# Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Epidemiological Data

#### 2.2. Estimation of the Delay Distributions

_{0}is the expected number of infected cases at time t = 0. The cumulative incidence I(t) is an integral of i(t) over the time interval from zero to t that can be written as $I\left(t\right)={{\displaystyle \int}}_{0}^{t}i\left(s\right)\mathrm{d}s={i}_{0}\left({e}^{rt}-1\right)/r$. The cumulative incidence is adjusted to the date of report by the factor u dependent on the parameters of the delay distribution. For the estimation of time delay distribution from illness onset to death, we accounted for right truncation and modeled and used a lognormal distribution with parameters adopted from an earlier study [14]. Let $f\left(t;\theta \right)$ be the lognormal distribution with parameters ${\theta}_{d}=\left\{{a}_{d},{b}_{d}\right\}$. Then, the cumulative incidence I(t) by date of report t can be adjusted to the time from illness onset to death and report by simply multiplying it by the factor $u\left(r,{\theta}_{d}\right)$, which is a consequence of the exponentially growing epidemic [10]. The factor u is defined by the following integral:

#### 2.3. Statistical Inference

## 3. Results

## 4. Discussion

_{0}> 1 does not guarantee that a single exported (and untraced) case would immediately lead to a major epidemic in the destination country as government responses such as border control, isolation of suspected cases, and intensive surveillance should serve to reduce opportunities for transmission to occur [17,18,19].

_{0}to be 1.6–4.2, endorsing the notion that COVID-19 infection in the ongoing epidemic possesses the potential to become a pandemic. The proposed approach can also help direct risk assessment in other settings with the use of publicly available datasets.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Estimates of the mean and standard deviation (SD) of the time from illness onset to reporting and death cases, accounting for right truncation, with novel coronavirus (COVID-19) infection in China, 2020. Inference of A and B was conducted among (

**A**) exported cases observed in other countries and (

**B**) deceased cases in China. (

**A**) Frequency distribution of the time from illness onset to reporting among exported cases employing a gamma distribution with a mean of 7.1 days (95% confidence interval [CI]: 5.9, 8.4) and SD of 4.4 days (95% CI: 3.5, 5.7). (

**B**) Frequency distribution of the time from illness onset to death with a mean of 19.9 days (95% CI: 14.9, 29.0) (shown in black) and SD of 11.4 days (95% CI: 6.5, 21.6) employing a lognormal distribution and accounting for right truncation. For reference, the estimate of the mean and its 95% credible intervals without accounting for right truncation are shown in grey. The values for distribution of time from illness onset to death are adopted from an earlier study [14]. The blue bars show empirically observed data collected from governmental reports (as of 24 January 2020).

**Figure 2.**Cumulative incidence and the confirmed case fatality risk of the novel coronavirus (COVID-19) outbreak in China, 2020. (

**A**,

**B**) Observed and estimated cumulative number of cases in China by the date of report. An exponential growth curve was extrapolated using the exported case data. Scenario 1 extrapolated the exponential growth from December to first case on 8 December 2019, while Scenario 2 started the estimation of the exponential growth only from 13 January 2020. The black line and shaded area represent median and 95% credible interval of the cumulative incidence in China, respectively. The blue bars show the cumulative number of reported cases from the government of mainland China. The cumulative number of reported cases was not used for fitting, but it was shown for comparison between the cumulative number of reported and estimated cases in China. There is a decrease in the cumulative number of reported cases in early January, because only 41 cases tested positive for the novel coronavirus among the reported 59 cases on 10 January 2020. Left-top panels on both

**A**and

**B**show the cumulative numbers of exported cases observed in other countries and the cumulative number of deaths in China, represented by dark and light green bars, respectively. (

**C**,

**D**) Confirmed case fatality risk (cCFR) by the date of reporting. Each value of cCFR was estimated as the ratio of cumulative number of estimated incidence to death at time t. The points and error bars represent the median and its 95% credible interval of the cCFR. All 95% credible intervals were derived from Markov chain Monte Carlo simulations.

**Figure 3.**Basic reproduction number of novel coronavirus (COVID-19) infections in China, 2020. Black lines and grey shades represent the median and 95% credible intervals of the basic reproduction number. Panel

**A**shows the result of Scenario 1, in which an exponential growth started from the assumed illness onset date of index case, while Panel

**B**shows the result from exponential growth from the first exported case (Scenario 2). The 95% credible intervals were derived from Markov chain Monte Carlo method.

Importing Locations | Date of Report (2020) | Cumulative Count | Estimated Incidence in China (95% CI) | |
---|---|---|---|---|

Scenario 1 | Scenario 2 | |||

Thailand | 13 January | 1 | 1828 (1397 2288) | 1369 (1003 1782) |

Japan | 16 January | 2 | 2120 (1605 2672) | 1829 (1392 2309) |

Thailand | 17 January | 3 | 2458 (1845 3119) | 2444 (1894 3033) |

South Korea | 20 January | 4 | 3832 (2802 4962) | 5882 (4252 7629) |

Taiwan, United States | 21 January | 6 | 4443 (3220 5792) | 7901 (5425, 10,662) |

Thailand | 22 January | 8 | 5151 (3700 6761) | 10,626 (6897, 15,003) |

Singapore, Vietnam | 23 January | 11 | 5972 (4252 7892) | 14,308 (8661, 21,250) |

Japan, Nepal, South Korea, Singapore, Thailand, United States | 24 January | 20 | 6924 (4885 9211) | 19,289 (10,901, 30,158) |

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## Share and Cite

**MDPI and ACS Style**

Jung, S.-m.; Akhmetzhanov, A.R.; Hayashi, K.; Linton, N.M.; Yang, Y.; Yuan, B.; Kobayashi, T.; Kinoshita, R.; Nishiura, H. Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases. *J. Clin. Med.* **2020**, *9*, 523.
https://doi.org/10.3390/jcm9020523

**AMA Style**

Jung S-m, Akhmetzhanov AR, Hayashi K, Linton NM, Yang Y, Yuan B, Kobayashi T, Kinoshita R, Nishiura H. Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases. *Journal of Clinical Medicine*. 2020; 9(2):523.
https://doi.org/10.3390/jcm9020523

**Chicago/Turabian Style**

Jung, Sung-mok, Andrei R. Akhmetzhanov, Katsuma Hayashi, Natalie M. Linton, Yichi Yang, Baoyin Yuan, Tetsuro Kobayashi, Ryo Kinoshita, and Hiroshi Nishiura. 2020. "Real-Time Estimation of the Risk of Death from Novel Coronavirus (COVID-19) Infection: Inference Using Exported Cases" *Journal of Clinical Medicine* 9, no. 2: 523.
https://doi.org/10.3390/jcm9020523