Trump: “This came unexpectedly, it came out of China, we closed it down, we stopped it, it was a very early shut down,” he told reporters this morning. Trump’s chief economic adviser, Larry Kudlow, declared on CNBC, “I would still argue to you that this thing is contained.”
International Journal of Infectious Disease,
Shi Zhao1,2,*, Qianyin Lin3 , Jinjun Ran4 , Salihu S Musa5 , Guangpu Yang6,7 , Weiming Wang8 , Yijun Lou5 , Daozhou Gao9 , Lin Yang10 , Daihai He5,*, and Maggie H Wang1,2
1 JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China
2 Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China
3 Michigan Institute for Data Science, University of Michigan, Ann Arbor, Michigan, USA
4 School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China
5 Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
6 Department of Orthopaedics and Traumatology, Chinese University of Hong Kong, Hong Kong, China
7 SH Ho Scoliosis Research Lab, Joint Scoliosis Research Center of Chinese University of Hong Kong and Nanjing University, Hong Kong, China
8 School of Mathematics and Statistics, Huaiyin Normal University, Huaian, China
9 Department of Mathematics, Shanghai Normal University, Shanghai, China
10 School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
The basic reproduction number of novel coronavirus (2019-nCoV) estimation based on exponential growth in the early outbreak in China from 2019 to 2020: A reply to Dhungana
Main text To the editor The ongoing outbreak of the novel coronavirus (2019-nCoV) pneumonia in Wuhan, China and other regions remains a major public health concern. We thank Dhungana’s comments to our study, Zhao et al. , recently published in the International Journal of Infectious Diseases. The estimates on the basic reproduction number, R0, were carried out in early outbreak as of January 22, 2020 when the surveillance data and the knowledge on the key epidemiological features of 2019-nCoV were limited. The assumptions of exponential growth as well as other similar growing patterns are commonly accepted and adopted to capture the growing trends during the early phase of an outbreak [2-4]. The exponential growing rate (γ), or the intrinsic growing rate, is estimated from the early epidemic curve and used to calculate the R0. We repeat the analysis in Zhao et al. , γ is estimated at 0.18 (95%CI: 0.14−0.22), 0.15 (95%CI: 0.12−0.18) and 0.11 (95%CI: 0.09−0.13) per day associated with 2-, 4- and 8-fold increase in the reporting rate, respectively. By using the serial interval (SI) estimate (mean ± SD at 7.5 ± 3.4 days) from Li et al. , we found the R0 at 3.33 (95%CI: 2.17−4.04), 2.69 (95%CI: 2.28−3.17) and 2.13 (95%CI: 1.88−2.42) associated with 2-, 4- and 8-fold increase in the reporting respectively. Our estimates were in line with the WHO estimates in both early version (2-fold case) and the published version. The key message as we highlighted in the paper is the changes in reporting rate. This is recently reconfirmed by Tuite and Fishman . We thank the editor and Dhungana to give us this opportunity to reclarify our key message that the reporting rate was not constant during the early outbreak and could affect the estimation of R0. There is indeed a large amount of later confirmed cases which were not counted in the early official daily situation reports [5, 7-9]. In other words, if the same reporting standard in the second half of January was applied to the first half of January, the number of cases would be much higher. Other teams either used retrospective dataset which was not publicly available on January 23, 2020 or used oversea reported cases which was not (to a much less extent) affected by the changes in reporting rate. By using the same analysis and dataset as in Zhao et al. , an additional sensitivity analysis on the R0 estimates and varying SI and reporting rate was conducted and shown in Fig 1. We report that R0 estimates increase while the mean of SI increases or the SD of SI decreases. By selecting mean between 7 and 8 days and SD between 3 and 4 days for SI of 2019-nCoV, the R0 estimates are largely consistent within a range from 2 to 4 in many existing literatures [5, 7-10], see panels (f), (g), (j) and (k) Fig 1. We conclude that our previous estimation and main conclusions in  hold based on the reasonable selection of the SI estimates of 2019-nCoV. Not only our early version (2-fold case) is in line with the WHO estimates, but also we pointed out the issue in the reporting rate changes in the official reported cases.
What is exponential growth?