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

Background: The 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. Methods: We 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. Findings: The 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. Interpretation: Based 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.

Estimating the daily trend in the size of the COVID-19 infected population in Wuhan (preprint)

There has been an outbreak of coronavirus disease (COVID-19) in Wuhan city, Hubei province, China since December 2019. Cases have been exported to other parts of China and many other countries. We provide estimates of the daily trend in the size of the epidemic in Wuhan based on detailed information of 10,940 confirmed cases outside Hubei province. In this modelling study, we first estimate the epidemic size in Wuhan from January 11, 2020, to February 13, 2020, based on the confirmed cases outside Hubei province that left Wuhan by January 23, 2020. Since some confirmed cases have no information on whether they visited Wuhan before, we adjust for these missing values. We then calculate the reporting rate in Wuhan from January 20, 2020, to February 13, 2020. Finally, we estimate the date when the first patient was infected. We estimate the number of cases that should be reported in Wuhan by January 11, 2020, is 4,094 (95% confidence interval [CI]: 3,980 – 4,211) and 58,153 (95% CI: 56,532 – 59,811) by February 13, 2020. The reporting rate has grown rapidly from 1.41% (95% CI: 1.37% - 1.45%) on January 20, 2020, to 32.15% (95% CI: 31.26% - 33.07%) on February 11, 2020, and reaches 61.89% (95% CI: 60.17% - 63.66%) on February 13, 2020. The date of first infection is estimated as November 30, 2019. The estimated reporting rate has increased rapidly to over 60% on February 13, 2020, mainly because the inclusion of 14,031 clinically diagnosed cases in the case reports of Wuhan. This might indicate that clinical diagnosis could be a good complement to the current method of confirmation. The currently reported number of 35,991 cases as of February 13, 2020, is still far below our estimate of 58,153. There may still be a lot of unreported cases. More thorough screening of all patients with a mild or moderate symptoms of respiratory diseases should be conducted to better control the spread of COVID-19.

Estimating the daily trend in the size of COVID-19 infected population in Wuhan (preprint)

There has been an outbreak of coronavirus disease (COVID-19) in Wuhan city, Hubei province, China since December 2019. Cases have been exported to other parts of China and more than 20 countries. We provide estimates of the daily trend in the size of the epidemic in Wuhan based on detailed information of 10,940 confirmed cases outside Hubei province.

Estimation of the Time-Varying Reproduction Number of 2019-nCoV Outbreak in China (preprint)

Background: The 2019-nCoV outbreak in Wuhan, China has attracted world-wide attention. As of February 11, 2020, a total of 44730 cases of novel coronavirus-infected pneumonia associated with COVID-19 were confirmed by the National Health Commission of China. Methods: Three approaches, namely Poisson likelihood-based method (ML), exponential growth rate-based method (EGR) and stochastic Susceptible-Infected-Removed dynamic model-based method (SIR), were implemented to estimate the basic and controlled reproduction numbers. Results: A total of 71 chains of transmission together with dates of symptoms onset and 67 dates of infections were identified among 5405 confirmed cases outside Hubei as reported by February 2, 2020. Based on this information, we find the serial interval having an average of 4.41 days with a standard deviation of 3.17 days and the infectious period having an average of 10.91 days with a standard deviation of 3.95 days. Conclusions: The controlled reproduction number is declining. It is lower than one in most regions of China, but is still larger than one in Hubei Province. Sustained efforts are needed to further reduce the Rc to below one in order to end the current epidemic.