Human mobility patterns are significantly influenced by socio-economic factors and urban topology. The COVID-19 pandemic dramatically altered these patterns, prompting a need to understand the changes in both the spatial and temporal dimensions of mobility. Previous research primarily focused on the spatial dimension, measuring changes in the distance traveled. However, the temporal dimension, encompassing the synchronization of daily routines, remained largely unexplored. This study addresses this gap by analyzing de-identified mobile phone data to examine how both spatial and temporal mobility changed during the COVID-19 pandemic in the United Kingdom. Understanding these changes is crucial for informing public health policies, predicting disease spread, and evaluating the effectiveness of mobility restriction measures. The use of location-based data from mobile phones provides a large-scale, near real-time perspective on human mobility, overcoming limitations of traditional surveys and censuses. This data allows for a detailed analysis of daily routines, commuting patterns, and the purpose of trips, providing valuable insights into the impact of the pandemic on various aspects of life.

Existing literature primarily focused on the changes in the spatial dimension of mobility during the COVID-19 pandemic, analyzing metrics such as the radius of gyration and locations visited. Temporal analyses were limited to trip duration, neglecting synchronized mobility patterns or other temporal aspects. These studies often lacked the longitudinal perspective to analyze mobility changes across multiple lockdowns. While the spatial patterns of human movement are well-documented, the temporal regularities driven by physiology, natural cycles, and social constructs are less studied. A few studies have explored these temporal regularities, aiming to classify individuals based on their temporal behavior or to uncover emergent social phenomena. In the context of the pandemic, research showed a shift in daily activities, with later morning starts and earlier evening ends, blurring the distinction between weekday and weekend routines. The limited existing research highlights the importance of investigating both the spatial and temporal dimensions to fully understand the pandemic's effects on human mobility.

This study leverages location-based service (LBS) data from de-identified mobile phone users in the UK from January 2019 to February 2021. The data, provided by Spectus and compliant with General Data Protection Regulation (GDPR), includes records of out-of-home trips. Two key metrics were used to analyze the data: 1. **Radius of gyration (RG):** This spatial metric quantifies the dispersion of a user's visited locations from their center of mass, providing a measure of the spatial extent of their movements. The RG was chosen due to its established use in human mobility studies and its application in assessing compliance with mobility restrictions during the pandemic. 2. **Mobility synchronization:** This temporal metric quantifies the co-temporal occurrence of daily mobility motifs, measuring the regularity and synchronization of daily routines, such as commuting. High synchronization is associated with increased social contact and higher risk of disease transmission. The data were analyzed at the local authority level, enabling comparison of mobility patterns across different geographical areas and socio-economic groups. The analysis included comparison of mobility patterns during the three UK lockdowns, examining the differences in spatial and temporal changes. Additional data from the Office for National Statistics (ONS) on unemployment rates, urban-rural classification, and the National Statistics Socio-Economic Classification (NS-SEC) were integrated to investigate the correlation between mobility patterns and socio-economic factors. Wavelet and Fourier transforms were employed to identify the main frequency components in mobility patterns and to calculate the mobility synchronization metric, focusing on periods of 12h, 8h, and 6h. The residual activity concept was utilized to highlight variations from the expected mobility patterns based on a 2019 baseline. The study also assessed changes in trip duration and the frequency of trips to green spaces.

The study revealed that during the lockdowns, the decrease in spatial mobility (measured by radius of gyration) was accompanied by an increase in asynchronous mobility dynamics. Upon lifting restrictions, spatial mobility recovered more quickly than temporal synchronization. The impact of lockdowns varied based on urbanization and economic factors. Rural and low-income areas experienced greater disruptions in spatial mobility, while urban and high-income areas were more affected in their temporal mobility. The second lockdown caused the most significant reduction in mobility synchronization, possibly linked to stricter stay-at-home policies. Analysis of urban and rural areas showed contrasting trends. Urban areas initially showed increased mobility during the first lockdown and then decreased during subsequent lockdowns, while rural areas exhibited the opposite pattern. This difference might be attributed to varying mobility restriction policies and pre-existing social vulnerabilities. Correlation analysis between mobility metrics and unemployment revealed a positive correlation before the pandemic, which weakened for spatial mobility and became negative for temporal mobility during the pandemic. Analysis using NS-SEC data indicated that areas with high concentrations of low-income, routine occupations experienced the most substantial reductions in both spatial and temporal mobility. Examining trip duration, the study showed a reduction in work-related trips, especially among high-income groups during lockdown. Finally, analysis of trips to green spaces showed a greater increase in these types of trips in rural areas after lockdown restrictions were lifted.

The findings highlight the complex interplay between spatial and temporal dimensions of mobility during the pandemic. The faster recovery of spatial mobility compared to temporal mobility indicates that while people resumed travel, the synchronization of their routines remained disrupted. The different impacts on urban and rural areas, as well as across socioeconomic groups, underscore the importance of considering these factors in public health policies. The shift in the correlation between unemployment and mobility, particularly the negative correlation between unemployment and temporal mobility during the pandemic, suggests complex economic factors influencing mobility patterns during crisis. The different responses across NS-SEC groups emphasize the need for targeted policies accounting for varying socio-economic circumstances. This research contributes to a more comprehensive understanding of the impact of pandemics and mobility restriction policies, providing insights into the spatial and temporal dynamics of human behavior during a crisis. These results should be considered in future modeling efforts of pandemic spread and the development of policies to manage pandemics and other large-scale emergencies.

This study provides a comprehensive analysis of the changes in the spatial and temporal dimensions of human mobility during the COVID-19 pandemic. The findings demonstrate that lockdowns led to a significant decrease in mobility and a shift toward asynchronous patterns, with variations across socioeconomic and geographic factors. These insights are crucial for informing future public health policies and understanding the broader societal implications of large-scale disruptions to human mobility. Future research could investigate the long-term impacts of the pandemic on mobility patterns and explore the potential for using mobility data to predict and mitigate the effects of future pandemics.

The study relies on de-identified mobile phone data, which may not fully represent the entire population. The data aggregation at the local authority level might mask variations within those areas. Furthermore, the analysis focuses on the UK context, and the findings may not be directly generalizable to other countries with different social, economic, and geographical characteristics. Finally, the analysis focuses primarily on the effects of national lockdowns, whereas regional and local variations in restrictions might have influenced mobility patterns.