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{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7014672","sourcedb":"PMC","sourceid":"7014672","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7014672","text":"Incubation period distribution\nUsing the duration of stay in Wuhan and the symptom onset date, we obtained a range of possible values for the incubation period of each case. We fitted three parametric forms for the incubation period distribution to these ranges: the Weibull distribution, the gamma distribution and the lognormal distribution. We used a Bayesian approach to fitting that allows for the use of prior knowledge to inform the analysis. We specified strictly positive flat prior probability distributions for the parameter values of the three distributions (Supplementary Material S2), which ensured our estimates are conservative. Because of the sufficient number of observations, the impact of the priors on the outcome was negligible. We used a uniform prior probability distribution over the exposure interval for the moment of infection for each case. We sampled from the posterior distribution using the rstan package [9] in R software version 3.6.0 (R Foundation, Vienna, Austria) (Supplementary Material S3).\nFigure 1 shows the exposure to reporting timeline for each case, where the cases without a maximum incubation period lack an unexposed (grey) period. However, the estimated infection times for these cases are close to the end of the exposure window, informed by the cases that do have a maximum incubation period.\nFigure 1 Exposure to reporting timeline for confirmed 2019 novel coronavirus (2019-nCoV) cases with travel history from Wuhan, sorted by symptom onset date, data 20–28 January 2020 (n = 88)\nThe analysis yields the probability of being infected (dark pink), i.e. the cumulative density function of the estimated infection moments, using the Weibull distribution. The Weibull distribution provided the best fit to the data (Table 1). The mean incubation period was estimated to be 6.4 days (95% credible interval (CI): 5.6–7.7). The incubation period ranges from 2.1 to 11.1 days (2.5th to 97.5th percentile) (Table 2 and Figure 2). The results using the gamma distribution provide a slightly poorer description of the data, but a similar range: from 2.4 to 12.5 days. Although the lognormal distribution provides the poorest fit to the data, the incubation period ranging from 2.4 to 15.5 days (2.5th to 97.5th percentile) may be relevant for a conservative choice of quarantine periods.\nTable 1 Estimated incubation period for travellers infected with 2019 novel coronavirus (2019-nCoV) in Wuhan, China, for different parametric forms of the incubation period distribution, data 20–28 January 2020\nDistribution Mean (days) SD (days) LOO ICb\nEstimatea 95% CI Estimatea 95% CI\nWeibull 6.4 5.6–7.7 2.3 1.7–3.7 486\nGamma 6.5 5.6–7.9 2.6 1.8–4.2 545\nLognormal 6.8 5.7–8.8 3.4 2.1–6.4 592\nCI: credible interval; LOO IC: Leave-one-out information criterion; SD: standard deviation.\na Posterior median.\nb LOO IC indicates the goodness-of-fit, where lower values indicate a better fit and differences larger than two are statistically relevant.\nTable 2 Percentiles of estimated incubation period for travellers infected with 2019 novel coronavirus (2019-nCoV) in Wuhan, China, for different parametric forms of the incubation period distribution, data 20–28 January 2020\nPercentiles Incubation period distribution (days)\nWeibull Gamma Lognormal\nEstimatea 95% CI Estimatea 95% CI Estimatea 95% CI\n2.5th 2.1 1.3–3.0 2.4 1.5–3.2 2.4 1.6–3.1\n5th 2.7 1.8–3.5 2.9 2.0–3.6 2.8 2.0–3.5\n50th 6.4 5.5–7.5 6.1 5.3–7.3 6.1 5.2–7.4\n95th 10.3 8.6–14.1 11.3 9.1–15.7 13.3 9.9–20.5\n97.5th 11.1 9.1–15.5 12.5 9.9–17.9 15.5 11.0–25.2\n99th 11.9 9.7–17.2 14.1 10.9–20.6 18.5 12.6–32.2\nCI: credible interval.\na Posterior median.\nFigure 2 The cumulative density function of the estimated Weibull incubation period distribution for travellers infected with the 2019 novel coronavirus (2019-nCoV) in Wuhan, China, data 20–28 January 2020\nPosterior median of mean is indicated by the dark blue line and the 95% credible interval by the light blue 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