Effects of non-compulsory and mandatory COVID-19 interventions on travel distance and time away from home, Norway, 2021

Background Given the societal, economic and health costs of COVID-19 non-pharmaceutical interventions (NPI), it is important to assess their effects. Human mobility serves as a surrogate measure for human contacts and compliance with NPI. In Nordic countries, NPI have mostly been advised and sometimes made mandatory. It is unclear if making NPI mandatory further reduced mobility. Aim We investigated the effect of non-compulsory and follow-up mandatory measures in major cities and rural regions on human mobility in Norway. We identified NPI categories that most affected mobility. Methods We used mobile phone mobility data from the largest Norwegian operator. We analysed non-compulsory and mandatory measures with before–after and synthetic difference-in-differences approaches. By regression, we investigated the impact of different NPI on mobility. Results Nationally and in less populated regions, time travelled, but not distance, decreased after follow-up mandatory measures. In urban areas, however, distance decreased after follow-up mandates, and the reduction exceeded the decrease after initial non-compulsory measures. Stricter metre rules, gyms reopening, and restaurants and shops reopening were significantly associated with changes in mobility. Conclusion Overall, distance travelled from home decreased after non-compulsory measures, and in urban areas, distance further decreased after follow-up mandates. Time travelled reduced more after mandates than after non-compulsory measures for all regions and interventions. Stricter distancing and reopening of gyms, restaurants and shops were associated with changes in mobility.

For the analyses presented here, the data are aggregated into three distinct measures: radius of gyration, time away from home, and maximum distance away from home. Each of these metrics is calculated for each individual subscriber each day and is then aggregated into an empirical distribution for each municipality and each day, represented as quantiles. This aggregation is performed automatically inside the mobile network operator's facilities, immediately after data acquisition. The resulting distributions are the only information that is stored. Data is not available approximately one day every three weeks due to anonymization purposes. On these days, all pseudonyms that identify individuals are replaced, and since individuals' homes and movements thus cannot be linked, data is not reported. A day is defined as 04:00 to 04:00 the next day, as we expect most people to be asleep/at home at 04:00. There could be some small effect of people being misassigned from going out, but we believe the effect to be small.

I. Radius of Gyration
The radius of gyration for one individual for a day is defined by the formula Figure S1. Map of Norway with selected cities labelled Cities used in analyses of national and local interventions are labelled. Cities included as control regions for the SDID analyses are also included.

Checking Effects of Shorter Window Sizes
We checked the effects of shorter window sizes for a few interventions, specifically the December 3, 9, and 15 national interventions. In Table S2, we compared the results we reported with unequal window sizes with the results we obtain when we use the same length window size for the week before and the week after each intervention. The same length window size is obtained by taking the shortest window length of the week before and after each intervention. From observation, the results with the same window lengths do not differ much from the original results, and the interpretation would be the same. However, the lack of consistent window length through the results is still an important limitation.

I. SDID Weights and Plots of Trends for Regional Interventions
In order to compare trends between the control regions and the region with the intervention (referred to as the treated unit), we used SDID to calculate weights for each control region to create a weighted average of the control regions that is as similar as possible to the treated unit. We present the weights for each control region for each application of SDID to improve interpretability. In addition, we created plots comparing the trend in the synthetic control, or the weighted average of the controls, and in the treated unit.

Least Populated Municipalities in Each County
The least populated municipalities were chosen based on the number of Telenor users on January 24, 2021. The number of users vary slightly between days.

F. Multiple Intervention Linear Regression
The model building followed this pipeline: We first identified the different categories of interventions, by analysing the different COVID-19 interventions that had been utilised in Norway and qualitatively categorising interventions in groups, see details below. We chose to use a linear regression model to increase interpretability of the results. We did consider using raw mobility as the outcome rather than the log of the relative change in mobility from before and after the intervention, but if we pursued such a model, we would not have been able to use data from multiple regions. It was important that we could train a model using data from multiple regions, as we did not have enough data from any one region to create a separate model. The models predict the log differences of the mobility after and before the intervention, computed using equation 2.
We utilise daily mean meanDistAway, timeAway, and maxDistAway as the mean metrics.
For all models, the variance inflation factor was computed for each feature to identify potential multi-collinearities. Almost all variance inflation factor (VIF) values are under 5, which is below the recommended upper threshold [56]. Therefore, multicollinearity is not a significant issue.
For some intervention time points, the time period of comparison overlapped with either another intervention or a major holiday period, defined as the time around Easter, Christmas, and New Year's. We manually created new periods of analysis for this intervention and used equation 3 to compute the log differences in weekly mobility for these interventions. Table S11 lists the time points for which equation 3 was used to compute the outcome.

All Results from Models
We report all covariates and their coefficients in all three linear regression models. The algorithm to identify non-intervention time points involves the following steps.
1. Start with a set of all dates, D. For each date t in the list of all national and local intervention dates, remove all dates from t-7 to t+6, inclusive. Only use national interventions when the region of interest is Norway. 2. Remove dates related to holidays. We removed one week before and after 12-28 and 4-5 to account for the winter and Easter holidays.