# Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Ingredients

- (i)
- We estimate the cumulative number of cases in China outside Hubei province after 23 January, using a time-dependent compartmental model of the transmission dynamics.
- (ii)
- We use that number as an input to the global transportation network to generate probability distributions of the number of infected travellers arriving at destinations outside China.
- (iii)
- In a destination country, we use a Galton–Watson branching process to model the initial spread of the virus. We calculate the extinction probability of each branch initiated by a single imported case, obtaining the probability of a major outbreak as the probability that at least one branch will not go extinct.

#### 2.2. Epidemic Size in China Outside the Closed Areas of Hubei

#### 2.3. Connectivity and Case Exportation

#### 2.4. Probability of a Major Outbreak in a Country by Imported Cases

#### 2.5. Dependence of the Risk of Major Outbreaks on Key Parameters

## 3. Results

#### 3.1. Epidemic Size in China

#### 3.2. Risk of Major Outbreaks

#### 3.3. Profile of Countries Benefiting the Most From Interventions

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Transmission Dynamics

## Appendix B. Calculating the Risk of Outbreaks by Importation

Parameter | Interpretation | Depends on … | Typical Range |
---|---|---|---|

C | Cumulative case number in China, outside the closed areas | properties of nCoV-2019, efficacy of Chinese control | $[100K,6000K]$ |

${R}_{\mathrm{loc}}$ | Local reproduction number in destination country | destination country | $[1,2.6]$ |

$\theta $ | Probability of a importation chance that a case from the origin travelling to and mixing into the local population of the destination country | China and destination country | $[0,0.00025]$ |

## Appendix C.

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**Figure 1.**Final epidemic sizes in China, outside Hubei, with ${R}_{0}=2.1,2.6,3.1$, as a function of the time when the control function $u\left(t\right)$ reaches its maximum (in days after 23 January). Rapid implementation of the control generates much smaller case numbers. The inset shows the estimations of the ascertainment rate for the week 25–31, with average $0.063$, based on the ratio of confirmed cases and the maximum likelihood estimates of the case numbers from exportation.

**Figure 2.**(

**Left**) Risk of major outbreaks as a function of cumulative number of cases in selected countries, assuming ${R}_{\mathrm{loc}}=1.6$ and baseline connectivity to China. Other countries in South America, including Mexico, are inside the green shaded area. (

**Right**) The effects of reductions of imported case numbers (either by travel restriction or entry screening) in the USA and Canada, assuming ${R}_{\mathrm{loc}}=1.4$.

**Figure 3.**Outbreak risks for highly connected countries in Asia. Thailand and the Republic of Korea are plotted; the curves for Japan and Taiwan are in between them. (

**Left**) We plot the risk vs. the efficacy of prevented importations when the cumulative number of cases reaches 150,000. (

**Right**) C = 600,000. Black parts of the curves represent situations when the four countries are indistinguishable.

**Figure 4.**Selected European countries with high, medium, and low connectivity to China. (

**Left**) The outbreak risk is plotted assuming their baseline connectivity $\theta $, and ${R}_{\mathrm{loc}}=1.4$ for each country, as the cumulative number of cases is increasing. A significant reduction in the risks can be observed (

**Right**), where we reduced ${R}_{\mathrm{loc}}$ to 1.1 and assumed a 50% reduction in importations.

**Figure 5.**Heatmap of the outbreak risks as functions of $\theta $ and ${R}_{\mathrm{loc}}$, when C = 200,000. The arrows show the directions corresponding to the largest reductions in the risk.

**Table 1.**Published estimates of the key epidemiological parameters of 2019-nCoV. Uncertainty range is given where provided.

${\mathit{R}}_{0}$ | Incubation Period | Method of Estimation | Reference |
---|---|---|---|

2.6 (1.5–3.5) | - | Epidemic Simulations | [19] |

2.2 (1.4–3.8) | - | Stochastic Simulations | [20] |

2.9 (2.3–3.6) | 4.8 days | Exp. Growth, Max. Likelihood Est. | [21] |

2.56 (2.49–2.63) | - | Exp. Growth, Max. Likelihood Est. | [17] |

3.11 (2.3–4.1) | - | SEIR | [22] |

2.5 (2.0–3.1) | - | Incidence Decay and Exponential Adjustment model | [23] |

2.2 (1.4–3.9) | 5.2 days (4.1–7.0) | Renewal Equations | [24] |

−(1.4–4.0) | - | SEIR | [25] |

4.71 (4.5–4.9) | $5.0$ days ($4.9$–$5.1$) | Dec. 2019, SEIJR, MCMC | [26] |

2.08 (1.9–2.2) | - | Jan. 2020, SEIJR, MCMC | [26] |

2.68 (2.4–2.9) | - | SEIR, MCMC | [27] |

- | 5.8 days 4.6–7.9) | Weibull | [28] |

- | 4.6 days (3.3–5.8) | Weibull incl. Wuhan | [29] |

- | 5.0 days (4.0–5.8) | Weibull excl. Wuhan | [29] |

- | 5.1 days (4.4–6.1) | LogNormal | [30] |

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**MDPI and ACS Style**

Boldog, P.; Tekeli, T.; Vizi, Z.; Dénes, A.; Bartha, F.A.; Röst, G.
Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China. *J. Clin. Med.* **2020**, *9*, 571.
https://doi.org/10.3390/jcm9020571

**AMA Style**

Boldog P, Tekeli T, Vizi Z, Dénes A, Bartha FA, Röst G.
Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China. *Journal of Clinical Medicine*. 2020; 9(2):571.
https://doi.org/10.3390/jcm9020571

**Chicago/Turabian Style**

Boldog, Péter, Tamás Tekeli, Zsolt Vizi, Attila Dénes, Ferenc A. Bartha, and Gergely Röst.
2020. "Risk Assessment of Novel Coronavirus COVID-19 Outbreaks Outside China" *Journal of Clinical Medicine* 9, no. 2: 571.
https://doi.org/10.3390/jcm9020571