Estimation of incubation period distribution of COVID-19 using disease onset forward time: a novel cross-sectional and forward follow-up study

Qin Jing; Chong You; Qiushi Lin; Taojun Hu; Shicheng Yu; Xiao-Hua Zhou

Based on the COVID-19 daily updates from provincial and municipal health commissions in China, we notice that there is an abundance of cases who asymptomatically left Wuhan, the epicenter of COVID-19, and developed symptoms outside Wuhan. Assuming that these cases were infected before their departure from Wuhan, the time differences between departure and symptoms onset is the censored observations of their incubation periods. Hence, we conducted a cross-sectional and forward follow-up study by assuming to catch those asymptomatic individuals at their departure time and followed them until their symptoms developed. Using the language of renewal processes, we can treat the development of the disease starting from infection by a pathogen as a stochastic process that could be observed from a specific time point in chronological order. In this study, the specific time point refers to the time of departure from Wuhan. For each prevalent case, the complete process from the infection to the onset of symptoms can be considered as a renewal process. As illustrated in Figure 1 , the backward recurrence time is hence defined as the time between infection and departure from Wuhan, and the forward recurrence time is the time between departure from Wuhan and symptom onset. Clearly, the forward time is observable and the corresponding observations are with good veracity, while the backward time is either unable to be observed or the corresponding observations are with large uncertainty due to recall bias. Note that for each infected individual, the backward time and forward time do not have to be same. However, when the renewal process reaches its equilibrium status, it becomes reversible, that is, the statistical properties of this process is the same as the one for time-reversed data in a same process. Hence, at equilibrium, the backward time can be treated as the forward time if time periods are reversed. 19 In order to model incubation using the renewal process properly, the following assumptions are established: