Estimation of incubation period distribution of COVID-19 using disease onset forward time: a novel cross-sectional and forward follow-up study
Authors: Qin Jing , You Chong , Lin Qiushi , Hu Taojun , Yu Shicheng , Zhou Xiao-Hua 
Published: March 2020

SummaryBackgroundThe current outbreak of coronavirus disease 2019 (COVID-19) has quickly spread across countries and become a global crisis. However, one of the most important clinical characteristics in epidemiology, the distribution of the incubation period, remains unclear. Different estimates of the incubation period of COVID-19 were reported in recent published studies, but all have their own limitations. In this study, we propose a novel low-cost and accurate method to estimate the incubation distribution.MethodsWe have conducted a cross-sectional and forward follow-up study by identifying those asymptomatic individuals at their time of departure from Wuhan and then following them until their symptoms developed. The renewal process is hence adopted by considering the incubation period as a renewal and the duration between departure and symptom onset as a forward recurrence time. Under mild assumptions, the observations of selected forward times can be used to consistently estimate the parameters in the distribution of the incubation period. Such a method enhances the accuracy of estimation by reducing recall bias and utilizing the abundant and readily available forward time data.FindingsThe estimated distribution of forward time fits the observations in the collected data well. The estimated median of incubation period is 8·13 days (95% confidence interval [CI]: 7·37-8·91), the mean is 8·62 days (95% CI: 8·02-9·28), the 90th percentile is 14·65 days (95% CI: 14·00-15·26), and the 99th percentile is 20·59 days (95% CI: 19·47, 21·62). Compared with results in other studies, the incubation period estimated in this study is longer.InterpretationBased on the estimated incubation distribution in this study, about 10% of patients with COVID-19 would not develop symptoms until 14 days after infection. Further study of the incubation distribution is warranted to directly estimate the proportion with long incubation periods.FundingThis research is supported by National Natural Science Foundation of China grant 8204100362 and Zhejiang University special scientific research fund for COVID-19 prevention and control.Research in contextEvidence before this studyBefore the current outbreak of coronavirus disease (COVID-19) in China, there were two other coronaviruses that have caused major global epidemics over the last two decades. Severe acute respiratory syndrome (SARS) spread to 37 countries and caused 8424 cases and 919 deaths in 2002-03, while Middle East respiratory syndrome (MERS) spread to 27 countries, causing 2494 cases and 858 deaths worldwide to date. Precise knowledge of the incubation period is crucial for the prevention and control of these diseases. We have searched PubMed and preprint archives for articles published as of February 22, 2020, which contain information about these diseases by using the key words of “COVID-19”, “SARS”, “MERS”, “2019-nCoV”, “coronavirus”, and “incubation”. We have found 15 studies that estimated the distribution of the incubation period. There are four articles focused on COVID-19, five on MERS, and six on SARS. Most of these studies had limited sample sizes and were potentially influenced by recall bias. The estimates for mean, median, and percentiles of the incubation period from these articles are summarized in Table 1.Added value of this studyIn the absence of complete and robust contact-tracing data, we have inferred the distribution of the incubation period of COVID-19 from the durations between departure from Wuhan and symptom onset for the confirmed cases. More than 1000 cases were collected from publicly available data. The proposed approach has a solid theoretical foundation and enhances the accuracy of estimation by reducing recall bias and utilizing a large pool of samples.Implications of all the available evidenceBased on our model, about 10% of patients with COVID-19 do not develop symptoms until 14 days after infection. Further study of individuals with long incubation periods is warranted.