COVID-19 is linked to changes in the time-space dimension of human mobility

The proliferation of digital traces from mobile devices enables near real-time portraits of urban dynamics and mobility, overcoming limitations of surveys and censuses. Prior to and during COVID-19, mobile phone-derived data (CDR/LBS) have been used to study motifs of daily activities, commuting, exploration, and predictability in human location patterns, which are tied to circadian rhythms, urbanization level, and socio-economic status. Most existing COVID-19 mobility studies focused on spatial changes (for example, radius of gyration or locations visited), with limited attention to synchronized temporal patterns. Few works explored temporal regularities or the emergence of phenomena such as temporal shifts in activity and weekday-weekend similarity during the pandemic. Because mobility patterns are built on space-time interaction, it is vital to study both dimensions. This study assesses the spatial dimension using the radius of gyration and introduces a mobility synchronization metric to quantify co-temporal occurrence of daily mobility motifs (for example, synchronized work departures). Increased synchronization implies higher contact rates and potential disease transmission. By combining these metrics, the study gauges how far infectious individuals could travel and how many people they might contact. Using de-identified, opt-in LBS data from January 2019 to February 2021 across the United Kingdom, the authors analyze changes in trip duration and frequency and disentangle how spatial and temporal dimensions were affected. As restrictions were lifted, the spatial dimension recovered faster than the temporal. The space-time components diverged during the second lockdown and realigned after the third. Trips are defined as events where a user leaves their home geofence; for each trip, total time out-of-home, inclusion of green areas, and distance travelled are recorded. Mobility metrics are coupled with urbanization, unemployment, occupation, and income data at the local authority level to examine heterogeneous impacts across rural/urban and socio-economic strata.

Mobile phone and location-based data have been extensively used to capture human mobility motifs, commuting patterns, and urban dynamics, informing public health responses and policy during epidemics. During COVID-19, aggregated mobility metrics were widely adopted to evaluate lockdown effectiveness, model transmission, study policy impacts and reopening strategies, and assess socio-economic and ethnic disparities. Prior literature largely emphasized spatial changes (for example, radius of gyration and visited locations) with temporal analyses often limited to trip duration or change over time; synchronized mobility patterns and other temporal facets were underexplored, especially across multiple lockdowns. Studies also documented temporal shifts during the pandemic (later morning activity, earlier evening activity, weekday-weekend convergence). Urbanization level influences mobility patterns and disease diffusion, with transport systems and inter/intra-urban connectivity affecting contagion risks. Socio-economic inequalities shape differential mobility responses to restrictions, with income and occupation linked to mobility reductions and segregation. This work addresses gaps by jointly quantifying spatial span and temporal synchronization across different lockdown phases and socio-demographic contexts.

Data: Spectus provided GDPR-compliant, de-identified LBS data from anonymous UK mobile users who opted in, covering January 2019 to early March 2021. Researchers accessed aggregate outputs via a secure sandbox. The dataset includes over 17.8 billion out-of-home trips and about 1 billion weekly radius of gyration (RG) records. Trips are recorded daily; RG is logged weekly. Representativeness was assessed via correlation between user counts and local authority population (r^2=0.775). Home location areas are inferred from location histories and dwell patterns; a home geofence is a 500 m square. Study design: The primary window analyzed is January 2019–February 2021 for UK local authorities, with detailed national lockdown periods referenced from official UK sources. Because policies varied across UK nations, regional analyses are provided in supplementary materials. Metrics: - Spatial dimension: Radius of gyration per user over time; regional mobility is the median of user RG within an 8-day window centered on a given day. RG quantifies how far visited locations spread from the trajectory’s center of mass. - Temporal dimension: Mobility synchronization captures the magnitude of periodicity in out-of-home trip time series (hourly aggregation). Using 2019 as baseline, wavelet and Fourier spectra identify strongest periodic components (24 h, 12 h, 8 h, 6 h). As the 24 h component dominates and was less affected during the pandemic, synchronization focuses on 12 h, 8 h, and 6 h. Synchronization is computed as the sum of powers at these periods from generalized Lomb-Scargle periodograms, yielding a value between 0 and 1 (higher indicates more people leaving home simultaneously). - Residual mobility activity: A normalized, Z-score-like residual highlighting deviations from expected behavior (baseline: 2019), computed per local authority and aggregated by urban-rural class. Definitions and additional analyses: - Trips: Events when a user exits their home geofence; for each trip, the study records duration outside before returning home, distance traveled, and whether a green area was included. - Work-related trips: Classified based on starting time windows indicative of commuting. - Green area trips: Identified via trips including green spaces (parks, sports facilities, play areas) using Ordnance Survey Open Greenspace data; categories like burial grounds/churchyards are excluded. Stratifications and external data: - Urbanization: English local authorities grouped into three classes per the ONS urban–rural classification. - Unemployment: Unemployment claimant count from ONS at local authority level. - Socio-economic/occupation: NS-SEC classification (ONS) used as a proxy for income/occupation structure; income estimates from ONS used to relate NS-SEC classes to income. Comparative periods and statistics: - Baseline year: 2019. - Pre-pandemic: April 2019–February 2020. - Pandemic: April 2020–February 2021. - Correlations: Kendall Tau correlations between mobility metrics (RG, synchronization) and unemployment claimant count computed overall and by urbanization level, separately for pre-pandemic and pandemic periods. - Visualization: Time series and maps of RG and synchronization; residual activity by urban–rural class; scatter plots comparing baseline, week-before-lockdown, and first week of lockdown. Privacy/aggregation: All analyses conducted on aggregated outputs at local authority level; no personal identifiers used.

- Divergent recovery of space-time mobility: From early 2020 to early 2021, radius of gyration (spatial span) and mobility synchronization (temporal regularity) tracked together until around week 18 of 2020. Thereafter, the spatial dimension recovered toward pre-pandemic levels, while temporal synchronization lagged, indicating more asynchronous mobility routines even as travel distances rebounded. After the third lockdown, spatial and temporal trends realigned, resembling pre-week-18 patterns. - Lockdown impacts differ by metric: The first national lockdown produced the largest reduction in radius of gyration across the UK nations. Temporal synchronization decreased during all three lockdowns, but the second lockdown showed the most substantial decrease: 78.34% of local authorities experienced a reduction in synchronization versus baseline, compared to 56.67% during the first and 34.02% during the third. Effects during the third lockdown are challenging to disentangle from end-of-year holiday changes in mobility. - Urban–rural heterogeneity: Residual activity analysis showed urban areas increased expected mobility during the first lockdown while rural areas decreased; this pattern reversed during the second and third lockdowns, potentially due to policy flexibility and pre-existing vulnerabilities. Rural areas generally have larger RG due to dispersed amenities and longer trips. Spatial reductions were more pronounced in rural areas, while temporal synchronization was more disrupted in urban areas, consistent with rises in flexible/staggered work schedules. - Unemployment associations shifted: Before the pandemic, both RG and synchronization were positively correlated with unemployment claimant counts across most areas. During the pandemic, the RG–unemployment correlation weakened but remained positive (more so in urban than rural areas), while the synchronization–unemployment correlation turned negative and was more impactful in rural districts than urban. Less urbanized areas tended to show lower spatial and higher temporal correlations with unemployment compared to more urbanized areas. - Socio-economic patterns (NS-SEC): Managerial occupations correlate positively with income; lower supervisory, semi-routine, and routine occupations correlate negatively. Areas with higher concentrations of managerial occupations exhibited larger RG and higher synchronization before and during the pandemic, whereas areas with more routine/semi-routine occupations showed the opposite. During the pandemic, all groups saw reductions, with low-income routine/semi-routine groups experiencing the greatest decreases in RG and synchronization. - Trip characteristics changed: During the first lockdown (week 13 of 2020), work-related trips shortened in duration relative to 2019; high-income groups saw the most pronounced reductions. Leisure-related trips involving green areas diverged between rural and urban areas after restrictions began to lift in summer 2020, with substantial differences emerging despite similar levels earlier in the year.

Findings demonstrate that spatial and temporal facets of mobility responded differently to COVID-19 restrictions. The first lockdown’s stricter and uniform policies across UK nations likely drove the largest spatial contraction (radius of gyration). By contrast, the second lockdown coincided with more flexible policy allowing those unable to work from home to attend workplaces under distancing rules; staggered/rotational shifts and flexible hours likely reduced co-temporal commuting, producing the largest drop in mobility synchronization. The decoupling—fast spatial recovery but lagging temporal synchronization—highlights the emergence of asynchronous mobility routines. Heterogeneous effects across urbanization and socio-economic strata emphasize that context matters: rural areas experienced larger spatial disruptions, while urban areas showed stronger temporal desynchronization. Unemployment associations flipped for temporal synchronization during the pandemic, reflecting differential labor market shocks and work patterns. NS-SEC-based analyses indicate that low-income routine/semi-routine groups bore the greatest mobility reductions, whereas managerial groups maintained higher mobility metrics but still declined. These insights are relevant to public health and urban policy: mobility synchronization provides an indicator of potential contact intensity, complementing spatial metrics like RG. Considering both dimensions enables more nuanced assessment of interventions (for example, stay-at-home orders, school/business closures) and supports targeted strategies that account for urban–rural differences and socio-economic disparities.

This work introduces a dual spatio-temporal framework to characterize pandemic-induced mobility changes: radius of gyration for spatial span and a synchronization metric for temporal regularity. Across UK local authorities (2019–2021), spatial mobility contracted most during the first lockdown and recovered more quickly than temporal synchronization, which was most suppressed during the second lockdown. Urban–rural and socio-economic disparities were pronounced: rural areas showed larger spatial disruptions; urban areas exhibited greater temporal desynchronization; low-income routine/semi-routine groups experienced the largest reductions. By disentangling space and time, the study offers actionable metrics for policymakers to evaluate intervention impacts and anticipate contact rates. Future research should further investigate causal mechanisms behind observed patterns (for example, policy stringency and duration, workplace scheduling practices), explore confounding seasonal/holiday effects, and assess long-term persistence of asynchronous routines and their health and equity implications.

- Attribution challenges: It is difficult to disentangle the effects of the third lockdown from end-of-year holiday mobility changes. Hypotheses about why the first lockdown most affected spatial mobility (for example, stricter policies, duration) require further investigation. - Data constraints: Raw mobile phone data cannot be shared due to privacy/contractual obligations; analyses rely on aggregated outputs at local authority level, which may limit granularity. Despite representativeness checks (r^2=0.775), selection biases and uneven coverage may remain. - Scope and definitions: Synchronization focuses on 12 h, 8 h, and 6 h periodicities (24 h component excluded due to dominance), which may omit some temporal structures. Work-related trips are inferred from start times, which may misclassify purposes. Green area trip analysis excludes certain categories (for example, religious grounds) and requires further study to explain rural–urban differences. - Policy heterogeneity: Variations in lockdown implementation across UK nations complicate national-level comparisons; detailed regional analyses are delegated to supplementary materials.