition (Nr) |
dr | Natural death rate in rats | 0.2 year-1 /365 = 0.00055 [0.1/365 = 0.00027, 0.3/365 = 0.00082] days-1 | Uniform | [25,26] |
pr | Probability of rats inheriting resistance | 0.65 [0.4–0.9] | Uniform | 0.5 [31]; 0.5–0.9 [32]; 0.4–0.8 [33] |
γr−1 | Duration of bubonic plague infectious period in rats | 5.15 [4.71–5.59] days | Normal | Based on low-moderate infection doses in rats outside of plague endemic areas in Madagascar [32] |
gr | Probability of rats recovering from bubonic plague | 0.06 [0.0–0.37] | Triangle | “24–37% of rats surviving a low- dose infection . . .compared with only 0–6% at high dose” [32] |
rf | Growth rate of fleas | 0.0084 [0.0084, 20/365 = 0.055] fleas/day | Uniform | [16,25,26] |
Kf | Flea carrying capacity per rat | 6 [3.29, 11.17] fleas | Normal | [16,25,26] |
df−1 | Flea lifespan | 5 [1, 11.66] days | Triangle | [16,34] |
βb | Transmission rate for bubonic plague from rat fleas to humans | 0.19 [0.01, 1] days-1 | Uniform | 0.18–0.20 [16] |
σb−1 | Duration of bubonic plague incubation period in humans | 4 [2, 6] days | Triangle | [35]; 4.3 days [36] |
γb−1 | Duration of bubonic plague infectious period in humans | 10 [3, 10] days | Triangle | 3.4 days [36]; 4–10 days [37]; 10 days [16]; |
gh | Probability of humans recovering from bubonic plague | 0.34 [0.30, 0.40] | Triangle | 0.40 [16]; “Among 511 plague cases occurring before 1942 (pre-antibiotics) with outcome information, 336 (66%) were fatal” [38] |
p | Probability of human bubonic plague developing into secondary pneumonic plague | 0.10 [0, 0.15] | Triangle | 3% [36]; <5% [18]; ~10% [39]; 8–10% [37]; ~12% [40]; 5–15% [41] |
Here we include the parameter, its description, expected value, range tested during the global sensitivity analysis (LHS-PRCC), and type of distribution used for sampling.