The influence of cross-border mobility on the COVID-19 epidemic in Nordic countries

Restrictions of cross-border mobility are typically used to prevent an emerging disease from entering a country in order to slow down its spread. However, such interventions can come with a significant societal cost and should thus be based on careful analysis and quantitative understanding on their effects. To this end, we model the influence of cross-border mobility on the spread of COVID-19 during 2020 in the neighbouring Nordic countries of Denmark, Finland, Norway and Sweden. We investigate the immediate impact of cross-border travel on disease spread and employ counterfactual scenarios to explore the cumulative effects of introducing additional infected individuals into a population during the ongoing epidemic. Our results indicate that the effect of inter-country mobility on epidemic growth is non-negligible essentially when there is sizeable mobility from a high prevalence country or countries to a low prevalence one. Our findings underscore the critical importance of accurate data and models on both epidemic progression and travel patterns in informing decisions related to inter-country mobility restrictions.


Model estimates
Posterior mean and 90% credible intervals.Note that y-axis does not include zero.3 Secondary effect estimations

Figure A :
Figure A: Estimates of the reproduction number R t,x .Posterior mean and 90% credible intervals.

Figure B :
Figure B: Estimated numbers of infectious individuals I t,x , in linear and log scales.Posterior mean and 90% credible intervals.

Figure C :
Figure C: The expected number of hospitalizations per week E w,x and the corresponding observed numbers observed numbers H w,x in linear and log scales.Posterior mean and 90% credible intervals, dots present the observed data.

Figure D :
Figure D: Estimated portion of Susceptibles in the population S t,x /N 0,x .Posterior mean and 90% credible intervals.Note that y-axis does not include zero.

Figure E :
Figure E: Changes in the population size in countries due to mobility N t,x /N 0,x , relative to the starting population size.Posterior mean and 90% credible intervals.Note that y-axis does not include zero.

Figure F :
Figure F: Estimates of the total number of new infections per day i total new t,x local and the net mobility effect Q t,x , shown at different linear scales.Posterior mean and 90% credible intervals.The upper row shows the i total new t,x on a larger scale, while the lower row zooms in to focus on Q t,x .

Figure G :.
Figure G: Estimates of new non-local infection by source, divided by the total number of new infection: Q long term t,x

Figure I :
Figure I: Estimates of non-local infections by country per day, divided by the total number of new infection.Lines show posterior mean and colored areas show 90% posterior intervals.Note that Figure 5 in the main text shows the same quantities in absolute scale.

Figure J :
Figure J: Alternative representation of the counterfactual analysis, where cross-country mobility is set to zero.Top row: black line shows the mean number of infections E(I t,x ) in the baseline scenario.Colored lines presents the number of infections in counterfactual scenarios E c (I t,x ), during the 50 day interval starting with the implementation of restrictions.Dots mark the start of the restriction.Mid row: same values, shown as a difference between counterfactual and baseline scenario E c (I t,x ) − E(I t,x ) .Bottom row: same values, divided by baseline scenario [E c (I t,x ) − E(I t,x )]/E(I t,x ).Note that Figure 8 in the main text shows the same quantities E(I t,x ) and E c (I t,x ) in log scale.

Figure K :
Figure K: Alternative representation of the counterfactual analysis, where mobility returns to the pre-pandemic levels.Top row: black line shows the mean number of infections E(I t,x ) in the baseline scenario.Colored lines presents the number of infections in counterfactual scenarios E c (I t,x ), during the 50 day interval starting with the implementation of restrictions.Dots mark the start of the restriction.Mid row: same values, shown as a difference between counterfactual and baseline scenario E c (I t,x ) − E(I t,x ).Bottom row: same values, divided by baseline scenario [E c (I t,x ) − E(I t,x )]/E(I t,x ).Note that Fig 9 in the main text shows the same quantities E(I t,x ) and E c (I t,x ) in log scale.

Figure L :
Figure L: Posterior correlation between values of R tx in each country.We see that for the majority of the values, sequential values (time difference one week) are slightly positively correlated; values 2-5 weeks apart are slightly negatively correlated and the rest are uncorrelated.Values at the beginning and end of the modelled period are more strongly correlated (both positively and negatively).

Figure M :
Figure M: Posterior correlation between selected values of R t for all countries.We see that the values of R tx are not correlated between different countries.