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Table 4 Median parameter estimates (2.5-97.5% credibility intervals) in model to explain the observations in Table 1.

From: Prior immunity helps to explain wave-like behaviour of pandemic influenza in 1918-9

Contrast R R 0 Z Φ1 Φ2 α1 α2 α3
All 12
populations
2.33
(1.57-3.96)
4.59
(3.10 - 6.74)
0.52
(0.41 - 0.66)
0.57
(0.42 - 0.71)
0.35
(0.23-0.46)
0.39
(0.25 - 0.52)
0.43
(0.30 - 0.59)
0.48
(0.31-0.65)
8 urban
populations
1.81
(1.16 - 2.94)
3.80
(2.53 - 5.92)
0.49
(0.34-0.62)
0.50
(0.34 - 0.76)
0.38
(0.24-0.57)
0.38
(0.20 - 0.58)
0.34
(0.21 - 0.49)
0.38
(0.22-0.59)
4 "school"
populations
2.84
(1.43-5.36)
4.73
(2.43-8.42)
0.61
(0.41-0.81)
0.74
(0.49 - 0.92)
0.38
(0.20-0.57)
0.49
(0.30-0.68)
0.64
(0.43-0.86)
0.71
(0.41-0.91)
  1. For parameter definitions, see methods text. Estimates for R 0 , Z, Φ 1 , Φ 2 , α 1 , α 2 , α 3 were derived from the joint distributions of the relevant hyperparameters; these parameters can be regarded as the typical values for populations such as those studied. By combining information from the joint distributions of R 0 and Z, it was also possible to derive the medians and credibility intervals for the effective reproduction number R = R 0 .Z, at the start of the first wave. Population-specific estimates are given in Tables S.3 & S.4. For detailed methods see the supplementary information in Additional file 1. Results to support the validity of estimation procedures are given in Additional File 1 - see Tables S1 & S2. and Figure S1.