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. 2010 May 5;277(1695):2857–2865. doi: 10.1098/rspb.2010.0575

Table 1.

Priors and posteriors for the model parameters. (For the posterior distributions, medians and 95% credible intervals (CI) are shown (see also the electronic supplementary material, table S4).)

model parameter prior distribution or mathematical expression prior median and 95% CI posterior median and 95% CI
herd 1 herd 2 herd 3 herd 4 herd 5
transition rate I −→ S, m (week−1) Dirichlet (α1, α2, α3), αi ∼ Uniform(0.5,10) 0.32 (0.01–0.76) 0.695 (0.542–0.844)
transition rate I− →I + , q (week−1) 0.017 (0.001–0.082)
time spent in state I− by an individual (weeks) 1/(m + q) 1.4 (1.0–4) 1.4 (1.1–1.8)
transition rate I +→ R, r (week−1) beta(1,1) 0.50 (0.03–0.98) 0.204 (0.121–0.294)
time spent in state I+ by an individual (weeks) 1/r 2.0 (1.0–33.3) 4.9 (3.4–8.3)
transition rate R → I + , s (week−1) beta(1,1) 0.50 (0.02–0.98) 0.037 (0.006–0.159) 0.170 (0.042–0.345) 0.036 (0.006–0.162) 0.380 (0.070–0.737) 0.277 (0.109–0.466)
time spent in state R by an individual (weeks) 1/s 2.0 (1.0–34.1) 26.6 ( 6.3–159.9) 5.9 (2.8–23.9) 28.1 (6.1–163.7) 2.6 (1.3–14.3) 3.6 (2.1–9.2)
quantity of bacteria shed by an I− per week, ɛ1 normal(0.25,0.25) 0.30 (0.02–0.76) 0.003 (0.000–0.018)
quantity of bacteria shed by an I+ per week, ɛ2 normal(0.25,0.25) 0.30 (0.02–0.76) 0.004 (0.000–0.016)
mortality rate of the bacterium, μ (week−1) 1/μ ∼ beta(2.16,38.51) 0.21 (0.07–0.80) 0.289 (0.079–0.926) 0.274 (0.079–0.869) 0.289 (0.082–0.874) 0.171 (0.068–0.407) 0.203 (0.071–0.760)
transition rate S → I − , p1 (infection risk at t0) beta(1.77,3.3) 0.33 (0.05–0.77) 0.135 (0.021–0.436) 0.124 (0.024–0.325) 0.073 (0.014–0.213) 0.466 (0.272–0.660) 0.230 (0.044–0.455)
bacterial load in the environment at t0, E0 −log(1 − p1) 0.40 (0.05–1.46) 0.146 (0.021–0.572) 0.133 (0.024–0.392) 0.076 (0.014–0.240) 0.627 (0.318–1.078) 0.261 (0.045–0.606)
transition rate S → I−, p5 (infection risk at t28) 1−exp(−E4) variable function of herds 0.095 (0.010–0.282) 0.136 (0.024–0.334) 0.044 (0.005–0.134) 0.403 (0.204–0.622) 0.428 (0.182–0.722)
bacterial load in the environment at t28, E4 E4= (1 − μ)E3 + ɛ1*I −+ ɛ2*I+ variable function of herds 0.100 (0.010–0.331) 0.146 (0.024–0.406) 0.044 (0.005–0.143) 0.517 (0.228–0.973) 0.558 (0.201–1.278)