# Assessing the Impact of Reduced Travel on Exportation Dynamics of Novel Coronavirus Infection (COVID-19)

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Epidemiological Data

#### 2.2. Statistical Model

#### 2.2.1. Reduced Number of Exported Cases

#### 2.2.2. Reduced Probability of a Major Epidemic Overseas

_{0}, i.e., the average number of secondary cases generated by a single primary case, and the dispersion parameter k. The probability of extinction $\pi $ defined by the first generating moment [15] is then modeled as:

_{0}is estimated to range from 1.5 to 3.7, and here we adopt 1.5, 2.2, and 3.7 as plausible values for our calculations [16,17,18]. The value of k, a dispersion parameter, is assumed to be 0.54 as estimated elsewhere [17].

#### 2.2.3. Time Delay to a Major Epidemic Gained from the Reduction in Travel Volume

_{d}= ln(2)/r = 4.95 days. The difference in the median date between (8) and (9) is thus described as:

## 3. Results

_{0}of 1.5, 2.2, or 3.7, and three different levels of contact tracing resulting in a success rate of isolation of the traced contacts of 10%, 30%, or 50%. Without the reduction in the travel volume, the probability of a major epidemic exceeded 90% in most scenarios. However, considering there have been six untraced cases in Japan under travel restrictions, the probability of a major epidemic more broadly ranged from 56% to 98%. Figure 3B shows the reduced probability of a major epidemic. Assuming an R

_{0}of 2.2, the absolute risk reduction was 7%, 12%, and 20%, respectively, for contact tracing levels leading to isolation at 10%, 30%, and 50%.

_{0}= 1.5 and 50% of contacts were traced. The smallest reduction was 1% when R

_{0}= 3.7 and 10% of contacts were traced. Using those estimated relative reductions, the median time of delay gained by travel volume reduction is shown in Figure 4. The time delay of a major epidemic was less than one day when R

_{0}is 2.2 and 3.7, and 1 to 2 days when R

_{0}is 1.5.

## 4. Discussion

_{0}at 1.5, 2.2, and 3.7. With reduced probability of a major epidemic, the time delay to a major epidemic was estimated at a maximum of 2 days in Japan and a minimum of less than 1 day. The estimated effect of the delay to a major epidemic outside China is smaller than what was anticipated for cities in China other than Wuhan. Tian et al. [21] estimated that the reduction in travel volume led to a 2.9-day delay in the spatial spread in China. To our knowledge, the present study is the first to have used simple stochastic process models to explicitly estimate the time delay to a major epidemic in Japan that gained by the drastic reduction in travel volume in and outside China.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Number of confirmed cases outside China by date of report. The bars measure the number of cases reported each day between 13 January and 6 February 2020. The black bars represent infections that are likely to have occurred in China while the grey bars indicate infections that are likely to have occurred outside China.

**Figure 2.**Observed and expected number of cases diagnosed outside China by date of report. Observed cases (dots) include those infected in China. An exponential growth curve was fitted to the observed data from 27 January 2020. The dashed lines represent the 95% confidence interval on and after 28 January 2020.

**Figure 3.**Probability of a major epidemic with various levels of transmissibility and traced contact. (

**A**) The solid lines represent the probability of a major epidemic in the counterfactual scenario, i.e., based on the expected number of cases diagnosed in Japan. Dashed lines represent the probability of a major epidemic in the presence of travel volume reductions, calculated using the number of traced and untraced cases was 6 in total in Japan from Day 58 to Day 67. Contact tracing leading to isolation was assumed at three different levels: 10%, 30%, and 50%. (

**B**) The vertical axis represents the reduced probability of a major epidemic due to travel volume reduction. The horizontal axis shows the proportion of cases traced, adopting the same scenarios as panel A.

**Figure 4.**Delay in the time to a major epidemic gained by travel volume reduction. The median delay is shown for Japan, using relative reduction in the probability of a major epidemic. The vertical axis represents the time delay to a major epidemic (in days), and the horizontal axis represents the proportion of contacts traced. Each shaped dot represents different values of the basic reproduction number.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Anzai, A.; Kobayashi, T.; Linton, N.M.; Kinoshita, R.; Hayashi, K.; Suzuki, A.; Yang, Y.; Jung, S.-m.; Miyama, T.; Akhmetzhanov, A.R.;
et al. Assessing the Impact of Reduced Travel on Exportation Dynamics of Novel Coronavirus Infection (COVID-19). *J. Clin. Med.* **2020**, *9*, 601.
https://doi.org/10.3390/jcm9020601

**AMA Style**

Anzai A, Kobayashi T, Linton NM, Kinoshita R, Hayashi K, Suzuki A, Yang Y, Jung S-m, Miyama T, Akhmetzhanov AR,
et al. Assessing the Impact of Reduced Travel on Exportation Dynamics of Novel Coronavirus Infection (COVID-19). *Journal of Clinical Medicine*. 2020; 9(2):601.
https://doi.org/10.3390/jcm9020601

**Chicago/Turabian Style**

Anzai, Asami, Tetsuro Kobayashi, Natalie M. Linton, Ryo Kinoshita, Katsuma Hayashi, Ayako Suzuki, Yichi Yang, Sung-mok Jung, Takeshi Miyama, Andrei R. Akhmetzhanov,
and et al. 2020. "Assessing the Impact of Reduced Travel on Exportation Dynamics of Novel Coronavirus Infection (COVID-19)" *Journal of Clinical Medicine* 9, no. 2: 601.
https://doi.org/10.3390/jcm9020601