Parameters, uncertainty and sensitivity analyses
As of February 20, 2020, COVID-19-specific estimates are available for most parameters, but many have been derived from limited or preliminary data and remain subject to considerable uncertainty. Table 1 and the Methods summarize the current state of knowledge. Here, we used two distinct approaches to incorporate parameter uncertainty into our analysis.
Table 1.  Parameter values estimated in currently available studies, along with accompanying uncertainties and assumptions.
Ranges in the final column reflect confidence interval, credible interval, standard error or range reported by each study referenced.
Parameter  Best estimate (Used in Figure 2)  Plausible range (Used in Figure 3)  References and notes
Mean incubation period  5.5 days Sensitivity: 4.5 or 6.5 days  4.5–6.5 days  3–6 days, n = 4 (Chan et al., 2020)* 5.2 (4.1–7.0) days, n < 425 (Li et al., 2020)† 5.2 (4.4–6.0) days, n = 101 (Lauer et al., 2020)† 6.5 (5.6–7.9) days, n = 88 (Backer et al., 2020)†
Incubation period distribution  Gamma distribution with mean as above, and standard deviation = 2.25
Percent of cases subclinical (No fever or cough)  Best case scenario: 5% Middle case scenario: 25% Worst case scenario: 50%  Clinical data: 83% fever, 67% cough, n = 6 (Chan et al., 2020) 83% fever, 82% cough, n = 99 (Chen et al., 2020) 98% fever, 76% cough, n = 41 (Huang et al., 2020) 43.8% fever at hospital admission, 88.7% fever during hospitalization, n = 1099 (Guan et al., 2020) Active monitoring after repatriation flights or on cruise ships: % asymptomatic at diagnosis 31.2% (111/355) (Japan Ministry of Health, Labor and Welfare, 2020) 65.2% (5 of 8) (Nishiura et al., 2020) 70.0% (7 of 10) (Dorigatti et al., 2020)
R0  No effect in individual-level analysis.  1.5–4.0  2.2 (1.4–3.8) (Riou and Althaus, 2020) 2.2 (1.4–3.9) (Li et al., 2020) 2.6 (1.5–3.5) (Imai et al., 2020) 2.7 (2.5–2.9) (Wu et al., 2020) 4.5 (4.4-4.6) (Liu et al., 2020) 3.8 (3.6-4.0) (Read et al., 2020) 4.08 (3.37–4.77) (Cao et al., 2020) 4.7 (2.8–7.6) (Sanche et al., 2020) 6.3 (3.3-11.3) (Sanche et al., 2020) 6.47 (5.71–7.23) (Tang et al., 2020)
Percent of travellers aware of exposure risk  20%  5–40%  We assume a low percentage, as no specific risk factors have been identified, and known times or sources of exposure are rarely reported in existing line lists.
Sensitivity of infrared thermal scanners for fever  70%  60–90%  Most studies estimated sensitivity between 60–88% (Bitar et al., 2009; Priest et al., 2011; Tay et al., 2015). But a handful of studies estimated very low sensitivity (4–30%). In general, sensitivity depended on the device used, body area targeted and ambient temperature.
Probability that travellers self-report exposure risk  25%  5–25%  25% is an upper-bound estimate based on outcomes of past screening initiatives. (Gostic et al., 2015)
Time from symptom onset to patient isolation (After which we assume travel is not possible)  No effect in individual-level analysis.  3–7 days  Median 7 days from onset to hospitalization (n = 6) (Chan et al., 2020) Mean 2.9 days onset to patient isolation (n = 164) (Liu et al., 2020) Median 7 days from onset to hospitalization (n = 41) (Huang et al., 2020) As awareness increases, times to isolation may decline.
* From family cluster.
† Parametric distributions fit to cases with known dates of exposure or travel to and from Wuhan. First, to estimate the probability that an infected individual would be detected or missed we considered a range of plausible values for the mean incubation time, and the fraction of subclinical cases. We focus on the incubation period and subclinical fraction of cases because screening outcomes are particularly sensitive to their values. All other parameters were fixed to the best available estimates listed in Table 1.
Second, we considered a population of infected travellers, each with a unique time of exposure, and in turn a unique probability of having progressed to the symptomatic stage. Here, the model used a resampling-based approach to simultaneously consider uncertainty from both stochasticity in any single individual’s screening outcome, and uncertainty as to the true underlying natural history parameters driving the epidemic. Details are provided in the methods, but briefly, we constructed 1000 candidate parameter sets, drawn using Latin hypercube sampling from plausible ranges for each parameter (Table 1). Using each parameter set, we simulated one set of screening outcomes for a population of 30 infected individuals. As of February 20, 2020, 30 approximates the maximum known number of cases imported to any single country (World Health Organization, 2020b), and thus our analysis incorporates a reasonable degree of binomial uncertainty. The actual number of infected travellers passing through screening in any given location may be higher or lower than 30, and will depend on patterns of global connectivity, and on the duration of the source epidemic (Chinazzi et al., 2020; de Salazar et al., 2020). Finally, we analysed the sensitivity of screening effectiveness (fraction of travellers detected) to each parameter, as measured by the partial rank correlation coefficient (PRCC) (Marino et al., 2008).