Several data types, from different sources, were employed to carry out the analysis. These are presented in Table 1 below. Two separate datasets containing population data were employed. One to represent dynamically moving populations, provided by Telia, Sweden’s largest telecommunications company with mixed public–private ownership, and one containing static population numbers, provided by Statistics Sweden. The former was based on location data from the mobile network, aggregated to a grid. The two grids had overlapping borders which made it possible to combine them in order to compare dynamic and static population counts. However, the grid with static population data from Statistics Sweden had a homogenous size on all grid cells—1 km2—while the grid cells in the Telia grid had varying sizes depending on population density and a need to ensure than enough individuals (a minimum of 5) were located within each cell at a certain hour to prevent the possibility of identifying individuals. These grid cells varied in size, ranging between 4096 and 0.25 km2.

The dynamic population data consisted of population counts aggregated to 22,763 individual grid cells in a grid covering all of Sweden. The population counts were aggregated based on the number of mobile phones located in a grid cell on an hourly basis for every day between January 1, 2019 and April 1, 2020. In other words, once per hour, the number of phones present in each grid cell were summarized. In total, the dataset contained 229,740,975 observations. Furthermore, the Telia population data contain no device-specific data, and the aggregation process works to make identification of an individual impossible.

To facilitate analysis of differences between urban and rural areas, urban, densely populated and rural area definitions from the Swedish Association of Local Authorities and Regions (SALAR) were used. It is an official national system of categorizing rural and urban areas in Sweden. The definitions rely on population size and commuting behavior—urban municipalities contain less than 20% of the population living in rural areas and have, together with neighboring municipalities, more than 500,000 residents. Densely populated municipalities have less than 50% of the population living rural areas and at least half of the population commute less than 45 min to cities with more than 50,000 residents. Rural municipalities have more than 50% of the population living in rural areas [33].

The road network covering all of Sweden was downloaded from the Swedish national road network database (Nationella vägdatabasen, NVDB) and consisted of 2,135,134 individual road segments, including speed limits for each segment. The road network was split at intersections to assure that each line was connected at an endpoint. This generated an additional 710,761 road segments, as several roads were split into shorter segments. Walking roads, i.e. roads with speed limits below 10 km/h, were removed, and the resulting road network contained 2,541,347 individual segments. Travel times were calculated for each road segment by dividing the length of each segment with the speed limits. All hospital based ED’s in Sweden (N = 68) were extracted manually as.kmz-files from Google Earth based on a list from a recent official report on the current state of Sweden’s EHC system [8], and were then geocoded into a GIS.

To facilitate an analysis where the static and dynamic population sizes could be compared, the first step of the analysis was to combine the grids from Statistic Sweden and from Telia. The two grids were imported to ESRI ArcGIS. Then, the static population data in the grid from Statistics Sweden was incorporated into the Telia grid. While the grids shared borders, the Telia grid cells had varying sizes. In the most densely populated areas, they were smaller than the grid cells from Statistics Sweden. Some had an area of 0.25 km2, compared to the grid from Statistics Sweden which had an area of 1 km2. Where this occurred, the grid cells from Statistic Sweden were divided into 4 smaller grid cells, each overlapping with the Telia grid cells. The population size was split equally between them, i.e. it was assumed that the static population was equally spread within the grid cell. In less densely populated areas, the Telia grids were larger—up to 4096 km2. Where this occurred, the static population size from all the overlapping grid cells in the Statistic Sweden grid was summarized and incorporated as a separate field in the Telia grid. This process generated one grid containing both static and dynamic population data.

The grid and the road network were imported to the GIS in order to calculate the travel times to the closest ED from each zone. All centroids located within 5000 m of the road network were snapped to the closest road network junction. The centroids of 466 grid cells, representing 2% of the total number of grid cells, were either inaccessible from the road network, or were located outside of the Swedish borders. These were generally located in e.g. the archipelago or in mountainous regions and would require either boat or helicopter transport. Also, we did not have access other nations (Norway and Finland) road networks, and could therefore not estimate travel times outside of Sweden. Therefore, these 466 grid cells were omitted from the analysis, and 22,297 of the Telia grid cells (98%) were included in the analysis.

The Closest Facility network analysis, a tool in the ArcGIS suite, was utilized to assess spatial accessibility. It calculates the shortest (quickest) route, based on a road network with information of travel times, by finding the combination of roads between two points with the lowest combined travel time. Travel times were estimated between the centroid of each grid cell and the closest ED, generating one individual route for each grid cell. Each generated route contained an identifying number, which was used as a common denominator to join the data on travel times back to the grid cells. As each grid cell was assigned a route which linked it to the closest ED, a separate variable was generated which indicated which catchment area each grid cell was connected to. Thus, the network analysis also generated the ED catchment areas.

The static populations were summarized in zones located within certain travel time thresholds derived from previous research. To assess how population accessibility vary temporally the dataset was split into different temporal categories—between hours of the day, between weekday and weekends and between months. As the total population sizes varied between the static and dynamic population datasets, we normalized the data before assessing where and when static population data over- or underestimates population size compared to dynamic population data. This was done by comparing the share of the total population that was present within e.g. a certain travel time threshold from an ED, where the share was calculated using the static population data total for the static data, and the dynamic population data total for the dynamic data. To assess whether, and to what degree, static population data over- or underestimates shares compared to dynamic population data, a ratio indicating the relationship between the two datasets was then calculated by dividing the population shares based on static population data with population shares based on dynamic population data. This was done for each hour of the day, separated first by weekdays (Monday-Friday) and weekends (Saturday and Sunday) and then by months.

Then, we compared static and dynamic population datasets for all Swedish ED’s catchment areas at two different time points—at mid-day (13:00) in January and July. This included four steps. First, we visualized over- and underestimations in the ED catchment areas at both time points. Secondly, to complement the spatial patterns observed in the visualizations, Moran’s I tests were conducted to assess whether there were statistically significant clusters in data. Spatial relationships were conceptualized as inversely distanced, meaning neighboring areas have larger influence than those further away. To ensure all ED catchment areas had at least one neighbor, a distance of 137,660 m was automatically set. This conceptualization of spatial relationships was motivated by the fact that the ED catchment areas differ greatly in geographical size, and ensured that neighborhoods did not differ greatly between the smaller ED catchment zones in urban areas (where several EDs are located close to each other) and the larger ED catchment zones in rural areas. Thirdly, analysis of variance (ANOVA) tests were run to see if the clusters of over- and underestimation were also present across different ED types. Fourth, and lastly, as the ANOVA tests indicated statistically significant differences between ED types, we ran Tukey post-hoc tests on the results from the ANOVA tests to assess whether those differences were statistically significant between all types of EDs, or only between some different levels.

A major limitation to this study relates to the dynamic data from the mobile network. Prior to being made available to us it was extrapolated using residential population data. This was done to compensate for the fact that Telia does not control the entire mobile phone market, and thus other operator’s users are not included in the dataset. Extrapolation likely makes the population numbers more realistic, but it entails that the total population size is estimated. The total population present in Sweden also varied over time, which could have several explanations. It could reflect how people move out of, and into, the country. But it is also likely a reflection of limitations to the data itself. For example, only around 30–35% of the population have Telia subscriptions, and some have several phones while others have no phone. Extrapolation made to the data prior to us receiving it therefore, to some degree, induced some uncertainty. Another potential limitation pertains to the Covid-19 pandemic. Travel behaviors may have been affected by recommendations from the public health authorities in Sweden in March, 2020. Due to the short period of time where this may have impacted the data, we did not consider this in the analysis. It is possible that it did impact the results, but likely not to a significant degree.

An official Swedish system of spatial division was employed to delimit urban and rural areas. What is ‘urban’ and what is ‘rural’ is, however, not self-evident—population’s or individuals may identify as urban despite living in a small town that, by official definitions, is considered rural. Urban–rural is thus, perhaps, rather a stratum than two separate, dichotomous categories. Moreover, populations are not necessarily either rural or urban—when rural residents commute to work in larger cities, for example, they would be considered urban during the working hours, and rural when they are at home. Our conceptualization of the urban and rural should be viewed as one possible conceptualization of many alternative ones, and due to the Modifiable Areal Unit Problem (commonly known as MAUP), another division might produce different findings. Another limitation is that the potential impact of weather, traffic and road conditions on travel times were not taken into consideration. However, there are conflicting results about the impact of such factors where studies have shown little effect [4] while others proclaim that they are important to consider [17].