Travel restrictions and SARS-CoV-2 transmission: an effective distance approach to estimate impact

Abstract Objective To estimate the effect of airline travel restrictions on the risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) importation. Methods We extracted passenger volume data for the entire global airline network, as well as the dates of the implementation of travel restrictions and the observation of the first case of coronavirus disease (COVID-19) in each country or territory, from publicly available sources. We calculated effective distance between every airport and the city of Wuhan, China. We modelled the risk of SARS-CoV-2 importation by estimating survival probability, expressing median time of importation as a function of effective distance. We calculated the relative change in importation risk under three different hypothetical scenarios that all resulted in different passenger volumes. Findings We identified 28 countries with imported cases of COVID-19 as at 26 February 2020. The arrival time of the virus at these countries ranged from 39 to 80 days since identification of the first case in Wuhan. Our analysis of relative change in risk indicated that strategies of reducing global passenger volume and imposing travel restrictions at a further 10 hub airports would be equally effective in reducing the risk of importation of SARS-CoV-2; however, this reduction is very limited with a close-to-zero median relative change in risk. Conclusion The hypothetical variations in observed travel restrictions were not sufficient to prevent the global spread of SARS-CoV-2; further research should also consider travel by land and sea. Our study highlights the importance of strengthening local capacities for disease monitoring and control.


Introduction
As of 25 May 2020, 347 697 deaths resulting from 5 392 654 laboratory-confirmed infectious cases of coronavirus disease (COVID-19) had been reported. 1,2 Global travel contributed to the rapid growth of cases in Wuhan, China and internationally, including other Asian countries, Europe and the United States of America. 1,3,4 Most of the current strategies to reduce the risk of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission are based on controlling interactions between humans, including case isolation, tracking patient contacts and screening air passengers crossing national borders.
International airline travellers departing from China have unintentionally transported SARS-CoV-2 all over the world. As of 30 January 2020, the Emergency Committee convened by the World Health Organization (WHO), acting according to International Health Regulations, described the unfolding outbreak as a Public Health Emergency of International Concern; the Committee proposed several recommendations to strengthen the monitoring and surveillance of the virus at an international level. Based on the available information at that time, the Committee did not recommend any restrictions on global travel or trade for any countries, including China. 5 Nevertheless, as during previous infectious epidemics such as Ebola virus, SARS and influenza H1N1-2009, by 26 February 2020, at least 80 countries and territories had adopted travel restrictions in response to the threat of importation of SARS-CoV-2.
Reacting to the rapid dissemination of emerging infectious diseases by airline travel, researchers have developed several mathematical modelling techniques. [6][7][8][9][10][11] In 2006, an overall review was published on the relationship between the global transportation network and the spread of infectious diseases. 12 Later, researchers proposed a new stochastic metapopulation model that incorporated travel records and census data in 220 countries to examine a prediction accuracy for the global spread of SARS. 11 A large-scale simulation examined the impact of travel restrictions on the delay of the Ebola epidemic, demonstrating that restrictions delayed the outbreak of Ebola for approximately 30 days in African countries. 9 Another study estimated the absolute (< 1%) and relative (~20%) reductions in risk due to travel restrictions, and concluded that such restrictions were not effective in preventing the global spread of Ebola. 10 Here we follow the methods used in that study. 10 It is still unclear how air travel restrictions contribute to the control of SARS-CoV-2 transmission. 4 We therefore evaluate the effect of travel restrictions on the risk of SARS-CoV-2 transmission, using a hazard-based model and the concept of effective distance. We apply our model to travel network Impact of travel restrictions on SARS-CoV-2 importation Shoi Shi et al. data to explore patterns of domestic and international population movement from Wuhan.

Data set
For the 80 countries with a travel restriction in place by 26 February 2020 (Table 1), we extracted the dates of the introduction of travel restrictions and of the identification of the first case of COVID-19 from publicly available secondary data sources. 13,14 To check the validity of these data sources, we confirmed all extracted dates with official announcements from individual governments. The travel restrictions were of the form: (i) entry or exit bans, defined as general restrictions on the ability of people to depart from their country for travel to China or the ability of foreigners to enter a country after travelling from or transiting via China; (ii) visa restrictions, defined as total or partial visa suspensions for travellers from China; or (iii) flight suspensions, defined as governmental bans on flights to or from China. 14, 15 We used Automatic Dependent Surveillance-Broadcast (ADS-B) exchange data to construct the airline transportation network encompassing the 200 countries and territories we included in this analysis. 16,17 These publicly available exchange data are in the form of an airline network diagram consisting of 1773 nodes (i.e. airports) and 23 505 edges (i.e. direct flights), as of 1 December 2019. The weight of each edge represents passenger volume on a direct flight between two nodes. We estimated passenger volume on any particular flight by multiplying the number of seats available on the aeroplane by a factor of 0.7. 10,18 The data and codes are available in the data repository. 17

Effective distance
We examined the impact of airline network restrictions on the transmission of SARS-CoV-2 by calculating effective distance 19 from the network diagram. We did not consider the incubation period of the virus and all passengers were considered equal in terms of the number of people they could potentially infect. We calculated effective distance, defined as the minimum distance between each node where both path length (i.e. distance between a pair of nodes) and the  18,20 and to determine the impact of travel restrictions on the spread of Ebola virus. 10 Effective distance d ij between the ith airport in the jth country and Wuhan airport is defined as the minimum of all possible effective path lengths (i.e. path length with passenger volume considered). The effective path length from Wuhan city to the ith airport, with a sequence of l -1 transit airports a a a Wuhan l , ,..., Where P l,m denotes the conditional (transition) probability that any particular individual travelled from the lth to the mth airport. 18 This transition probability is estimated as P l,m = w lm / Σ n w ln where w lm is the passenger volume that travelled from the lth to the mth airport. To take into account the fact that the network diagram and the associated effective distances changed with the introduction of travel restrictions, we made the assumption that 75% of the number of direct flights were cancelled (where the number of direct flights that took place on 1 December 2019 is considered as 100%). 9, 10 We denote the effective distance before and after the travel restrictions d ij 0 and d ij 1 , respectively.

Hazard-based model
We modelled the risk of importing S A R S -C o V -2 b y e s t i m a t i n g survival probability. We define the survival probability as where t = 0 corresponds to the date of observation of the first case of COV-ID-19 in Wuhan city (i.e. 8 December 2019) and T is a random (continuous) variable indicating the time from t = 0 to its importation at the ith airport in the jth country. The hazard function for (. . .continued) Impact of travel restrictions on SARS-CoV-2 importation Shoi Shi et al.
virus importation for the ith airport in the jth country is defined: 10 ,19 where β j is a (country-specific) parameter that represents the risk of importing SARS-CoV-2. This formulation allows the median time of importation to be expressed as a function of the effective distance d ij . Using this hazard function, we model the probability density function of survival probability as: where t ij is survival time at the ith airport in the jth country. We categorized the 200 countries or territories included in the analysis into three separate groups: A, those that imported SARS-CoV-2 before travel restrictions were put in place; B, those that imported SARS-CoV-2 after the introduction of travel restrictions; and C, those that had not imported the virus as of the end of this study (26 February 2020). 10,18 All category A,B and C countries or territories are listed in Table 1.
We define the likelihood of a country falling into category A, that is, the likelihood of a country importing the virus before the implementation of travel restrictions, as where λ ij 0 represents the hazard function calculated according to the effective distance before the travel restriction, that is, d ij 0 . Similarly, we define the likelihood of a country falling into category B as where λ ij 1 indicates the hazard function calculated from the effective distance after the travel restriction d ij 0 ( ) and t s is the time between first reported case of the disease in Wuhan (8 December 2019) and the day on which the WHO described the outbreak as a Public Health Emergency of International Concern (30 January 2020, i.e. t s = 53 days). L B is therefore the joint likelihood of avoiding the importation of the virus for t s days before travel restrictions and the probability of importing the virus during t ij − t s (i.e. the survival time after 30 January 2020).
We define the likelihood of a country falling into category C as where t l is the end of this study (26 February 2020). Equation 6 is the joint likelihood of the probability of avoiding the importation of SARS-CoV-2 for t s days before the travel restriction and for t l − t s days after the travel restriction. Finally, we estimate the countryspecific risk of importing SARS-CoV-2 by optimizing the product L A L B L C . We used a maximum likelihood approach to estimate β j and calculated 95% confidence intervals based on the empirical Fisher information matrix.

Hypothetical scenarios
We calculated the effect of travel restrictions on the risk of virus importation by comparing the observed risk and that of three different hypothetical scenarios. . We considered three hypothetical scenarios that would all lead to different flight volumes (i.e. numbers of direct flights): H1, no travel restrictions had been introduced; H2, travel restrictions had been introduced, but only 25% or 50% of flights were cancelled instead of the current assumption of 75%; and H3, in addition to the travel restrictions introduced in the 80 countries listed in Table 1, we assumed that travel restrictions had also been introduced in the 10 highest-passenger-volume (i.e. hub) airports not included in Table 1

Change in risk
To quantify the effect of travel restrictions on virus importation, we calculated the absolute and relative change in risk. The absolute change in risk is simply the difference between the observed risk and the risk incurred under a particular hypothetical scenario, defined as R R ij O ij H − . The relative change in risk is the absolute change in risk under a particular hypothetical scenario expressed as a proportion of the observed risk, that is, 1 A negative (positive) relative change in risk implies that the risk of virus importation under the hypothetical scenario would be higher (lower) than the observed risk.

Results
We list the countries that introduced travel restriction policies and/or experienced importation of the virus in Table 1. A total of 28 countries had cases of COVID-19 as at 26 February 2020. A total of 21 of these countries imported the virus before implementing travel restrictions (category A) and seven countries imported the virus after the introduction of travel restrictions (category B). The arrival time of the virus ranged from 39 to 80 days since the first case was identified in Wuhan on 8 December 2019. Fig. 1 and Fig. 2 depict the entire global airline network diagram and the flight network from all of China (as well as from Wuhan city only) before the introduction of travel restrictions, respectively.
We plot the estimated relative change in risk of importing the virus, because of the three different hypothetical travel restrictions and associated changes in effective distance, in Fig. 3, Fig. 4 and Fig. 5, respectively. The    Impact of travel restrictions on SARS-CoV-2 importation Shoi Shi et al.
median relative change in risk and the corresponding interquartile range for all countries and territories, and three hypothetical scenarios analysed are available in the data repository. 17 We plot the relative change in risk of virus importation under hypothetical scenario 1 in Fig. 3. We modelled the median (25% and 75% percentiles) of the estimated change in absolute and relative risk as 0.000 (0.000 and 0.000) and 0.000 (−0.115 and 0.049), respectively. When we reduced the global passenger volume between China and other airports as defined in hypotheti-cal scenario 1, we observed a positive relative change in risk (i.e. lower risk of virus importation) in the coastal areas of Africa and South America, as well as in Europe and South-East Asia. Fig. 4 shows the change in relative risk under hypothetical scenario 2. We calculated the median (25% and 75% percentiles) of the estimated change in absolute and relative risk as −0.000 (−0.045 and 0.000) and −1.000 (−7.400 and 0.000) for only 25% flight cancellation and 0.000 (−0.039 and 0.000) and 0.000 (−3.000 and 1.000) for only 50% flight cancellation, respectively. Of the total number of airports considered, 45.5% (757/1662) and 44.6% (742/1662) showed large increases in risk (i.e. relative change in risk of < −1.0) for only 25% and 50% of flights cancelled, respectively. Note that the geographical distribution of the relative change in risk in Fig. 4 is similar to that in Fig. 3, except for the positive change in relative risk (i.e. lower risk of virus importation) under the hypothetical scenario 2 where 25% of flight has been cancelled in Australia and central Europe in Fig. 4.
We modelled the estimated absolute and relative change in risk of virus  Notes: In addition to the travel restrictions introduced in the 80 countries listed in Table 1, we assumed that travel restrictions had also been introduced in the 10 highest-passenger-volume airports not included in Table 1 importation under the assumption of hypothetical scenario 3 (Fig. 5) as 0.000 (−0.394 and 0.002) and 0.000 (−3.000 and 1.000), respectively. The results under these assumptions are geographically similar to those under hypothetical scenario 1 (Fig. 3); by introducing travel restrictions at the next 10 highestpassenger-volume hub airports, airports in coastal Africa and South America and all of Europe and South-East Asia could observe a reduction in risk of virus importation.

Discussion
We have shown that the impact of travel restrictions was limited for most airports, with almost zero (median) change in risk of virus importation. The degree of travel restriction was assumed to be a 75% reduction in the flight volume. As a result, almost all airports would have observed a minor relative change in risk. To investigate the effect of passenger volume on the relative change in risk, we changed the passenger volume reduction from 75% to 50% or 25%. We observed a volume-dependent increase in risk in several areas including North America, part of Europe and the Russian Federation. Notably, when evaluating the effect of cancelling only 25% or 50% of flights (as opposed to 75% in the original assumption), the overall geographical distribution of the relative change in risk was similar, suggesting that passenger volume has a nonlinear effect on risk and the optimal volume reduction may depend on the particular airport and its network. From our results, we can conclude that travel restrictions based on reductions in passenger volume would only make a minor contribution to the prevention of virus importation among countries.
To confirm the expected reduced risk because of imposing travel restrictions at more hub airports, we estimated the relative change in risk under such an assumption. Notably, this result may be equivalent to evaluation of the effect of imposing lockdown in a country close to China, as hypothetical scenario 3 assesses the effect of closing three airports in China with direct flights from Wuhan and seven hub airports from six other countries. We observed that almost all airports experienced a decreased risk of virus importation under this scenario. However, Australia, India and the United States showed an increased risk of virus importation. A possible explanation for this result is that imposing travel restrictions at hub airports increases the number of passengers at other airports; this in turn changes the relative importance of specific airports, meaning that other airports could achieve hub airport status. These results suggest that careful consideration of which hub airports to restrict is essential.
Our study had limitations. First, as in previous studies, 10,21 the infected individual was assumed to be randomly selected from the source of the virus (i.e. China). If infected individuals had particular characteristics, such as a pref-erence for a particular route from China to other destinations (e.g. according to cost or visa restrictions), our results may be biased. Second, we did not control for any covariates (e.g. culture, religion or country income level), something which should be addressed in future studies. 10 Air travel is not the only force driving the spread of the virus. In countries sharing a land border or separated by a small stretch of water, the effect of sea and land travel on the spread of the virus could be greater than that of air travel; we therefore propose further research in calculating the effective distance between locations based on the transportation data from air, sea and land travel.
Impact of travel restrictions on SARS-CoV-2 importation Shoi Shi et al.