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. 2020 Feb 1;9(2):388.
doi: 10.3390/jcm9020388.

Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-Driven Modelling Analysis of the Early Outbreak

Shi Zhao  1   2 , Salihu S Musa  3 , Qianying Lin  4 , Jinjun Ran  5 , Guangpu Yang  6   7 , Weiming Wang  8 , Yijun Lou  3 , Lin Yang  9 , Daozhou Gao  10 , Daihai He  3 , Maggie H Wang  1   2
Affiliations

Estimating the Unreported Number of Novel Coronavirus (2019-nCoV) Cases in China in the First Half of January 2020: A Data-Driven Modelling Analysis of the Early Outbreak

Shi Zhao et al. J Clin Med. .

Abstract

Background: In December 2019, an outbreak of respiratory illness caused by a novel coronavirus (2019-nCoV) emerged in Wuhan, China and has swiftly spread to other parts of China and a number of foreign countries. The 2019-nCoV cases might have been under-reported roughly from 1 to 15 January 2020, and thus we estimated the number of unreported cases and the basic reproduction number, R0, of 2019-nCoV.

Methods: We modelled the epidemic curve of 2019-nCoV cases, in mainland China from 1 December 2019 to 24 January 2020 through the exponential growth. The number of unreported cases was determined by the maximum likelihood estimation. We used the serial intervals (SI) of infection caused by two other well-known coronaviruses (CoV), Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS) CoVs, as approximations of the unknown SI for 2019-nCoV to estimate R0.

Results: We confirmed that the initial growth phase followed an exponential growth pattern. The under-reporting was likely to have resulted in 469 (95% CI: 403-540) unreported cases from 1 to 15 January 2020. The reporting rate after 17 January 2020 was likely to have increased 21-fold (95% CI: 18-25) in comparison to the situation from 1 to 17 January 2020 on average. We estimated the R0 of 2019-nCoV at 2.56 (95% CI: 2.49-2.63).

Conclusion: The under-reporting was likely to have occurred during the first half of January 2020 and should be considered in future investigation.

Keywords: China; modelling; novel coronavirus; outbreak; reproduction number; underreporting.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The estimates of the unreported cases between 1 and 15 January 2020, the basic reproduction number (R0), and fitting results of the number of 2019-nCoV cases time series. Panel (a) shows the likelihood profile (ℓ, dark green curve) of the estimated number of unreported cases (ξ), and the cutoff threshold (horizontal red dashed line) for the 95% CI. The relationship between the number of unreported cases (ξ) and R0, where the bold curve is the mean estimation, and the dashed curves are the 95% CI of estimated R0. In panels (a,b), the green shading area represents the 95% CI (on the horizontal axis), and the vertical green line represents the maximum likelihood estimate (MLE) of the number of unreported cases. With the MLE of R0 at 2.56, panels (c,d) show the exponential growth fitting results of the cumulative number of cases (Ci) and the daily number of cases (εi) respectively. In panels (c,d), the gold squares are the reported cases, the blue bold curve represents the median of the fitting results, the dashed blue curves are the 95% CI of the fitting results, and the purple shading area represents the time window from 1 to 15 January 2020. In panel (c), the blue dots are the cumulative total, i.e., reported and unreported, number of cases. In panel (d), the grey curves are the 1000 simulation samples.
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