Time series association between COVID-19 incidence and human mobility

Before conducting time series analysis, we first filtered the counties among the 588 metropolitan statistical areas that had an average number of COVID-19 cases greater than the median number of cases of all counties during our study period. By differencing the data and conducting the ADF test, we identified 425 counties that had stationary time series for both COVID-19 cases and human mobility. Then, to find an optimal lag length for the Granger causality test, we computed AIC for each county and then calculated the mean of AIC values of all counties for each wave. As a result, in all three waves, the curve of mean AIC values of counties flattens around lags of seven and eight days, and then AIC maintains similar values as the lag length becomes longer. We chose to use a 7-day lag due not only because it has the lowest AIC values in waves 2 and 3, but also there is evidence from the previous studies of the earlier waves that found a 7-day lag between the contact with an infected person and the manifestation of clinical symptoms [9].

Next, we performed the Granger causality analysis for each of the three waves to identify the significant time series associations between COVID-19 cases and human mobility flows. Figure 2 shows the number of statistically significant counties for each of four possible cases in bidirectional relationships: (1) COVID-19 incidence Granger-causes human mobility, (2) human mobility Granger-causes COVID-19 incidence, (3) significant in both ways, and (4) no significant relationship. The results in Fig. 2 reveal some interesting findings regarding the temporal variations in those bidirectional relationships. First, more than half of the counties do not have any statistically significant relationship between COVID-19 incidence and mobility across all periods. Second, among the counties with significant relationships, overall, it is more common for COVID-19 cases to have a stronger effect on human mobility than human mobility does on COVID-19 incidence across different periods mainly because of NPIs. Third, the number of counties where COVID-19 cases Granger-cause mobility flows is 130, 85, and 50 in waves 1, 2, and 3, respectively. The number keeps decreasing over the three waves. This supports the fact that human mobility was most strictly restricted during the earlier periods of the pandemic due to the enforced stay-at-home orders [28] and the fear of infection was also the highest in this early phase of the pandemic [12]. On the other hand, mobility has a significant influence on COVID-19 cases in only a few counties, which shows that mobility flows do not Granger-cause COVID-19 cases as much as the effect of COVID-19 on mobility. However, it is notable that the number of counties where mobility Granger-causes COVID-19 cases increase sharply in wave 3. It implies that the increase in mobility due to the reopening policies and the availability of COVID-19 vaccines in late 2020 results in having more influence on COVID-19 cases.

Fig. 2

The number of counties with statistically significant relationships by directions

We further disaggregate this time-series trend in Fig. 2 and investigate more detailed temporal patterns on how relationships between COVID-19 cases and human mobility changed or remained stable. Figure 3 shows how each of four possible cases in bidirectional relationships evolves throughout three different waves of the pandemic. In Fig. 3, the width of grey flow lines indicates the number of counties. Note that this Sankey diagram only includes counties with at least one significant relationship over three waves.

Fig. 3

The number of counties that changed or remained stable in terms of the direction and significance of the association between disease incidence and mobility

The most frequent pattern of change (i.e., the widest flow line) is that COVID-19 incidence Granger-causes mobility in wave 1 without any significant relationship in waves 2 and 3. This result supports the previous findings that the correlation between COVID-19 cases and mobility was the strongest during the initial lockdown and became weaker since other factors resulted in complex disease dynamics as time passed [8]. Another notable pattern is that approximately half of the counties without any significant relationships in wave 1 changed to have a significant relationship that COVID-19 incidence Granger-causes mobility in wave 2, and the relationship of more than half of those counties again became insignificant in wave 3. Such information is hidden when aggregated as in Fig. 2, although we can still find the general trend of decreasing number of counties where COVID-19 cases Granger-cause mobility from Fig. 2.

Although Granger causality helps identify the direction and significance of the association between two time series trends, these associations can vary in form such as positive and negative associations. Consequently, each of the four associations in Fig. 3 could have two distinct forms, which makes a total of eight possible scenarios. Figure 4 illustrates the time series trends of these eight distinct scenarios drawn from our county-level time series analysis results. When COVID-19 incidence Granger-causes human mobility with a negative association, there are two possible scenarios. In Kings County, NYC, the increasing trend of COVID-19 incidence Granger-causes and precedes the decreasing trend of mobility in (Fig. 4b). Second, the decreasing COVID-19 incidence Granger-causes and precedes the increasing mobility trend in Queens County, NYC (Fig. 4c). The presence of these two distinct forms of associations can be attributed to specific behavioral patterns observed during the pandemic. When the disease incidence is on the rise, people tend to exhibit increased caution and reduce their mobility, leading to a subsequent decline in mobility trends (as observed in Kings County, NYC). Conversely, when the pandemic situation is less severe and disease incidence is declining, individuals tend to become more willing to travel, resulting in a subsequent increase in mobility trends (as observed in Queens County, NYC). These patterns highlight the relationship between the severity of the pandemic and individuals' willingness to travel, ultimately influencing the direction of the association between COVID-19 incidence and mobility. The association can also be positive in the form of increasing or decreasing trends. Figure 4a illustrates a positive association such that both COVID-19 cases and mobility flows are increasing, while Fig. 4d illustrates that both trends are decreasing. In both cases (Fig. 4a, d), the trend of COVID-19 Granger-causes and precedes that of mobility flows. This implies that human mobility flows are affected by many factors other than the pandemic severity, such as better mask-wearing and social distancing policies, which is also discussed in the previous study [1].

Fig. 4

Eight possible scenarios in the bidirectional relationship between COVID-19 incidence and mobility flows. Each of A–H in a red box indicates each scenario

Likewise, when mobility flows Granger-cause and precede COVID-19 incidence, the association can be both positive and negative. The increasing COVID-19 cases can be followed by the increasing mobility flows (Fig. 4e) since increased mobility can be a proxy of more social interactions and a higher risk of infections. On the contrary, the decreasing trend of mobility can Granger-cause the decreasing COVID-19 incidence (Fig. 4h). However, if there are negative associations, it is also possible that the trend of COVID-19 cases is increasing although mobility flows are decreasing (Fig. 4g) or vice versa (Fig. 4f), which implies confounding factors affecting the COVID-19 incidence trend.

We further investigated the distribution of the counties with significant Granger-causality across eight types of scenarios. To do so, for each county and for each wave, we performed the analysis of (1) Pearson correlation to examine if two trends of COVID-19 and mobility have a positive or negative association and (2) a simple linear regression to decide if each of COVID-19 and mobility trends is increasing or decreasing. As a result, we found that when COVID-19 trend Granger-causes mobility trend, they are more likely to have positive correlation where both trends are increasing in wave 1 and wave 2. In wave 3, however, the most common scenario is that those two trends have a negative correlation where COVID-19 cases are increasing, and mobility flows are decreasing. On the other hand, when mobility trend Granger-causes COVID-19 trend, those two trends are more likely to have negative associations in waves 1 and 3, but positive associations are more common in wave 2. More detailed results can be found in the Appendix.

Spatial and temporal variations of COVID-19 incidence and mobility relationship

We investigate how bidirectional relationships between COVID-19 incidence and human mobility are spatially distributed and how those spatial distributions change over time (i.e., across different waves). Figure 5 demonstrates the spatial variations in the relationship between COVID-19 incidence and human mobility with different directions of their relationship for each period. During wave 1, COVID-19 hit urban areas harder than rural areas [29]. The areas where COVID-19 Granger-causes mobility (in orange) also include metropolitan areas such as New York City, Chicago, Atlanta, Minneapolis, and San Francisco. This suggests that increased incidence of COVID-19 in large and dense metropolitan areas forced people reduce their mobility more substantially than in suburban and low-density urban areas. In contrast, wave 2 is when reopening policies started to be implemented, and many metropolitan areas of the South and Southwest experienced a surge. Some of those areas including Houston, Charlotte, and Las Vegas have a significant relationship that COVID-19 cases Granger-cause human mobility as shown in orange in Fig. 5. However, in this period, COVID-19 virus was not limited to metropolitan areas and had been widely spread to suburban and some rural areas as well [28]. As a result, the number of counties with significant relationships between COVID-19 cases and mobility in metropolitan areas became smaller. For example, some cities such as Chicago, Kansas City, and Indianapolis which had significant relationships in wave 1 are no longer significant in wave 2. Wave 3 is when the COVID-19 pandemic is the most severe with a peak of daily cases and deaths over the country. Like in wave 2, the number of counties where COVID-19 Granger-causes mobility keeps getting smaller in wave 3. Interestingly, on the other hand, the number of counties where mobility Granger-causes COVID-19 cases has increased. Indeed, in some areas such as Kansas City and Indianapolis where COVID-19 Granger-causes mobility in wave 1, the direction becomes the opposite in wave 3. Spatial variations during this period may be explained by the fact that the lift of lockdown policy was implemented by different states without a national mandate [8].

Fig. 5

Spatial and temporal variations of COVID-19 and mobility relationship. (‘COVID-19 ↔ Mobility’, ‘COVID-19 → Mobility’, ‘Mobility → COVID-19’, and ‘Not Significant’ indicates ‘COVID-19 and Mobility simultaneously’ Granger-cause each other’, ‘COVID-19 Granger-causes mobility’, ‘Mobility Granger-causes COVID-19’, ‘There is no significant relationship’, respectively)

To further investigate if counties that have significant Granger causality are spatially clustered, we employed univariate local joint count statistics developed by Anselin and Li [30]. This is a local indicator of spatial association which is appropriate when a variable of interest is binary. This method allows us to statistically test if a county with a specific type of significant Granger causality result is surrounded by counties with the same significant Granger causality result than would be expected under conditions of spatial randomness. Here, we have two granger causality types: (1) COVID-19 incidence granger-causes mobility flows, and (2) Mobility flow granger-causes COVID-19 incidence. So, for each of three waves and for each of two granger causality types, we computed local join count statistics. Table 1 shows the number of counties that are significantly locally clustered with other counties with the same Granger causality type at the 0.05 level of significance. The numbers in parentheses indicate the total number of counties with significant Granger causality of each type. So, during wave 1 for example, there are 149 counties where COVID-19 Granger-causes mobility, and among them, 23 counties are locally clustered. Interestingly, these local clusters are mostly located near metropolitan areas including New York City (NY), Philadelphia (PA), Charlotte (NC), Chicago (IL), and Dallas (TX). The discovery of these clusters near these major metropolitan areas during different waves indicates that urban centers, with their higher population density and mobility, played a crucial role in the dynamics of COVID-19 spread and response.

Table 1 Number of counties that are locally clustered with other counties having the same Granger causality at the 0.05 level of significance

These findings reveal that counties with a particular type of Granger causality (either COVID-19 incidence Granger-causing mobility flows or mobility flows Granger-causing COVID-19 incidence) tend to be geographically clustered rather than randomly distributed. This clustering is observable in each of the three waves of the pandemic, for both types of Granger causality. The number of counties showing significant local clustering with similar Granger causality types suggests that the pandemic’s impact and the response in terms of mobility were not uniform across the U.S. but concentrated in specific regions.

Assessing similarity between time series of COVID-19 incidence and human mobility

The results from the Granger causality analysis identifies the existence of statistically significant associations between the two time series trends. However, the magnitude of association among the trends is unknown. We computed DTW distances between the standardized series of COVID-19 cases and mobility flows for each county and each wave to compare the similarity between the two trends across different geographies and throughout the different waves. Figure 6 highlights geographic variations in DTW distances over three time periods. The DTW distances are classified into five classes using Jenks’ natural breaks. To fairly compare different waves, we first defined classes based on all DTW distance values over three waves and then apply the same classification to all of the three waves. Overall, the degree of similarity is the highest in wave 1, and while it is gets gradually smaller in waves 2 and 3. This implies that the relationship between COVID-19 cases and mobility was strongest in wave 1, but other factors began to affect COVID-19 cases as the pandemic continued, which also corresponds with the results of the Granger causality test. Also, more importantly, the results from DTW demonstrate that even though there are statistically significant relationships between COVID-19 cases and mobility flows consistently over periods, the degree of such relationships may vary across space and time. For example, in Las Vegas, COVID-19 Granger-caused mobility flows in all three waves (Fig. 5); however, the DTW distance of that area was the largest in wave 2 and the smallest in wave 1 (circles in Fig. 6), which shows that the degree of their correlations changed over different waves.

Fig. 6

DTW distances for mobility and COVID-19 incidence in study areas. The value becomes smaller as two time series have more similar trends. Counties with shorter distances (in blue color hue) have more similar trends

To better understand the changes in the degree of similarity between COVID-19 case and mobility trends, we further investigated how DTW distances varied over time and whether the trends in cases and mobility were positively or negatively correlated (Table 2). We could confirm that the similarity between the two trends of COVID-19 cases and mobility flows became weaker, indicated by increasing DTW distances. More interestingly, however, the DTW distances showed notable differences based on the nature of the association (positive or negative) between the two trends, as determined by Pearson’s correlation coefficient. Specifically, when there was a positive correlation between COVID-19 incidence and mobility trends (i.e., both trends moved in the same direction), we found that the similarity in their patterns weakened. In contrast, a stronger similarity was observed when the trends were negatively associated (i.e., moving in opposite directions). Despite these variations, the overarching trend points to a general decline in the similarity between COVID-19 case numbers and mobility patterns. This finding suggests that the dynamics of the pandemic and public response, as reflected in mobility changes, have evolved in complexity. Initially, more direct relationships might have existed, but over time, factors such as changes in public behavior, and policy interventions could have influenced these patterns.

Table 2 Descriptive statistics of DTW distances between two trends of COVID-19 incidence and mobility flows