Table 1.
Results of fitting eight model variants to weekly mortality data for 16 cities for which data on the timing of interventions were available
| Model variant | Mean posterior log likelihood | μ, per-capita death rate, % | R0 | κ, threshold for contact reduction (per 100,000) | T, memory period for contact reduction | pc, effectiveness of control measures, % | Reduction in mortality due to controls, % | Reduction in mortality for optimal controls, % |
|---|---|---|---|---|---|---|---|---|
| 1 | −2,318 | Per city, 1.1 (0.7–1.8) | Per city, 2.0 (1.4–2.8) | Per city, 99 (10–538) | Per city, 12.2 (0.1–58.1) | Per city, 26 (0–49) | 13 (0–36) | 47 (0—100) |
| 2 | −4,764 | Per city, 1.2 (0.7–2.6) | Per city, 1.9 (1.4–2.8) | No reactive contact reduction | No reactive contact reduction | Per city, 37 (0–83) | 33 (21–57) | 88 (36–100) |
| 3 | −4,652 | Per city, 1.2 (0.7–2.5) | Per city, 2.1 (1.3–3.2) | Per city, 55 (3.8–185) | Per city, 1.4 (0.1–8.6) | No effect of controls | No effect of controls | No effect of controls |
| 4 | −3,168 | Per city, 1.1 (0.6–1.8) | Common, 1.96 (1.95, 1.97) | Per city, 186 (7.5–828) | Common, 20.4 (20.1, 20.6) | Per city, 36 (0–55) | 28 (7–64) | 68 (28–100) |
| 5 | −7,627 | Per city, 1.2 (0.7–1.8) | Common, 1.79 (1.78, 1.80) | No reactive contact reduction | No reactive contact reduction | Per city, 40 (0–86) | 43 (30–72) | 92 (35–100) |
| 6 | −3,824 | Per city, 1.2 (0.7–2.1) | Per city, 1.9 (1.5–2.6) | Common, 22.0 (21.5, 22.5) | Common, 7.25 (7.08–7.40) | Per city, 23 (0.1–68) | 6 (2–25) | 44 (1–100) |
| 7 | −4,609 | Per city, 1.1 (0.6–1.6) | Common, 1.99 (1.98, 2.0) | Common, 21.4 (20.8, 21.9) | Common, 13.7 (13.1, 14.1) | Per city, 30 (0–72) | 14 (2–30) | 51% (24–100) |
| 8 | −6,362 | Common, 1.21 (1.20, 1.21) | Common, 1.94 (1.93, 1.95) | Per city, 78 (2.7–530) | Common, 7.18 (7.00, 7.36), | Per city, 20 (0–54) | 12 (2–51) | 38 (0–100) |
Markov-Chain Monte-Carlo methods were used for fitting. Model fit is characterized by the mean log-likelihood from the posterior distribution (Fig. 3 gives a qualitative indication of the quality of fit for model variant 4; see SI Appendix also). Where a parameter was estimated on a per-city basis, the average and range across all cities of the mean posterior estimates of that parameter are shown. For parameter estimates assumed to be common to all cities, the mean and 95% credibility estimates of the parameter from the posterior distribution are shown. In addition, the time of introduction of the first infection into each city is fitted as a city-specific parameter for all models (estimates not shown). The last two columns show the average and range (across cities) of the estimated reduction in total mortality achieved by the implemented controls (represented as a percentage of the observed total mortality), and the average and range of reduction in mortality that would have been achieved had the period for which controls were most effective in each city been extended to cover September 1918 to May 1919, respectively.