Materials and methods

Modeling strategy
The model’s structure is summarized above (Figure 1), and detailed methods have been described previously (Gostic et al., 2015). Here, we summarize relevant extensions, assumptions and parameter inputs.

Extensions
Our previous model tracked all the ways in which infected travellers can be detected by screening (fever screen, or risk factor screen at arrival or departure). Here, we additionally keep track of the many ways in which infected travellers can be missed (i.e. missed given fever present, missed given exposure risk present, missed given both present, or missed given undetectable). Cases who have not yet passed the incubation period are considered undetectable by fever screening, even if they will eventually develop symptoms in the future. In other words, no traveller is considered ‘missed given fever present’ until they have passed the incubation period and show detectable symptoms. Infected travellers who progress to symptoms during their journey are considered undetectable by departure screening, but detectable by arrival screening.
Additionally, we now provide a supplementary user interface, which allows stakeholders to test input parameters of interest using up-to-date information. Here, in addition to the analyses presented in this study, we implemented the possibility that some fraction of infected travellers deliberately evade screening.

Basic reproduction number, R0
Existing point estimates for R0 span a wide range (2.2–6.47), but most fall between 2.0 and 4.0 (Table 1). The vast majority of these estimates are informed by data collected very early in the outbreak, before any control measures were in place. However, several studies already demostrate decreases in the reproductive number over time, as a consequence of social distancing behaviors, and containment measures (Kucharski et al., 2020; Liu et al., 2020). Realistically, R0 will vary considerably over time, and across locations, depending on the social context, resource availability, and containment policies. Our analysis considers a plausible range of R0 values spanning 1.5–4.0, with 4.0 representing a plausible maximum in the absence of any behavioral changes or containment efforts, and 1.5 reflecting a plausible lower bound, given containment measures may already be in place at the time of introduction.

Fraction of subclinical cases
To estimate the upper-bound fraction of subclinical cases, we draw on data from active surveillance of passengers quarantined on a cruise ship off the coast of Japan, or passengers of repatriation flights. These data show that 50–70% of cases are asymptomatic at the time of diagnosis (Dorigatti et al., 2020; Nishiura et al., 2020; Schnirring, 2020c; Schnirring, 2020b). We estimate that 50% subclinical cases is a reasonable upper bound: due to intensive monitoring, cases in repatriated individuals or in cruise ship passengers will be detected earlier than usual in the course of infection--and possibly before the onset of symptoms. From clinical data (where severe cases are likely overrepresented), we estimate a lower bound of 5%: even among clinically attended cases, 2–15% lack fever or cough, and would be undetectable in symptom screening (Chan et al., 2020; Chen et al., 2020; The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team, 2020; Huang et al., 2020). In addition to the upper and lower bound scenarios, we consider a plausible middle-case scenario in which 25% of cases are subclinical. A very recent delay-adjusted estimate indicates 30-40% of infections on the cruise ship quarantined off the coast of Japan are asymptomatic, so the truth may fall somewhere between our middle and worst-case scenarios (Mizumoto et al., 2020).

Incubation period distribution
We use a gamma distribution to model individual incubation times. We choose this form over the Weibull and lognormal distribution for ease of interpretation (gamma shape and scale parameters can be transformed easily to mean and standard deviation). So far, best-fit gamma distributions to COVID-19 data have had mean 6.5 and standard deviation 2.6 (Backer et al., 2020), or mean 5.46 and standard deviation 1.94 (Lauer et al., 2020). Here, to model uncertainty around the true mean incubation time, we fix the standard deviation to 2.25 (intermediate between the two existing estimates), and allow the mean to vary between 4.5 and 6.5 days (Figure 2—figure supplement 2). The 95th percentile of the distributions we consider fall between 8.7 and 10.6 days, slightly below the officially accepted maximum incubation time of 14 days, and consistent with existing estimates (Table 1; Backer et al., 2020; Lauer et al., 2020).

Effectiveness of exposure risk questionnaires
The probability that an infected traveller is detectable using questionnaire-based screening for exposure risk will be highest if risk factors with high sensitivity and specificity are known. Currently, official guidance recommends asking whether travellers have visited a country with epidemic transmission, a healthcare facility with confirmed cases, or had close contact with a confirmed or suspected case (World Health Organization, 2020c). Given the relative anonymity of respiratory transmission, we assume that a minority of infected travellers would realize that they have been exposed before symptoms develop (20% in Figure 2, range 5–40% in Figure 3). Further, relying on a previous upper-bound estimate (Gostic et al., 2015) we assume that only 25% of travellers would self-report truthfully if aware of elevated exposure risk.
Table 1 summarizes the state of knowledge about additional parameters, as of February 20, 2020.

Code and data availability
All code and source data used to perform analyses and generate figures is archived at https://github.com/kgostic/traveller_screening/releases/tag/v2.1. (Gostic, 2020; copy archived at https://github.com/elifesciences-publications/traveller_screening).