Human movement can inform the spatial scale of interventions against COVID-19 transmission

The UK enacted an intensive, nationwide lockdown on March 23 2020 to mitigate transmission of COVID-19. As restrictions began to ease, resurgence in transmission has been targeted by geographically-limited interventions of various stringencies. Determining the optimal spatial scale for local interventions is critical to ensure interventions reach the most at risk areas without unnecessarily restricting areas at low risk of resurgence. Here we use detailed human mobility data from Facebook to determine the spatially-explicit network community structure of the UK before and during the lockdown period, and how that has changed in response to the easing of restrictions and to locally-targeted interventions. We found that the mobility network became more sparse and the number of mobility communities decreased under the national lockdown. During this period, there was no evidence of re-routing in the network. Communities in which locally-targeted interventions have happened following resurgence did not show reorganization but did show small decreases in measurable mobility effects in the Facebook dataset. We propose that geographic communities detected in Facebook or other mobility data be part of decision making for determining the spatial extent or boundaries of interventions in the UK. These data are available in near real-time, and allow quantification of changes in the distribution of the population across the UK, as well as people's travel patterns to give data-driven metrics for geographically-targeted interventions.


Introduction
Fine-scale geographic monitoring of large populations provides a valuable resource for increasing the accuracy and responsiveness of epidemiological modelling, outbreak response, and intervention planning in response to public health emergencies like the COVID-19 pandemic (1)(2)(3)(4)(5) . Population and mobility datasets collected from the movement of individuals' mobile phones provide empirical, near-real time metrics of population movement between different geographic regions. (6) The COVID-19 pandemic response could potentially benefit from the availability of new data sources for measuring human movement, aggregated from mobile devices by network providers and popular applications including Google Maps, Apple Maps, Citymapper, and Facebook. (7) Travel and movement behavior during epidemics may change in response to imposed interventions, perceived risk, and due to seasonal activities such as vacations (8,9) . During the COVID-19 pandemic, mobility data has been used to assess adherence to movement restrictions (10,11) , the impact of movement restrictions on the transmission dynamics of COVID-19 (12)(13)(14) , the socioeconomic impacts of large scale movement restrictions (15,16) .
These are typically retrospective, describing past movement patterns to understand their impact, although the use of movement datasets to assist in developing policy responses to target key populations at risk during a disease outbreak is increasing (17) . Following the relaxation of nationwide restrictions in May 2020, the United Kingdom adopted a policy of targeted local interventions, aimed at reducing transmission in areas with resurgences, to avoid reimposing national restrictions (18) . However, the effectiveness of these measures will depend, amongst other things, on how the interconnections between areas change over time, and how 'local' areas are defined. We used mobility data from Facebook to investigate changes in travel behaviour in response to national and local policy changes. Large-scale movement datasets quantify these interconnections and could inform the appropriate geographic extent of control measures.
3 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020. 10.26.20219550 doi: medRxiv preprint / In this analysis, we used Facebook Data for Good UK movement and population data (March 19 to October 16 2020), which records approximately 15 million daily locations of 4.8 million users (19) , and UK census population, age, ethnicity, and socioeconomic deprivation data to understand the changes of travel behavior in response to initially stringent movement restrictions and subsequent easing between March and September 2020 (20) . Using network analytic methods to understand the structure of interconnected communities in the movement network, and traced the evolution of these geographic communities through time, comparing them to intervention measures implemented in response to local outbreaks.
We also analysed temporal changes in population movements, identifying outflows from population centers preceding the implementation of movement restrictions, as well as patterns of increased movement most likely resulting from holiday travel. We determined limitations of the dataset for quantifying movement patterns, and discuss the implications of the identified movement patterns on future policy responses.

Data representativity
We used anonymised, aggregated mobility and population data from Facebook (19) . These data record the number of users who have opted-in to Location History data sharing with the Facebook mobile app in a ~5km 2 grid cell, giving the population size and the number of Facebook users travelling between cells, in eight-hour windows from March 19th to September 10th 2020 (Supplemental Figure 1). Before being shared with the research team, data were aggregated by Facebook from individual adult user geolocation trajectories into between-cell flux data, assigning users to a grid cell by their modal location in a given time period. Movement flux between squares that involved fewer than 10 users were not shared to preserve privacy (Supplemental Figure 2).
To understand how representative Facebook data were of the general population, we explored the size of the population of Facebook users included in the movement dataset, and compared this population to 2011 UK Census estimates. In the dataset, there were an average of 15.06 million daily movements, ranging from 15.86 million on April 7th, to 14.27 million on June 28th ( Figure 1a).

4
. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020. 10.26.20219550 doi: medRxiv preprint / The percentage of Facebook users per cell was comparable in the four nations of the UK (Fig   1b) and was fairly homogeneous across the entire study area (Fig 1d). The ratio of number of Facebook users and total population was relatively constant across cells (Fig 1c). There were no strong associations between the percentage of Facebook users and the average age, percent minority ethnic, population density, or index of multiple deprivation of each cell (Supplemental Figures 3-5). CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / numbers, which are suppressed for privacy reasons. Note however, 12 cells around the town of Swindon are missing due to a data processing error prior to data sharing (shown in white).

Network Structure
To quantify how the structure of the overall network changed during the first wave of the epidemic, we computed the edge betweenness centrality of connections between cells, a measure of the relative importance of a given connection in the network. There was a large To understand the changes in movement volume across the study period and identify similarities between travel networks of different dates we compared the network on each day using Canberra distance (21) , which measures the difference between two matrices, where a smaller value means greater similarity. This comparison of network pairs shows the increasing dissimilarity of the network caused by decreased movement as lockdown measures were implemented in late March. The regeneration of the weekend difference in mobility after lockdown is clearly visible (Figure 2d). Similarities between weekend flows are observed throughout the time series with greater similarity between weekends and mid-lockdown travel, as overall volume of travel decreased during lockdown.
6 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.  The thickness of edges corresponds to their betweenness centrality. c) The density of betweenness centrality for all journeys by weekday, showing a weekly pattern of lower betweenness on weekend days. d) Canberra distance, a measure of matrix similarity, between pairs of daily weighted, directed network adjacency matrices.

Community Detection
We used movement between cells to identify geographically-explicit "communities of interaction" in the weighted, directed network of user movements between cells, where the weights are the frequency of cell-to-cell movements. These communities partition the cells in the movement network into groups with relatively higher within-group connectivity than between-group connectivity.
To determine daily community structure we used the InfoMap algorithm (22) , a flow-based community detection method demonstrated to have high accuracy and relatively low computational complexity for large networks (23) . We conducted sensitivity analyses using the Leiden algorithm (24) , finding close agreement between the spatial intersection and community boundaries identified by both methods (see Methods), where Leiden identified larger communities of which InfoMap communities were usually a subset (Supplemental Figures 9-10).
The geographic distribution of communities before the nationwide UK lockdown on March 23rd became fragmented during lockdown as the cell-level network became more sparse because 7 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / fewer cells were reported by Facebook due to lower numbers. The geographic extent of communities was smaller (Figure 3a and Supplemental Figure 11). As restrictions on travel in the UK were eased in early July, the geographic community structure began returning to pre-lockdown number, geographic extent, and location of communities around population centers.
The community structure of the movement data changed on weekends, showing an increase in the number and a decrease in the size of communities, due to reduced travel on weekends and bank holidays (Figure 3b, Supplemental . This fragmentation of the movement network on weekends reflects more local patterns of movement, and an absence of weekend commuting travel. This weekend effect was particularly pronounced in London, which on weekdays exhibited strong interconnectedness across the entire metropolitan area, but on weekends consistently fractured into four separate communities (Supplemental Figure 12).
The network structure during lockdown shares similarities in the number of communities and the volume of between tile-travel compared to typical weekends, where commuting travel is reduced, and overall travel between cells decreases. We did not observe reorganisation of the network around population centres through rerouting of connections, or other responses to the nationwide or local interventions.
We tracked the temporal evolution of communities using a heuristic approach (25) , transferring community labels between time steps based on the proportion of community members shared between time steps. This approach allowed identification of the spatial extent of mobility communities extent and persistence through time. We found that the most persistent communities existed around residential areas, with the exception of London which split into more communities on weekends (Supplemental Figure 12-13). We also identified the communities which overlapped certain administrative geographies (Figure 4a,b), allowing us to combine these communities with data on the date and extent of local area interventions.
8 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / Figure 3. Community detection using the InfoMap algorithm . Communities detected on a) March 19th, the date of maximum network travel, April 16th, the same week day during nationwide lockdown, and October 15th. Missing tiles recorded fewer than 10 people moving and have been censored for privacy and appear white. All cells with data are assigned to a single community. b) The number of communities on each day, with weekends (grey lines) and bank holidays (blue lines), and the dates of snapshots in 1a (red points).

Local Lockdown Extents
Motivated by the need to identify communities associated with epidemic resurgences and responses to reactive interventions, we compared the extent and date of local interventions with the spatial extent and temporal persistence of network communities. We examined movement changes before, during, and after the first "local lockdown" in the UK, which happened around the city of Leicester on June 29th. The local intervention area was much smaller than the community containing Leicester (Figure 4a). We observed a decrease in internal movement in the Leicester community following the local intervention lasting approximately two weeks ( Figure   9 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / 4b, c). Other mobility datasets, such as that from Google (26)   In the UK, Leicester was the first area to have a local intervention, and other areas followed with different rules and stringency. There was closer agreement between movement communities and the geographic extent of local area interventions from July onwards, particularly in Manchester (Supplemental Figure 14). Some interventions also spanned multiple movement communities, as in the North West and North East of England (Supplemental Figures 15-16).
Early local intervention measures at limited spatial extents may not have fully encompassed the area of transmission resurgence, however UK policy has changed over time, and has begun to enforce collaborative local area interventions comprising multiple Local Authorities, which include constituent parts of mobility communities detected here. Additionally, movement communities evolve over time, and have the potential to shift following local area interventions,

10
. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / requiring an understanding of real-time patterns of movement to monitor the appropriateness of a given measure.

Changes in Facebook population distribution
The major holiday season in the UK occurred between July and September, and we used Facebook population data, collected in higher resolution cells than mobility data, to determine if there was a reorganization of population distribution during this period. We found a decrease in the number of Facebook users in some areas preceding the enforcement of lockdown restrictions in March (Fig 5a & b), which were generally urban areas (Supplemental figure 17).
We also found a sizable summer increase in Facebook population in holiday destinations, most notably in Cornwall ( Figure 5).
The same pattern of high volumes of travel to tourist sites can be observed when analysing the maximum deviations from baseline movement during weekends (Friday, Saturday, Sunday) recorded by the Facebook movement dataset. Those journeys which experience greater than 100% deviation from baseline on Fridays, Saturdays, or Sundays identify major holiday destinations, Cornwall, Brighton, and Blackpool, and North Berwick (Supplemental Figure 18) (27) . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint estimates for April and July, shows the average proportion of Facebook users compared to census small area population. Blue dashed line shows the relationship over all months, and blak and red show relationship in April and July. d) A map of the absolute difference between population estimates in April and July. Note that the overall number of movements recorded by Facebook also decreased between April and July ( Figure 1).

Discussion
This study used a large, anonymized movement dataset to detect geographically-explicit community structure in the mobility network, and assessed how those communities were affected by interventions. Using these communities we can delineate local areas of high mobility that can be used to determine the spatial scale of locally-targeted interventions to mitigate disease resurgences during the COVID-19 pandemic. We also explored the structure of the UK travel network through the pandemic, identifying variations in the central connections between population centres and changes in the structure of closely connected communities.
Gridded mobility datasets such as those made available by Facebook provide granular, near real-time information about the movement patterns of a large sample of the population. While these datasets could usefully inform epidemic responses (15,(28)(29)(30) , there remain questions about the generalizability of the movement recorded in these datasets to the overall population movements in the UK (31,32) . The privacy preserving structure of the Facebook movement dataset means that low frequency journeys are not recorded, precise locations are replaced by modal locations, and data is provided in a grid so cells vary in population size. By comparing to Google mobility data, we showed that this can obscure changes in mobility occurring at a finer spatial scale, and thus limits the granularity at which local patterns can be identified from one data source alone. Ideally, multiple mobility data can be analysed in concert to assess changes in response to interventions.
Using a network analysis of mobility data, we identified geographically distinct communities with strong interconnections , which are a potentially more relevant target area for coordinated responses than traditional administrative boundaries. We found that these communities were stable around population centres between March and October (Supplemental Figure 13), but can be affected by public health interventions such as national travel restrictions. If restrictions are changed in the UK, the boundaries and size of communities could change, especially if home-working decreases and commuting behaviour returns to previous levels.

12
. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / Following COVID-19 resurgence in a particular area, determining the geographic limit of reactive interventions should be driven by areas at risk of increased transmission, which may not intersect with administrative boundaries. We found that while communities tended to stabilise around populous areas, there was disagreement between the extent of these communities and the boundaries at which local area interventions have been introduced in the UK. This demonstrates the potential value of the approach for the formulation of policies to contain outbreaks or resurgence.
In response to the nationwide lockdown starting March 23rd, the UK mobility network changed drastically. The movement community structure over time became more sparse and the patterns appeared similar to those present on weekends prior to the lockdown. We did not find evidence of large scale restructuring or rerouting, either in communities or in the betweenness-structure of edges in the network during this time. We found variations in the size and interconnection of communities in relation to changes in overall travel and small decreases in travel following local area interventions. The summer period brought large changes in Facebook population sizes in the UK, with a decrease in population around major population centers and an increased population in some rural areas (most notably in Cornwall) that tend to be holiday destinations.
Quantifying these changes in real-time is critical for informed decision-making about the scale of interventions and areas at risk of introductions.
There are several caveats to the methods of community detection used in this study, as the extent of communities could be influenced by the level of aggregation of the Facebook mobility data, and cells were assigned to a single community each day. We conducted a sensitivity analysis using two methods for identifying communities but there are a wide variety of community detection algorithms which emphasize different aspects of network structure.
Questions also remain about the general reliability of community detection methods, developed on well understood network structures, applied to real-world networks (33) . The effect of local area interventions on travel depends on the specifics of each intervention and their stringency.
Additionally, interventions occur at multiple spatial scales, and across overlapping time periods.
For example, in the UK, national interventions coincide with local interventions, and each may contribute differently to changes in movement behaviour. Finally, we assessed the 13 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020.

15
. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

Community Detection
Community detection methods are algorithms for identifying groups of meaningfully connected vertices. Many methods exist, with various tradeoffs on computational performance, resolution, or other characteristics (23,33,35,36) . In this study, we employed two different algorithms, InfoMap and Leiden. InfoMap assesses the movement of a random walker around a network, identifying the partition of the network that minimizes the description length required to describe the movements of the walker (22) . The Leiden algorithm maximizes the modularity of different node partitions, identifying the partition for which communities possess stronger connections to community members than to other nodes (24) . We used the Leiden implementation in the leidenalg Python package with resolution optimised by the algorithm (37) .
We tested the effect of the community detection algorithm, and found that they aligned hierarchically, where the Leiden algorithm identified geographically larger communities. If the communities detected by a one method are largely a superset of the communities detected by another, with shared boundaries between the defined communities, this likely represents a differing hierarchical structure, compared to a different interpretation of community structure. We assessed the agreement between community detection methods to understand the stability of detected communities by comparing the proportion of nodes in each community detected using InfoMap with all communities determined using Leiden, and vice versa (Supplemental Figure 9). This comparison allows for the computation of the proportion of shared nodes between both 17 . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / algorithms. The maximum and mean overlap of communities in each algorithm helped to identify the agreement between each method of community detection. In general we found that Leiden detected larger communities, for which the InfoMap communities were (for the most part) sub-communities.

Community Label Inheritance
The community detection methods used in this study identified communities each day. To track the evolution of communities over the study period, we employed a heuristic approach, assigning the label of a given community identified in a certain time step to that community with the highest number of shared nodes in the following time step (25) . When multiple communities in a certain time step "claim" the same community in the following timestep, the community with the closest size to the community in the following timestep "wins" the right to pass its own label to the following time step. This situation typically occurs when a large community incorporates members from smaller communities. When a community divides into a collection of smaller communities, the community with the largest proportion of shared nodes inherits the original community label while other communities are assigned new unique identifiers.

Canberra Distance
To assess the differences in network structure between travel matrices, we used Canberra distance, a distance metric for comparing the similarity between pairs of matrices. This metric describes the distance between two vectors in n-dimensional space. To construct symmetric matrices with identical members through time (including censored edges), all cells which recorded travel at any point in the time series were transformed into an empty symmetric matrix.
Matrix values were then inserted from the movement data on each day. Canberra distance was computed for each pair combination of movement matrices, resulting in a Canberra distance value comparing each pair of dates in the time series.

COVID-19 Data
We used confirmed COVID-19 cases from the UK Pillar 1 and Pillar 2 testing schemes. Data were available with data of specimens at the Lower Tier Local Authority level (38) .

18
. CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted October 27, 2020. ; https://doi.org/10.1101/2020.10.26.20219550 doi: medRxiv preprint / Google Mobility Data We used data from Google mobility reports (26) , a freely available service giving information on trends in movements to locations of 6 broad types: Retail and Recreation, Supermarket and Pharmacy, Parks, Public Transport, Workplaces, and Residential. We excluded Parks from the analysis, because they are likely low risk for transmission.

Code and Data Availability
All code is available on Github at https://github.com/hamishgibbs/facebook_mobility_uk Ethics Approval Author Contributions RME conceived the project, and planned the methods and analytical plan with HG, CABP, EN, and YL. JC and LS contributed to analysis of census variables. CABP and LD contributed to community detection methods and analysis of the methods. JC and CG contributed to analysis of spatial data. YL and EN contributed to statistical analysis of the mobility, census, and case data. AJK acquired the data and contributed to the analysis and understanding of Facebook data. HG wrote and implemented the majority of the code, and made the figures, with input from all authors. HG and RME wrote the first draft, to which all authors contributed. All authors interpreted the findings and were involved in the analysis and decision to publish. Facebook had no role in study design, the analysis, or decision to publish.