key: cord-0691975-70jf0j9l
authors: Chun, June Young; Baek, Gyuseung; Kim, Yongdai
title: Transmission onset distribution of COVID-19
date: 2020-08-06
journal: Int J Infect Dis
DOI: 10.1016/j.ijid.2020.07.075
sha: 7ed86085127440961a4b5d298691a64811ac19f2
doc_id: 691975
cord_uid: 70jf0j9l

OBJECTIVES: The distribution of the transmission onset of COVID-19 relative to the symptom onset is a key parameter for infection control. It is often not easy to study the transmission onset time, as is difficult to know who infected whom exactly when. METHODS: We inferred transmission onset time from 72 infector-infectee pairs in South Korea, either with known or inferred contact dates by means of incubation period. Combining this data with known information of infector’s symptom onset, we could generate the transmission onset distribution of COVID-19, using Bayesian methods. Serial interval distribution could be automatically estimated from our data. RESULTS: We estimated the median transmission onset to be 1.31 days (standard deviation, 2.64 days) after symptom onset with peak at 0.72 days before symptom onset. The pre-symptomatic transmission proportion was 37% (95% credible interval [CI], 16–52%). The median incubation period was estimated to be 2.87 days (95% CI, 2.33–3.50 days) and the median serial interval to be 3.56 days (95% CI, 2.72–4.44 days). CONCLUSIONS: Considering the transmission onset distribution peaked with the symptom onset and the pre-symptomatic transmission proportion is substantial, the usual preventive measure might be too late to prevent SARS-CoV-2 transmission.

SARS-CoV-2, a novel coronavirus first reported in Wuhan City, China in December 2019, has been spreading globally and the World Health Organization declared it as a pandemic on March 11, 2020 (Zhu et al., 2020) . A total of 3,096,626 cases of coronavirus disease 2019 , and 217,896 confirmed deaths were counted world widely by April 30, 2020.

Considering its global threat, the transmission dynamics of COVID-19 should be made explicit.

There have been studies reporting the estimated serial interval and incubation period, based on the early epidemics in China (Backer et al., 2020 , Lauer et al., 2020 , Nishiura et al., 2020 . The serial interval is the duration between the symptom onset of successive cases, and the incubation period is the time since infection to the symptom onset. Those are key epidemiological parameters, giving essential insight to infer the transmission potential or to determine the quarantine duration (White and Pagano, 2008) .

There have been multiple reports of pre-symptomatic transmission of SARS-CoV-2, highlighting the difficulty of containment and mitigation of the disease (He et al., 2020 , Liu et al., 2020 , Wei et al., 2020 . However, transmission onset distribution of COVID-19 has never J o u r n a l P r e -p r o o f been studied before. It is not easy to study the transmission onset time, as is difficult to know who infected whom exactly when. In this report, we tried to estimate the transmission onset distribution relative to the symptom onset by means of solid epidemiologic data of infectorinfectee pairs in South Korea.

We searched public reports of confirmed COVID-19 patients by government and each municipal website of South Korea. As of March 31, 9,887 cases have been confirmed of which 8,260 (83.5%) cases were linked to certain clusters such as religious groups, hospitals, or longterm healthcare facilities. Five-hundred and sixty cases (5.7%) were imported from abroad. We screened all available cases between January 23 to March 31, 2020 and selected the pairs with clearly defined contact history. We excluded cases from main clusters unless the causal relationship between an infector and infectee pair was evident.

For each pair of cases, we collected information on the dates of symptom onset of both the infector and the infectee, exposure dates of the infectee by the infector, and the dates of confirmation of both. Considering the South Korean quarantine policy, the confirmation date could be regarded as the date on which isolation started. Demographic information of age and sex were also gathered.

We tried to estimate the time difference between an infector's symptom onset and its transmission onset time. We defined symptom onset date ( ), an infectee's infection date ( ), an infector's transmission onset date ( ), and contact time of the pair as ( , ), where subscripts L and R denote the left and right boundaries, meaning the earliest and the latest contact dates respectively. The aim of the study is to estimate the timing of relative to the ( − ), which we denominate as . We put as an infectee and as the corresponding There are three possible scenarios for in our data.

(i) There is an exact calendar date of an exposure. In this case, we could directly achieve the timing of transmission as = , = , .

(ii) There is a specified duration of exposure ( , < , ).

(iii) There is a continuous exposure such as household members ( , = −∞, , = ).

Recall that the aim is to estimate the distribution ( ) of based on the data ( , , , , , ) for infectees. We consider the following parametric model for ( ):

is the gamma distribution with the J o u r n a l P r e -p r o o f parameter and (− , 0)(⋅) is the uniform distribution with the support (− , 0). In the model, is the shift parameter for cases with transmission prior to the symptom onset. We introduced the term (1 − ) (− , 0)(⋅) to make the effect of negative outliers of be minimal to the estimation of the parameter. That is, we considered to be an outlier if < − . In the model, > 0 is an arbitrary limit for an outlier of . In the analysis, we used = 14, since the usual incubation period is within 14 days.

A difficulty in estimating is that the exact is not observed for cases in categories (ii) and (iii). However, conceptually we could impute the timing of transmission by use of the estimated incubation period distribution (Reich et al., 2009 For sensitivity analysis, we utilized the incubation period distribution of a previous study and replicated the same analysis as above (Lauer et al., 2020) . Moreover, we hold the parameter as 4, and compared the result using the same procedure, since the minimum of from our J o u r n a l P r e -p r o o f

We found 89 infectees with defined source of infection (infector) and contact history. Four infectors (4.5%) were asymptomatic until diagnosed, and thus were excluded from the analysis.

Sixteen infectees (18.0%) were asymptomatic when diagnosed, among which 13 cases had no specified contact date and were unable to guess the infection time. In short, 72 infector-infectee pairs were included in the study (Fig 1) . were female. The infectees had 40 unique infectors. The average number of transmissions per infector was 1.8, with a maximum of four cases (Fig 2) .

We estimated the incubation period distribution of COVID-19 using a lognormal model. with the best-fit using a lognormal distribution (Table 2) .

Based on the 72 infecfor-infectee pairs, the Bayes estimate of the transmission onset distribution after a smoothing procedure was given as Fig 3A. The mean and median values J o u r n a l P r e -p r o o f were 1.31 days (95% CI, 0.38-2.55) and 0.68 days (95% CI, -0.09-1.73) after infectors' symptom onset, respectively, with the peak at 0.72 days before symptom onset. The presymptomatic transmission proportion was 37% (95% CI, 16-52%).

For sensitivity analysis, applying the incubation period of previous study, the transmission onset distribution was inferred as Fig 3B. The mean and median values were 0.59 days (95% CI, -0.33-1.79) and 0.12 days (95% CI, -0.75-1.06) after the infector's symptom onset, respectively, with the peak at 0.41 days before symptom onset. The pre-symptomatic transmission proportion was 48% (95% CI, 29-67%). With a fixed parameter of as 4, the mean and median were 0.59 (95% CI, -0.34-1.79) and -0.07 days (95% CI, -0.91-0.99), with the pre-symptomatic transmission proportion of 51% (95% CI, 37-64%).

The transmission onset distribution is of utmost interest to clinicians and public health workers, but it has not been widely studied to date due to lack of epidemiological information. Based on concrete data, we hereby present that the transmission of COVID-19 could start before the symptom onset, and the probability peaked as the symptom start and declined thereafter.

Interestingly, the trend of this distribution looks similar with published SARS-CoV-2 viral load kinetics though it could not include the viral load data before the symptom onset (Kim et al., 2020 , Zou et al., 2020 .

In South Korea, the first COVID-19 case was identified on January 19, 2020 in a traveler from J o u r n a l P r e -p r o o f Wuhan City, who was quarantined immediately at the airport screening. Until February 18, 2020, there were only imported cases from abroad or cases from their close contacts who were under the surveillance. The situation was totally changed after an outbreak with an unknown source of infection occurred within a religious community, resulting in a total of 5,210

confirmed cases in that single cluster as of April 12, 2020, a number which is almost half and 48% (95% CI, 32-67%) in Singapore (Ganyani et al., 2020 , He et al., 2020 , Liu et al., 2020 .

This study has several limitations. First, the dates of symptom onset and contact time were identified from epidemiological investigation and it could be false due to recall bias. Second, J o u r n a l P r e -p r o o f For the lognormal distribution, parameter 1 and parameter 2 are the mean and SD of the natural logarithm and for all other distributions, parameter 1 and parameter 2 are the shape and scale parameters, respectively. -77.5 -192.8 -189.8 For the lognormal distribution, parameter 1 and parameter 2 are the mean and SD of the natural logarithm and for all other distributions, parameter 1 and parameter 2 are the shape and scale parameters, respectively.

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