The difference in the incubation period of 2019 novel coronavirus (SARS-CoV-2) infection between travelers to Hubei and non-travelers: The need of a longer quarantine period

Data collected from the individual cases reported by the media were used to estimate the distribution of the incubation period of travelers to Hubei and non-travelers. Upon the finding of longer and more volatile incubation period in travelers, the duration of quarantine should be extended to three weeks.


Introduction
An epidemic of viral pneumonia started in Wuhan, the capital of Hubei province in China, in December 2019. A new coronavirus was identified and named by the World Health Organization as SARS-CoV-2. It has been found that it is genetically similar to SARS-CoV and MERS-CoV 1 . Recently, snakes have been suggested as the natural reservoirs of SARS-CoV-2, assuming that the Huanan Seafood Wholesale Market in Wuhan is the origin of the virus 2 .
Different preventive measures have been implemented by health authorities with the 14-day quarantine being the commonly used. While previous studies have estimated the incubation period of SARS-CoV-2 to help determining the length of quarantine, it has recently been observed that some patients rather had mild symptoms such as cough and low-grade fever or even no symptoms 3 and that the incubation period might have been 24 days 4 , constituting greater threats to the effectiveness of entry screening. Against this background, the present work estimated the distribution of incubation periods of patients infected in and outside Hubei.

Methods
Because the details of most cases were reported by the media and were not available on the official web pages of the local health authorities in China, three searches for individual cases reported by the media between 20 th January 2020 and 12 th February (first cases outside Hubei reported on 20 th January 2020) with search terms "pneumonia" AND "Wuhan" AND "age" AND "new" in Chinese were performed on Google from 7 th , 8 th , and 9 th February. The inclusion of the search term "age" intended to narrow down the search results since the presence of "age" in an article implied a description of an individual case.
Individual cases with time of exposure and symptom onset as well as type of exposure were eligible for inclusion. There was no language restriction. Since most patients did not have complete information about the source of infection, the time of exposure was allowed to be a time interval within which the exposure was believed to lie. In contrast, patients could recall the exact date of symptom onset. The present paper considered two types of exposure, (i) traveling to Hubei, China, and (ii) contact with the source of infection such as an infected person or places where infectious agents stayed. For data accuracy, only confirmed cases outside Hubei province and within China were considered.
The following data were abstracted, (i) location at which the case was confirmed, (ii) gender, (iii) age, where F and S were the CDF of the incubation period and the time of symptom onset, respectively. Therefore, to find the maximum likelihood estimates of  , the maxima of the sum of the individual log-likelihood functions, either The results of maximum likelihood estimation are shown in Table 1. The AIC suggested that the Weibull distribution provided the best fit to the data. Both indicator variables of the shape and scale parameters were significant in the Weibull model, suggesting different incubation period distributions between the two groups of patients.

Discussion
The very first observation of the incubation period of SARS-CoV-2 came from the National Health Such difference might be due to the difference in infectious dose since travelers to Hubei might be exposed to different sources of infection multiple times during their stay in Hubei. In contrast, patients with no travel history to Hubei were temporarily exposed to their infected relatives, friends or colleagues with mild or even no symptoms.
It is possible that the incubation period of non-travelers was highly volatile, as suggested by the higher variance in the gamma model that provided slightly poorer fit. This could potentially pose a threat to the effectiveness of the existing preventive measures. The duration of quarantine period must be considered with caution.
As a comparison, previous studies on the incubation period for SARS-CoV-2 are shown in Table 2.
The 95 th percentiles reported in previous studies varied between 10.3 and 13.3 days, consistent with the current practice of quarantine period of 2 weeks. However, the present study found that the 95 th percentile of non-travelers could be 14.6 days and up to 17.1 days under 95% level of confidence.
Coupled with the high variability of the incubation period, it is suggested that the duration of the quarantine period of 3 weeks is deemed more suitable. [