# 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

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**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