Framework for assessing and easing global COVID-19 travel restrictions

Abstract

During the COVID-19 pandemic, many countries implemented international travel restrictions that aimed to contain viral spread while still allowing necessary cross-border travel for social and economic reasons. The relative effectiveness of these approaches for controlling the pandemic has gone largely unstudied. Here we developed a flexible network meta-population model to compare the effectiveness of international travel policies, with a focus on evaluating the benefit of policy coordination. Because country-level epidemiological parameters are unknown, they need to be estimated from data; we accomplished this using approximate Bayesian computation, given the nature of our complex stochastic disease transmission model. Based on simulation and theoretical insights we find that, under our proposed policy, international airline travel may resume up to 58% of the pre-pandemic level with pandemic control comparable to that of a complete shutdown of all airline travel. Our results demonstrate that global coordination is necessary to allow for maximum travel with minimum effect on viral spread.

Figure 1

Schematic of the local epidemiological compartmental model which describes the state of the country at any given time. The population of each country is divided into six mutually exclusive compartments: susceptible (S), undetected infected (I), active confirmed (A), confirmed recovered (R), confirmed deceased (D), and unconfirmed removed (Z). The basic reproductive number in this model is given by $R_0=\alpha /(\gamma +\beta )$.

Figure 2

Model fit for different countries. For each country, the fit is demonstrated by the number of accumulated confirmed cases and the accumulated confirmed deaths. In each plot, the red line is the real data, the blue line is the median fitted values, and the shaded region is the 95$\%$ confidence interval. Eight countries are fitted including: the United States of America (USA), Brazil (BRA), Russia (RUS), the United Kingdom (GBR), Spain (ESP), Italy (ITA), France (FRA), and India (IND). Estimated parameter values for the eight countries are as below. Here T(1) is the change point of the transmission rate $\alpha$, such that $\alpha$ = ${\alpha }_1$ when $t\le T(1)$ and $\alpha$ = ${\alpha }_2$ when $t>T(1)$.

Figure 3

(a) Prediction of the average number of undetected infected cases for different travel regulation policies. “Fully open” indicates no travel restrictions are in place, “Fully closed” indicates no travel is permitted, and “Average control” denotes our proposed policy whereby the number of daily undetected infected cases should stay below a threshold of $c=70$ (the dashed line) on average. (b) Scatter plot for the relative change in the total number of new cases for each country in the two most extreme scenarios, fully closed and fully open for the first two weeks of June 2020. The 97.5th percentile value of relative change in each country’s number of new cases under the “Fully closed” scenario (x-axis) is plotted versus the corresponding number for the “Fully open” scenario (y-axis). The closer a country is to the reference line $x=y$, the less benefit that country gains from travel restrictions.

Figure 4

(a) Airline traffic network of countries in the top 5$\%$ of mutual global airline travel volume in the first two weeks of June 2020. Each node corresponds to a country and thicker edges carry more travel. (b) Heat map of empirical travel volume in the first two weeks of June 2020 (compared to the first two weeks of June 2019), and (c) heat map of hypothetical travel volume in the first two weeks of June 2020 under our proposed policy (compared to the first two weeks of June 2019).

Figure 5

Airline travel network visualizations and corresponding heat maps for eight countries: the United States of America (USA), Brazil (BRA), Russia (RUS), the United Kingdom (GBR), Spain (ESP), Italy (ITA), France (FRA), and India (IND). (a) Actual airline travel volume in the first two weeks of June 2020; (b) hypothetical travel volume in the same period following our proposed policy; heat maps of (c) empirical and (d) hypothetical travel volumes normalized by travel volumes from the first two weeks of June 2019.

Figure 6

Applying the proposed average control policy in practice: (a) schematic of the network meta-population model with travel regulation; (b) using the minimum value of the proportion of permissible incoming travel for pairwise zoning of countries; (c) travel from Country A to C and from A to D have been assigned the same zone whereas travel from Country A to B has been assigned a different zone; (d) simplifying the approach by assigning a country to the most conservative of pairwise zones (here, blue).