2. Methods

2.1. Epidemiological Data
An epidemiological dataset of confirmed cases with COVID-19 infection diagnosed outside China was collected from government and news websites quoting official outbreak reports. For each case, the date of reporting and country of diagnosis were recorded. The data included only cases diagnosed outside China, but for whom infection may have occurred either in or outside China. The dataset is available as Supplementary Material (Table S1). All cases were confirmed using reverse transcriptase polymerase chain reaction (RT-PCR) apart from two cases in Australia that were clinically diagnosed. The endpoint for data collection was set at 6 February 2020.

2.2. Statistical Model
We considered the impact of reduced travel volumes on COVID-19 transmission dynamics outside China. Specifically, we quantified the impact on: (i) the number of exported cases, (ii) the probability of a major epidemic, and (iii) the time delay to a major epidemic.

2.2.1. Reduced Number of Exported Cases
Figure 1 shows the observed number of infections in and outside China. The first exported case in Thailand was reported on 13 January 2020. Assuming the epidemic start date is set at 1 December 2019 (Day 0), the city of Wuhan was put in lockdown from Day 53 (or 23 January 2020). Considering that the mean incubation period of COVID-19 approximately is 5 days, the impact of reduced travel volumes would start to be interpretable from Day 58 (28 January 2020). We used data from Day 43 (13 January) onwards because the first case diagnosed outside China was reported on that day.
To estimate the reduced volume of exported cases, we employ a counterfactual model. If we let c(t) be the incidence of exported cases on Day t, Poisson regression was used to fit the following model through Day 57:(1) E(c(t))=c0exp(rt), where c0 is the initial value at t = 0 and r is the exponential growth rate of exported cases outside China. Using the estimated parameters and their covariance matrix, we obtain the expected number of exported cases from Day 58 onwards. Supposing that h(t) is the observed number of cases on day t, the reduced travel volume of exported cases by Day 67 is calculated as:(2) V=∑t=5867(h(t)−E(c(t))). 

2.2.2. Reduced Probability of a Major Epidemic Overseas
We assumed that the distribution of the number of secondary cases generated by a single primary case follows a negative binomial distribution with the basic reproduction number R0, i.e., the average number of secondary cases generated by a single primary case, and the dispersion parameter k. The probability of extinction π defined by the first generating moment [15] is then modeled as:(3) π=1(1+R0k(1−π))k.
R0 is estimated to range from 1.5 to 3.7, and here we adopt 1.5, 2.2, and 3.7 as plausible values for our calculations [16,17,18]. The value of k, a dispersion parameter, is assumed to be 0.54 as estimated elsewhere [17].
Supposing that there are n untraced cases that were independently introduced, the probability of a major epidemic is:(4) p=1−πn.
Now we compare two scenarios: the observed data as influenced by the reduction in travel volume, and a counterfactual scenario in which travel volume reduction does not take place. The cumulative number of exported COVID-19 cases observed in the former scenario is denoted m, while m¯ describes the number of cases in the counterfactual scenario. This leads to the following sums:(5) m=∑t=5867h(t), and (6) m¯=∑t=5867E(c(t)).
Accordingly, the reduced probability of a major epidemic is calculated as:(7) ε=πm−πm¯.
It should be noted that the probability of a major epidemic is evaluated at the country level, and only results for Japan are presented here. Whereas, the proposed method can equally handle the probability of a major epidemic for each importing country.
For the computation, we first subtracted m¯, the integral of E(c(t)), by the integral of h(t), assuming that all cases h(t) were already traced, and then we multiplied the difference by 0.9, 0.7, or 0.5 if only 10%, 30%, or 50% of contacts were traced, respectively. For m, we accounted for three symptomatic cases that were regarded as locally acquired infections in reports and diagnosed between Day 58 and Day 67. Assuming that the asymptomatic ratio was 50% [19], we considered that in total there were m = 6 untraced cases including the diagnosed cases.

2.2.3. Time Delay to a Major Epidemic Gained from the Reduction in Travel Volume
Lastly, we measured the time delay to a major epidemic gained from the reduction in travel volume using the hazard function of a major epidemic, λ(t), in the absence of travel volume changes. We model the probability of a major epidemic by time t in the absence of travel volume reduction as follows:(8) H0(t)=1−exp(−∫0tλ(s)ds).
In the presence of travel volume reduction, the hazard is reduced by the relative reduction factor in the probability of a major epidemic: (9) H1(t)=1−exp(−1−πm1−πm¯∫0tλ(s)ds).
Here, we consider the median time to a major epidemic in (8) and (9). Since an exponential growth of cases has been observed, we let the hazard be an exponential function. Then, the integral of the hazard function holds the form: C⋅(exp(rt)−1), where C is a constant (assumed to be one for the following calculation), and r is the exponential growth rate estimated at 0.14 per day [16]. The doubling time is then calculated as td = ln(2)/r = 4.95 days. The difference in the median date between (8) and (9) is thus described as:(10) D=ln(C1−πm1−πm¯+ln(2)C1−πm1−πm¯+ln(2)1−πm1−πm¯)tdln(2).
All computations were conducted in JMP Version 14.0 (SAS Institute, Cary, North Carolina). The confidence intervals were calculated using profile likelihood method.