# Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Section

#### 2.1. Data

#### 2.2. The Model

_{q}), isolated exposed (E

_{q}) and isolated infected (I

_{q}) compartments.

_{q}or S

_{q}, depending on whether they are effectively infected or not [20], while the other proportion, 1 − q, consists of individuals exposed to the virus who are missed from the contact tracing and move to the exposed compartment, E, once effectively infected or stay in compartment S otherwise. Let the transmission probability be β and the contact rate be constant c. Then, the quarantined individuals, if infected (or uninfected), move to the compartment E

_{q}(or S

_{q}) at a rate of βcq (or (1 − β)cq). Those who are not quarantined, if infected, will move to the compartment E at a rate of $\mathsf{\beta}\mathrm{c}\left(1-q\right)$. The infected individuals can be detected and then isolated at a rate ${d}_{I}$ and can also move to the compartment R due to recovery.

#### 2.3. Model-Based Method for Estimation

#### 2.4. Likelihood-Based Method for Estimation

#### 2.5. Simulation

## 3. Results

#### 3.1. Likelihood-Based Estimates

#### 3.2. Model-Based Estimates

## 4. Discussion

_{0}= 4.91) in Beijing, China, in 2003 [26], and MERS in Jeddah (R

_{0}= 3.5–6.7) and Riyadh (R

_{0}= 2.0–2.8), Kingdom of Saudi Arabia, in 2014 [27].

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Chen, Y.; Liu, Q.; Guo, D. Coronaviruses: Genome structure, replication, and pathogenesis. J. Med. Virol.
**2020**. [Google Scholar] [CrossRef] [PubMed] - Kahn, J.S.; McIntosh, K. History and recent advances in coronavirus discovery. Pediatr. Infect. Dis. J.
**2005**, 24, S223–S227. [Google Scholar] [CrossRef] [PubMed] - Hui, D.S.C.; Zumla, A. Severe acute respiratory syndrome: Historical, epidemiologic, and clinical features. Infect. Dis. Clin. North Am.
**2019**, 33, 869–889. [Google Scholar] [CrossRef] [PubMed] - de Wit, E.; van Doremalen, N.; Falzarano, D.; Munster, V.J. SARS and MERS: Recent insights into emerging coronaviruses. Nat. Rev. Microbiol.
**2016**, 14, 523–534. [Google Scholar] [CrossRef] - Killerby, M.E.; Biggs, H.M.; Midgley, C.M.; Gerber, S.I.; Watson, J.T. Middle East respiratory syndrome coronavirus transmission. Emerg. Infect. Dis.
**2020**, 26, 191–198. [Google Scholar] [CrossRef] [Green Version] - Kim, K.H.; Tandi, T.E.; Choi, J.W.; Moon, J.M.; Kim, M.S. Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, 2015: Epidemiology, characteristics and public health implications. J. Hosp. Infect.
**2017**, 95, 207–213. [Google Scholar] [CrossRef] [Green Version] - Willman, M.; Kobasa, D.; Kindrachuk, J. A Comparative analysis of factors influencing two outbreaks of middle eastern respiratory syndrome (MERS) in Saudi Arabia and South Korea. Viruses
**2019**, 11, 1119. [Google Scholar] [CrossRef] [Green Version] - Kwok, K.O.; Tang, A.; Wei, V.W.I.; Park, W.H.; Yeoh, E.K.; Riley, S. Epidemic models of contact tracing: Systematic review of transmission studies of severe acute respiratory syndrome and Middle East respiratory syndrome. Comput. Struct. Biotechnol. J.
**2019**, 17, 186–194. [Google Scholar] [CrossRef] - Cohen, J.; Normile, D. New SARS-like virus in China triggers alarm. Science
**2020**, 367, 234–235. [Google Scholar] [CrossRef] - Lu, H.; Stratton, C.W.; Tang, Y.W. Outbreak of pneumonia of unknown etiology in Wuhan China: The mystery and the miracle. J. Med. Virol.
**2020**. [Google Scholar] [CrossRef] [Green Version] - Parry, J. China coronavirus: Cases surge as official admits human to human transmission. BMJ
**2020**, 368, m236. [Google Scholar] [CrossRef] [PubMed] [Green Version] - World Health Organization (WHO). Coronavirus. Available online: https://www.who.int/health-topics/coronavirus (accessed on 23 January 2020).
- Egger, M.; Johnson, L.; Althaus, C.; Schöni, A.; Salanti, G.; Low, N.; Norris, S.L. Developing WHO guidelines: Time to formally include evidence from mathematical modelling studies. F1000Research
**2017**, 6, 1584. [Google Scholar] [CrossRef] [PubMed] - Chen, T.; Rui, J.; Wang, Q.; Zhao, Z.; Cui, J.-A.; Yin, L. A mathematical model for simulating the transmission of Wuhan novel coronavirus. bioRxiv
**2020**. [Google Scholar] [CrossRef] - Imai, N.; Dorigatti, I.; Cori, A.; Donnelly, C.; Riley, S.; Ferguson, N.M. Report 2: Estimating the Potential Total Number of Novel Coronavirus Cases in Wuhan City, China. Available online: https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/2019-nCoV-outbreak-report-22-01-2020.pdf (accessed on 23 January 2020).
- World Health Organization (WHO). Novel Coronavirus—China, Disease Outbreak News: Update. Available online: https://www.who.int/csr/don/12-january-2020-novel-coronavirus-china/en/ (accessed on 23 January 2020).
- World Health Organization (WHO). Situation Report. Available online: https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200123-sitrep-3-2019-ncov.pdf (accessed on 23 January 2020).
- Health Commission of Hubei Province. Available online: http://wjw.hubei.gov.cn/bmdt/ztzl/fkxxgzbdgrfyyq/ (accessed on 23 January 2020).
- National Health Commission of the People’s Republic of China. Available online: http://www.nhc.gov.cn/xcs/xxgzbd/gzbd_index.shtml (accessed on 23 January 2020).
- Castillo-Chavez, C.; Castillo-Garsow, C.W.; Yakubu, A. Mathematical models of isolation and quarantine. JAMA
**2003**, 290, 2876–2877. [Google Scholar] [CrossRef] [Green Version] - Tang, S.; Xiao, Y.; Yang, Y.; Zhou, Y.; Wu, J.; Ma, Z. Community-based measures for mitigating the 2009 H1N1 pandemic in China. PLoS ONE
**2010**, 5, e10911. [Google Scholar] [CrossRef] [Green Version] - Xiao, Y.; Tang, S.; Wu, J. Media impact switching surface during an infectious disease outbreak. Sci. Rep.
**2015**, 5, 7838. [Google Scholar] [CrossRef] - White, L.F.; Pagano, M. A likelihood-based method for real-time estimation of the serial interval and reproductive number of an epidemic. Stat. Med.
**2008**, 27, 2999–3016. [Google Scholar] [CrossRef] [Green Version] - World Health Organization (WHO). Available online: https://www.who.int/news-room/detail/23-01-2020-statement-on-the-meeting-of-the-international-health-regulations-(2005)-emergency-committee-regarding-the-outbreak-of-novel-coronavirus-(2019-ncov) (accessed on 23 January 2020).
- Bogoch, I.I.; Watts, A.; Thomas-Bachli, A.; Huber, C.; Kraemer, M.U.G.; Khan, K. Pneumonia of unknown etiology in Wuhan, China: Potential for international spread via commercial air travel. J. Travel Med.
**2020**. [Google Scholar] [CrossRef] - Gumel, A.B.; Ruan, S.G.; Day, T.; Watmough, J.; Brauer, F.; van den Driessche, P.; Gabrielson, D.; Bowman, C.; Alexander, M.E.; Ardal, S.; et al. Modelling strategies for controlling SARS outbreaks. Proc. R. Soc. Lond. B.
**2004**, 271, 2223–2232. [Google Scholar] [CrossRef] - Majumder, M.S.; Rivers, C.; Lofgren, E.; Fisman, D. Estimation of MERS-Coronavirus reproductive number and case fatality rate for the Spring 2014 Saudi Arabia outbreak: Insights from publicly available data. PLoS Curr.
**2014**, 18, 6. [Google Scholar] - Li, Q.; Guan, X.; Wu, P.; Wang, X.; Zhou, L.; Tong, Y.; Ren, R.; Leung, K.S.M.; Lau, E.H.Y.; Wong, J.Y.; et al. Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. N. Engl. J. Med.
**2020**. [Google Scholar] [CrossRef] [PubMed] - Zhao, S.; Lin, Q.; Ran, J.; Musa, S.S.; Yang, G.; Wang, W.; Lou, Y.; Gao, D.; Yang, L.; He, D.; et al. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak. Int. J. Infect. Dis.
**2020**. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Guerra, F.M.; Bolotin, S.; Lim, G.; Heffernan, J.; Deeks, S.L.; Li, Y.; Crowcroft, N.S. The basic reproduction number (R0) of measles: A systematic review. Lancet Infect. Dis.
**2017**, 17, e420–e428. [Google Scholar] [CrossRef] - Rothe, C.; Schunk, M.; Sothmann, P.; Bretzel, G.; Froeschl, G.; Wallrauch, C.; Zimmer, T.; Thiel, V.; Janke, C.; Guggemos, W.; et al. Transmission of 2019-nCoV infection from an asymptomatic contact in Germany. N. Engl. J. Med.
**2020**. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hui, D.S.; Azhar, E.E.I.; Madani, T.A.; Ntoumi, F.; Kock, R.; Dar, O.; Ippolito, G.; Mchugh, T.D.; Memish, Z.A.; Drosten, C.; et al. The continuing 2019-nCoV epidemic threat of novel coronaviruses to global health-The latest 2019 novel coronavirus outbreak in Wuhan, China. Int. J. Infect. Dis.
**2020**, 91, 264–266. [Google Scholar] [CrossRef] [Green Version] - Cheng, V.C.C.; Wong, S.C.; To, K.K.W.; Ho, P.L.; Yuen, K.Y. Preparedness and proactive infection control measures against the emerging Wuhan coronavirus pneumonia in China. J. Hosp. Infect.
**2020**. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**(

**A**) Cumulative diagnoses and revised case data (dataRev1) in mainland China, the blue curve is the best fitting curve of model (1) to dataRev1. (

**B**) Data information of cumulative quarantined/released population.

**Figure 2.**Diagram of the model adopted in the study for simulating the novel coronavirus (2019-nCoV) infection. Interventions including intensive contact tracing followed by quarantine and isolation are indicated.

**Figure 3.**Sensitivity analyses with respect to contact rate, c (

**A**,

**B**), and quarantine rate, q (

**C**,

**D**), on the log number of infected individuals and cumulative reported cases.

**Figure 4.**Contour plot of R_c, with the parameter of baseline transmission probability and the contact rate, c (

**A**), or the quarantine rate, q (

**B**). (

**B**) shows that a higher transmission probability of the virus will significantly increase the basic reproduction number.

**Figure 6.**The effects of no travel restrictions (

**A**) versus travel restriction (

**B**) in the Hubei Province on the Coronavirus disease in Beijing city.

Parameter | Definitions | Estimated Mean Value | Standard Deviation | Data Source |

$c$ | Contact rate | $14.781$ | $0.904$ | MCMC |

$\beta $ | Probability of transmission per contact | $2.1011\times {10}^{-8}$ | $1.1886\times {10}^{-9}$ | MCMC |

$q$ | Quarantined rate of exposed individuals | $1.8887\times {10}^{-7}$ | $6.3654\times {10}^{-8}$ | MCMC |

$\sigma $ | Transition rate of exposed individuals to the infected class | $1/7$ | – | WHO |

$\lambda $ | Rate at which the quarantined uninfected contacts were released into the wider community | $1/14$ | – | [18,19] |

$\varrho $ | Probability of having symptoms among infected individuals | $0.86834$ | $0.049227$ | MCMC |

${\delta}_{I}$ | Transition rate of symptomatic infected individuals to the quarantined infected class | $0.13266$ | $0.021315$ | MCMC |

${\delta}_{q}$ | Transition rate of quarantined exposed individuals to the quarantined infected class | $0.1259$ | $0.052032$ | MCMC |

${\gamma}_{I}$ | Recovery rate of symptomatic infected individuals | $0.33029$ | $0.052135$ | MCMC |

${\gamma}_{A}$ | Recovery rate of asymptomatic infected individuals | $0.13978$ | $0.034821$ | MCMC |

${\gamma}_{H}$ | Recovery rate of quarantined infected individuals | $0.11624$ | $0.038725$ | MCMC |

$\alpha $ | Disease-induced death rate | $1.7826\times {10}^{-5}$ | $6.8331\times {10}^{-6}$ | MCMC |

Initial Values | Definitions | Estimated Mean Value | Standard Deviation | Data Source |

$S\left(0\right)$ | Initial susceptible population | $11,081,000$ | – | [18] |

$E\left(0\right)$ | Initial exposed population | $105.1$ | $35.465$ | MCMC |

$I\left(0\right)$ | Initial symptomatic infected population | $27.679$ | $11.551$ | MCMC |

$A\left(0\right)$ | Initial asymptomatic infected population | $53.839$ | $25.25$ | MCMC |

${S}_{q}\left(0\right)$ | Initial quarantined susceptible population | $739$ | – | [18] |

${E}_{q}\left(0\right)$ | Initial quarantined exposed population | $1.1642$ | $0.20778$ | MCMC |

$H\left(0\right)$ | Initial quarantined infected population | $1$ | – | [18] |

$R\left(0\right)$ | Initial recovered population | $2$ | – | [18] |

R_{0} | V = 2 (dataRev1) | V = 3 (dataRev1) | V = 2 (dataRev2) | V = 3 (dataRev2) |
---|---|---|---|---|

E = 2 | 1.4546 | 1.6560 | 1.4545 | 1.6554 |

E = 3 | 1.7459 | 1.7155 | 1.7456 | 1.7145 |

E = 4 | 2.5828 | 2.4462 | 2.5815 | 2.4427 |

E = 5 | 3.9893 | 3.7134 | 3.9802 | 3.6956 |

E = 6 | 6.3901 | 5.8303 | 6.3164 | 5.7304 |

E = 7 | 10 | 9.2564 | 9.6409 | 8.7299 |

E = 8 | 10 | 10 | 10 | 10 |

$\mathbf{Parameter}\text{}\mathit{c}$ | $\mathit{c}$ | $0.8\mathit{c}$ | $0.5\mathit{c}$ | $0.3\mathit{c}$ | $0.1\mathit{c}$ |
---|---|---|---|---|---|

Peak Time | $19.3$ days | $22.6$ days | $33.8$ days | $61.3$ days | $3.4$ days |

Value of $I$ at peak time | $1.63\times {10}^{5}$ | $1.5\times {10}^{5}$ | $1.15\times {10}^{5}$ | $6.68\times {10}^{4}$ | $2.42\times {10}^{3}$ |

Parameter $q$ | $q$ | $5q$ | $10q$ | $15q$ | $20q$ |

Peak time | $19.3$ days | $15.1$ days | $12.8$ days | $11.4$ days | $10.3$ days |

Value of $I$ at peak time | $1.63\times {10}^{5}$ | $3.76\times {10}^{4}$ | $1.98\times {10}^{4}$ | $1.38\times {10}^{4}$ | $1.08\times {10}^{4}$ |

^{−7}).

Date | 01/23 | 01/24 | 01/25 | 01/26 | 01/27 | 01/28 | 01/29 |
---|---|---|---|---|---|---|---|

Predicted confirmed cases | 876 | 1266 | 1828 | 2634 | 3784 | 5419 | 7723 |

Predicted confirmed cases (reduced contact by 50%) | 868 | 1207 | 1624 | 2128 | 2736 | 3464 | 4335 |

Predicted confirmed cases (reduced contacts by 90%) | 862 | 1163 | 1480 | 1802 | 2120 | 2430 | 2731 |

Real data of confirmed cases | 830 | 1287 | 1975 | 2744 | 4515 | 5974 | 7711 |

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**MDPI and ACS Style**

Tang, B.; Wang, X.; Li, Q.; Bragazzi, N.L.; Tang, S.; Xiao, Y.; Wu, J.
Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. *J. Clin. Med.* **2020**, *9*, 462.
https://doi.org/10.3390/jcm9020462

**AMA Style**

Tang B, Wang X, Li Q, Bragazzi NL, Tang S, Xiao Y, Wu J.
Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions. *Journal of Clinical Medicine*. 2020; 9(2):462.
https://doi.org/10.3390/jcm9020462

**Chicago/Turabian Style**

Tang, Biao, Xia Wang, Qian Li, Nicola Luigi Bragazzi, Sanyi Tang, Yanni Xiao, and Jianhong Wu.
2020. "Estimation of the Transmission Risk of the 2019-nCoV and Its Implication for Public Health Interventions" *Journal of Clinical Medicine* 9, no. 2: 462.
https://doi.org/10.3390/jcm9020462