Data on the imported COVID-19 epidemics in Guangzhou were obtained from the official website of the Guangzhou Health Commission and the notification of imported epidemics published by the Guangzhou Center for Disease Control and Prevention as of twenty-four o’clock on August 31, 2022. The following were excluded from the study: (1) duplicate cases; (2) cases with excessive missing information; and (3) native cases. A total of 1,029 imported COVID-19 cases were collected in this study, and after cases with missing test data from entry to the first nucleic acid positivity were excluded, a total of 743 cases were used to calculate the survival analysis. This study was reviewed by the Institutional Review Board of the Guangzhou Center for Disease Control and Prevention.

Retrospective collection of information on reported inbound cases (confirmed cases and asymptomatic patients) in Guangzhou from March 1, 2020, to August 31, 2022, and extraction of demographic characteristics such as age, gender, occupation, and nationality of the patients, as well as information on their entry into China, history of sojourn, history of COVID-19 vaccination, and information on nucleic acid testing.

(1) Quarantine period: The quarantine period refers to the duration of the quarantine. Counting from the last day of contact with the patient, the quarantine period for the contact is established according to the longest incubation period of the disease. During the quarantine period the contact is placed under medical observation, retained for examination or other necessary measures, (2) Confirmed cases (9): patients who met the relevant epidemiologic history, clinical manifestations, and tested positive for COVID-19 nucleic acid by real-time fluorescence RT-PCR, (3) Asymptomatic patients: no clinical symptoms and respiratory specimens with positive COVID-19 pathogenicity test, (4) Imported cases (imported asymptomatic patients): cases with a history of residence in an outbreak country or region within 14 days before the positive nucleic acid test, and exclude infection in China, (5) The time interval between entry and the first positive nucleic acid test: the starting time of observation was the entry time of each study subject, with the first positive nucleic acid test result as the outcome event, and the survival time was defined as the interval from entry to the first positive nucleic acid test. Assuming that E and S are the entry time of a case and the time point at which a case’s nucleic acids can be first detected as positive, respectively, the time interval between entry and the first positive nucleic acid test is T = S−E. When both E and S fall on limited intervals, the observation is called the doubly interval-censored data. Accordingly, when one of E and S is an exact value and the other falls on a limited interval, the observation is called the singly interval-censored data. When both E and S are exact values, the observed data is the fully data (10). The time of entry was determined for all cases in this study, and the time point at which nucleic acids could be first detected as positive fell on a limited interval, so the observations were singly interval-censored data, i.e., T = (S_L−E, S_R−E), where the subscripts L and R denote the time of the last negative before a positive nucleic acid result, and the time of the first positive result (i.e., the lower and upper limits), respectively. When the interval between the positive result and the last negative result before the positive result was less than or equal to 1 day (performed with a time distance of 24 h) (11), both were considered to have occurred on the same day, i.e., L = R, then the time interval between entry and the first positive nucleic acid test (T) is fully data. In contrast, data were interval-censored if the time interval between the positive result and the last negative result was greater than 1 day because L did not equal R.

Statistical analysis was performed using R4.0.4 and SAS 9.4 software. Epidemiological characteristics of imported COVID-19 cases were analyzed using descriptive methods, count data were expressed as frequency, constitutive ratio, or proportion (%), and differences between groups were analyzed using the chi-square test or Fisher’s exact probability method. Differences were considered statistically significant at p < 0.05.

Distributional and point estimates of the time interval between entry and the first positive nucleic acid test for imported cases were based on a parametric survival analysis model of the failure data (12, 13). The model is log T = μ + σ log T 0 if there is no covariate, or log T = x , β + σ log T 0 if there is a covariate. Where T represents the failure time, μ represents the location parameter, σ represents the scale parameter, T 0 represents some sample that is in the baseline distribution, and x represents the value vector of the covariates. The model was fitted using the parametric method; the distributions commonly used for T are the Weibull distribution, the Log-normal distribution, etc.; the maximum likelihood method was used for the fitting, and the log-likelihood function was:

Where the first term of the formula sums over no censored data, the second term sums over right-censored data, the third term sums over left-censored data, and the last term sums over interval-censored data.

The covariate-free model was first used to fit the model using Log-normal, Log-logistic, Weibull, and Gamma distributions, respectively, to estimate the parameters of the time interval between entry and the first positive nucleic acid test and their distributional characteristics for each distribution, and to determine the fitted optimal distribution based on the maximum likelihood method and Bayesian Information Criterion; The distribution was then applied to a univariate covariate model analysis to analyze the individual effects of each factor on the time interval between entry and the first positive nucleic acid test, and those factors with p < 0.05 in the univariate analysis were entered into the multivariate analysis. Afterward, the factors that were statistically significant in the multivariate analysis were analyzed in subgroup analysis to estimate their percentile at some critical time of the time interval between entry and the first positive nucleic acid test.

The degree of risk of an indigenous outbreak due to imported cases was defined as follows: the time interval between entry and the first positive nucleic acid test ≤ P95 as low risk; > P95 as high risk. A decision tree model was used to combine statistically significant variables from the univariate analysis with the outbreak data to construct a dataset for the COVID-19 outbreak risk simulation model for Guangzhou City. Utilizing 70% of the data for training purposes and 30% for testing, a decision tree is built using the classification and regression trees (CART) algorithm (14), which can rank the importance of the influencing factors and construct a multi-risk factor-based simulation model of COVID-19 outbreak risk for inbound travelers in Guangzhou City.

In this study, 520 (50.53%) of the 1,029 imported cases were asymptomatic patients, and 509 (49.47%) were confirmed cases. The majority of imported cases were male (67.54%) and young adults (52.67%), and there were more imported cases from Asia (78.23%) and foreign nationalities (63.75%). Entry/exit high-risk occupational groups refer to those who work in key areas such as border crossings with a high risk of disease transmission, including crew members, seafarers, logistics personnel at airports and customs, and other occupational groups closely related to entry/exit. These groups accounted for 28.09% of the population. Imported cases from different VOC periods were dominated by the Omicron period, which accounted for 61.80% of the total. In addition, there were differences in the composition of asymptomatic patients and confirmed cases in terms of age, import source, nationality, and occupation, with Chinese nationals predominantly confirmed cases and foreigners predominantly asymptomatic patients (Table 1).

The Log-normal, Log-logistic, Weibull, and Gamma distributions were employed to approximate the time interval between entry and the first positive nucleic acid test in Guangzhou. The optimal distribution model was determined through the Bayesian information criterion (BIC) or the maximum likelihood method (15). The log-likelihood ratio (LLR) and Bayes calculated from both the Log-normal and Log-logistic distributions were relatively close, and the location parameter estimates were generally similar. However, the Weibull and Gamma distributions estimate model parameters that were not statistically significant. Moreover, given that the Log-normal distribution has a lower likelihood ratio and BIC compared to the Log-logistic distribution, and since it is more commonly used in estimating latency distributions, it is considered to be the optimal choice for analyzing the time interval between the entry and the first positive nucleic acid test for COVID-19. The mean time interval between entry and the first positive nucleic acid test estimated by the Log-normal distribution was 0.4 days with a 95% confidence interval of (0.32, 0.51) days, which means that 50% of the imported cases tested positive within 1 day of entry. In addition, approximate 95% (94.51%) of the imported cases first tested positive within 14 days of entry (Table 2).

Log-normal distribution has been employed in the univariate survival analysis. In total, various aspects such as sex, age, region, nationality, entry/exit risk occupation, international student status, background disease condition, vaccination history, and VOC period were investigated and analyzed. The results indicated that there was a statistically significant difference for the factors of entry/exit high-risk occupations (p < 0.0001), Oceania (p = 0.02), Africa (p < 0.0001), COVID-19 vaccination with 2 doses (p < 0.0001), COVID-19 vaccination with 3 or more doses (p < 0.0001), Alpha period (p < 0.0001), Beta period (p < 0.0001), and Omicron period (p = 0.0001) (Table S1).

Factors with p < 0.05 in the univariate survival analysis were calculated in the multivariate analysis, which found that the mean time interval between entry and the first positive nucleic acid test for inbound travelers in entry/exit high-risk occupations was 29% shorter (OR 0.29, 95% CI 0.18–0.46, p < 0.0001) than that of low-risk occupations, those from Africa were 37% shorter (OR 0.37, 95% CI 0.17–0.78, p = 0.01) than those from Asia, those who received 3 or more doses of the COVID-19 vaccinations were 1.88 times higher (OR 1.88, 95% CI 1.13–3.12, p = 0.01) than that of those who did not, and those in other VOC periods were lower than in the Delta period (Table 3).

The study established the time interval between entry and the first positive nucleic acid test as 14 days, which can inform the quarantine period for inbound travelers. Therefore, we focused on the 14-day centile, which was defined as the proportion of imported cases with a positive first nucleic acid test within 14 days of entry. By calculating the 14-day centile for different factors, the proportion of different types of inbound travelers who did not test positive until after the end of the quarantine period can be derived, thus identifying priority risk groups. The factors with statistical significance in the multivariate survival analysis were entered into subgroup analysis, and the 14-day centile of the time interval between entry and the first positive nucleic acid test was calculated. The results found that 6.52% of entry/exit low-risk occupational cases first tested positive 14 days after entry, which was higher than the proportion of high-risk occupational cases; 5.44% of Asian cases tested positive 14 days after entry, whereas basically all African cases could be detected as positive within 14 days of quarantine; and the proportion of cases who had received 3 or more doses of the COVID-19 vaccinations was 8.18%, which was far higher than the proportion of unvaccinated cases. As the Guangzhou COVID-19 Nucleic Acid Detection System was not fully standardized until May 2021, many of the nucleic acid positive detection times for imported cases in Guangzhou prior to May 2021 were missing. Consequently, the mean time interval between entry and the first positive nucleic acid test result in the Alpha and Beta periods was lower than that in the Delta period during multivariate analyses, possibly due to a lack of representative samples. As a result, subgroup analyses were only conducted for the Delta and Omicron periods, which mainly occurred after May 2021. The analysis found that 12.50% of imported cases in the Delta period first tested positive 14 days after entry, while 5.50% of imported cases in the Omicron period were tested 14 days after entry (Table 4).

Cases detected within the quarantine period have a lower risk of causing an indigenous outbreak so the degree of risk of an indigenous outbreak due to imported cases was defined as follows: the time interval between entry and the first positive nucleic acid test ≤ P95 as low risk; > P95 as high risk. Factors with p < 0.05 at univariate survival analysis were calculated in the decision tree model, which had an average accuracy value of 92.83%. The decision tree model was constructed with four layers reflecting the importance of each factor in predicting the risk of causing an indigenous outbreak. The first layer was divided by VOC period, indicating that VOC period had the greatest influence, while the second layer of influencing factors was the entry/exit risk occupation, the third layer was the region, and the fourth layer was the COVID-19 vaccination doses.

We found that the probability that an imported case during the Delta period causes an indigenous outbreak to be a low risk was 0.84, which gave a high-risk probability of 0.16, which was higher than in other periods such as the Omicron period. Among Delta-period inbound travelers, the probability of an entry/exit low-risk occupational case causing a high risk of an indigenous outbreak was 0.24, which was higher than that of an entry/exit high-risk occupational case (0.06). As Europe and North America were nonsignificant factors in the univariate analysis, the model did not predict risk for these cases. The orientation of the factors influencing the risk of an indigenous outbreak resulting from imported cases, as revealed by the decision tree analysis, is in line with the orientation of the factors influencing the duration of the time interval between entry and the first positive nucleic acid test, as determined by the multivariate analysis (Figure 1).