In December 2019, a novel coronavirus called COVID-19 began spreading across the globe. To fight this pandemic, the U.S. government issued a national emergency on March 13 and launched the Coronavirus Guidelines for America on March 16, in which a social distancing intervention was strongly suggested 1,2 . Accordingly, statewide mobility restrictions were successively announced upon the arrival of pandemic. The first stay-at-home order in the U.S. began in California on March 19 and quickly swept the nation. By mid-April, stay-at-home orders were instituted across all but eight states. Yet despite the fact that it has been two months since the U.S. declared the nationwide national emergency, COVID-19 cases are still increasing at an alarming speed. This indicates that more effort on reinforced interventions is needed to help stop the spread of this pandemic. Particularly, with a nationwide partial reopening of society, decision makers and social practitioners need research basics to make better plans and adjust measures according to local social and economic features. As revealed in earlier studies, the transmission of COVID-19 is positively associated with various social and economic factors, such as gross domestic product (GDP) and human development index 3,4 . Some studies have investigated different income groups during the pandemic and presented a consistently obvious mobility gap [3] [4] [5] [6] [7] . It is noteworthy that disadvantaged people encounter even more challenges under this pandemic. Research reveals that low-income individuals are under increased pressure due to the threat of unemployment, poor working conditions, limited health insurance, etc., as well as the stringent choice between health and income, which are both significant to household subsistence 5 . Such a dilemma not only poses a threat to public health, it also makes it more difficult to contain the pandemic.
In this paper, we specifically investigate low-income communities in terms of social distancing behavior. Multifaceted social distancing performance metrics are compared between different income groups, including percentage of staying home, miles traveled per person, trips per person, work trips per person, non-work trips per person, and social distancing index. We aim to answer the following questions. Are there any significant differences in these metrics between different income communities? Which aspects of social distancing behavior indicate these differences?
Does income really have an impact on the communities after addressing the effects of various confounding factors? If yes, how is the income influencing each aspect of behavior in terms of significance level, degree, and direction? What are the differences between communities of different income levels in their best performance of being social distancing? Which income level communities made more efforts to achieve the best social distancing performance? Which income group performs more consistent and long-lasting social distancing behavior? And which mobility metric is most influenced by income?
Mobile device location data, an emerging data source for analyzing mobility behaviors, has been actively utilized to investigate public mobility during the pandemic [8] [9] [10] [11] [12] [13] . With access to a high frequency and large coverage of real-world mobile device location data, the authors were able to quickly develop an analysis at census tract level. Various mobility metrics were produced at census tract level using the previously developed algorithm. We investigated the response of different income group communities regarding social distancing performance (i.e., "best performance", "effort", and "consistency"). The temporal mobility patterns for different income groups are first analyzed through Repeated Measures ANOVA and post-hoc analysis, which statistically indicates the significant differences for pairwise comparison between days [14] [15] [16] . Based on the temporal analysis, we then proposed the hypothesis that high-income communities outperformed lowincome communities in social distancing performance. This hypothesis is confirmed through Welch's t-test and propensity score modelling [17] [18] [19] . Our study enhances the awareness of discrepancies between high-and low-income communities and provides evidence to policymakers regarding interventions on the pandemic. With partial reopening underway in all 50 states, our paper can also guide the implementation of partial reopening policies.
According to the U.S. Internal Revenue Code section 45D(e)(1), we classified any census tract with at least 20% poverty rate or median household income no more than 80% of the metropolitan area or statewide median income as a low-income community. In this section, we primarily explore the temporal patterns of the six mobility metrics of both low-and high-income groups. Fig. 1 shows the temporal changes from March 2 to April 17. It is obvious that both income groups experienced two critical changing points, e.g., March 13 and April 13. The finding is in line with our previous studies at the state and national level, which suggested that March 13 (the national emergency declaration date) and April 13 (one month after the declaration) are two critical timepoints for mobility metrics changes 7, 13 . The week before March 13 is called an inertia period, meaning the mobility change gradually bottoms out; the week of March 13 is called fatigue period, meaning relaxed efforts of social distancing and mobility begin to rebound despite ongoing mobility restriction orders. In addition, there exists notable differences between the two income groups in all mobility metrics. Interestingly, the status between the two income groups exchanged during the pandemic with regards to the social distancing index, percentage of staying home, and miles traveled per person (Fig. 1a, b, c) . The difference between the two income groups gradually enlarges during the pandemic with regards to the three other metrics: trip rate, work trip rate, and non-work trip rate (Fig. 1d , e, f). During the two weeks before the national emergency declaration, there was already a difference between the two income groups regarding trip rate and non-work trip rate and this difference was shrinking. On the other hand, after the declaration, the difference gradually grows and the two income groups once again become quite different from each other.
Putting work trip rate into context, before the pandemic, the two income groups are very similar to each other while there is a disparity between them during the pandemic. Fig. 1 also indicates that on average, the percentage change for high-income communities is bigger than low-income communities. Although high-income communities have a smaller average value of social distancing index and percentage of staying home before the pandemic, they made more effort to follow social distancing and therefore they have a larger average value for these two metrics afterwards. Similarly, high-income communities' percentage reduction in miles traveled per person and the three trip rate-related metrics are obviously larger than those of low-income communities. Under the pandemic, high-income communities seem to be at a lower risk of exposure to the virus according to those six aspects of social distancing performance. results of three metrics for both groups are presented in the significance plots (Fig. 2) , which reveal the following findings. First, significant change of means at a 99.9% confidence interval, denoted by the dark green cells, are observed earlier in high-income communities regarding the three metrics. This indicates that high-income communities responded earlier to the mobility interventions. Among these three metrics, high-income communities responded 10 days earlier in terms of work trips per person and miles travelled per person compared with low-income communities (Fig. 2a, e) . Second, the behavior change took place more quickly and more clearly in high-income communities, while the low-income communities reacted inconsistently in stay-athome percentage and miles travelled per person metrics. This is supported by the cleared pink square observed in the significance plots of the high-income group (Fig. 2c , e). Another interesting finding is that the social distancing behavior of high-income communities is more consistent regarding all the metrics. After the behavior change stage, high-income people keep following social distancing. However, low-income communities show more fluctuations in mobility patterns. 
Based on the preliminary results from the section above, we proposed the hypothesis that highincome communities perform better than low-income communities in three aspects: (1) highincome communities have greater "best performance"; (2) high-income communities made more "effort" in social distancing; and (3) high-income communities have a higher social distancing consistency. "Best performance" means the best experienced value during the five weeks after March 13 in each mobility metric. For example, the maximum value of social distancing index and percentage of staying home, the minimum value of miles traveled per person, trip rate, work trip rate, and non-work trip rate are referred to as "best performance." "Effort" means the percentage change in each metric by comparing "best performance" with the baseline, which is the weekday average for the two weeks before March 13. "Consistency" refers to the stability of the status of following social distancing in the late stage of the quarantine, which is the fourth and fifth week after the pandemic. The fourth week is the week before April 13, during which each mobility metric gradually stabilized, as shown in Fig. 1 . Then during the week after April 13, each metric shows a rebounding trend. We use the standard deviation of each mobility metric during these two weeks as the indicator of social distancing consistency. Based on those three aspects and the six mobility metrics, we have eighteen scenarios in total to compare the high-and low-income communities. The previous section gave us some insight into the difference between income groups at the average level. Here, we examined in more detail through the corresponding distribution by income groups (Fig. 3) . Generally, the distributions of both income groups are close to normal distribution and high-income communities tend to perform better based on the distribution. As for the best performance, the mean of social distancing index and percentage of staying home for high-income communities is larger than that of low-income communities, while the mean of other metrics for high-income communities is smaller. This is consistent with Fig. 1 .
As for "effort" (percentage change), we can see that on average high-income communities made more effort since the mean value of the percentage increase in social distancing index and staying home of high-income communities and the percentage reduction in miles traveled per person and the three trip related metrics of the high-income group are larger than the low-income communities. As for the variation, the high-income communities tend to have a smaller standard deviation, meaning that they are more stable during the late stage of the quarantine period. behavior is tabulated by three types of indicators (best performance, percentage change, and variation) and six mobility metrics for each community. Therefore, there are 18 scenarios. Each subplot presents the corresponding distribution by high-and low-income groups. In addition, the mean value and coefficient of variation (CV) by income groups are annotated. A major finding is that, in each scenario, high-income communities perform better than low-income communities.
Based on current analysis, we applied one-sided Welch t-tests to eighteen scenarios to test the common hypothesis that high-income communities outperform low-income communities. When comparing the best performance and efforts, the alternative hypothesis used for the percentage of staying home and social distancing index is that high-income communities' mean is greater than low-income communities' mean, while for the other mobility metrics vice versa. When comparing the consistency, the alternative hypothesis used for all mobility metrics is that high-income communities' mean is smaller than low-income communities. The results for all scenarios are summarized in Table. 1, which indicates the alternative hypothesis of sixteen scenarios are supported at 99% confidence level.
As for the comparison of best performance, it seems that the means of high-and low-income communities are quite close. However, the two income groups are significantly different for four metrics including social distancing index and the three trip rate related metrics. On average, highincome communities achieve a higher social distancing index while low-income communities have a higher trip rate, work trip rate, and non-work trip rate. Communities in high-and low-income groups do not differ significantly with regards to percentage of staying home and miles traveled per person. As for the effort (percentage change) of following social distancing, an obvious difference in mean can be seen for metrics like percentage of staying home (high-income 138% vs. low-income 117%) and social distancing index (high-income 182% vs. low-income 153%) and such difference is significant at 99% confidence level. Although the two income groups show very close percentage change in the other four metrics, high-income communities still significantly perform better than low-income communities at 99.9% confidence level. According to the 95% confidence interval, high-income communities are expected to have 21% more percentage increase in the percentage of staying home and 28.5% more percentage increase in the social distancing index on average. Among the four trip-related metrics, the largest difference is observed in the miles traveled per person (<= -4.3%). In addition, the difference in work trip rate (<= -2.0%) is more obvious than in non-work trip rate (<= -1.3%). Teleworking might result in a more obvious reduction of work trip rate in high-income communities than in low-income communities. Since non-work trips account for a larger proportion of total trips, the difference between the two income groups regarding the best performance of work trip rate (<=-0.02) is smaller than that of non-work trip rate (<=-0.06) although we see a more obvious difference in the percentage change of work trip rate (-2.0% vs. -1.3%). Overall, high-income communities made more effort to achieve social distancing. Furthermore, we compared the two groups regarding their consistency of social distancing during quarantine inertia and fatigue period (the fourth and the fifth week after national emergency declaration). During the fourth week, people's behavior change to achieve quarantine slowed down. Then during the fifth week, those efforts of being social distancing were relaxed and less attention was paid to quarantine, which is indicated by the bouncing back phenomenon in Fig.   1 . The standard deviation during these two weeks for each mobility metric and each performance indicator informs us the consistency performance. The one-sided Welch t-test shows that the mean value of variation of high-income communities is lower than that of low-income communities for all six mobility metrics. Moreover, each difference is statistically significant at 99% confidence level. After a period of mobility change due to social distancing orders, high-income communities present a more stable and consistent status of social distancing. Table 1 : One-sided Welch t-test results for eighteen scenarios considering three types of indicators and six mobility metrics. The alternative hypothesis of each scenario is that highincome communities perform better than low-income communities. For instance, the best performance on social distancing index of the high-income group is hypothesized to be higher than the low-income group; the percentage change of trip rate for the high-income group is hypothesized to be smaller than the low-income group (since the percentage change is negative, the smaller it is the better); the variation during the inertia and fatigue period of high-income communities regarding any mobility metric is smaller than that of low-income communities. The null hypothesis for all scenarios is rejected; that is, high-income communities perform better in all eighteen scenarios. Furthermore, the statistical difference between the two groups at 95% confidence level for each scenario is presented.
Mobility 
Previous analysis is based on the average behavior of both income groups. Simply comparing the average is not adequate to draw a conclusion. In this section, we additionally conducted a causal inference of income on human mobility change. Since there might be some systematic biases between the two income groups caused by the confounding variables, we specifically addressed those covariates to strengthen the analysis on the income effect using propensity score matching The results above present the impact of high-income for each scenario. In order to compare different scenarios, the dataset of each mobility metric regarding best performance and consistency were standardized (rescaling the data to a have a mean of zero and a standard deviation of 1)
because of different units. The same PSM modeling procedure was applied. Again, the results in table 3 show that high-income has a significant causal effect at 99% confidence level and this causal effect improves the social distancing performance in each scenario. Furthermore, different degree of such impact is observed when comparing the scenarios. As for the best performance, high-income has the largest influence on the maximum of social distance index, the second largest influence on the minimum of trips per person, and the third largest influence on the minimum of non-work trip rate. During the quarantine period, high-income has a larger impact on the best performance of non-work trip rate (ATE: -0.369, ATET: -0.350) than on that of work trip rate (ATE: -0.198, ATET: -0.200). Being high-income is more promising to furthermore reduce the extremum of non-work trip rate than to reduce the extremum of work trip rate. Regarding the consistency, the income has a more obvious impact on the variation of the three trip-related metrics. And the largest impact is observed on reducing the variation of work trip rate (ATE: -0.314, ATET: 0.291) during the quarantine inertia and fatigue period. Then the income has the forth impact on the social distancing index, which is followed by miles traveled per person. The least causal impact of income is observed on the consistency of percentage of staying home. The difference between communities of the two income levels in the variation of percentage of staying home is not as notable as that in other metrics. 
This paper investigates the disparities between income groups under the COVID-19. Due to the rapid human-to-human transmission of the novel coronavirus, travel restrictions became a particularly important way to help contain the outbreak of the pandemic. Although state and local governments issued various mobility interventions such as school closings, cancelling public events, and stay-at-home orders, seldom are interventions customized for communities of different income levels. However, community infection control is of great importance to help contain COVID-19. In order to assist policymakers with improving community-targeted interventions, our paper investigated the mobility gap between communities by income level. The nationwide highfrequency mobility location data integrated from over 100 million anonymous devices on a monthly basis serves as valuable data support for our paper. This enables us to detect the differences between communities through real-world observations. We made the best use of this dataset and produced multiple mobility metrics to conduct a multi-level analysis. We conducted the analysis in eighteen scenarios featured by six derived mobility metrics and three indicators of social distancing performance. A major finding is that high-income communities perform better than low-income communities in each of the eighteen scenarios. Being high-income improves the best status of complying with social distancing, improves the efforts made to achieve the best performance, and makes the social distancing behavior more consistent and stable during the quarantine inertia and fatigue period. This informs us of the reality that low-income communities face under the pandemic with regard to social distancing behavior. When implementing mobility restrictions, low-income communities should be given more attention. They need additional assistance to fight against the pandemic. Furthermore, income has a larger influence on reducing work trip rate than on reducing non-work trip rate. High-income individuals have more opportunity to work from home while low-income individuals probably need to go to an essential frontline job. This might also be the reason why high-income communities have a more stable and consistent status of keeping social distancing during the quarantine inertia and fatigue period. By comparing the causal impact of income on the percentage reduction of travel distance and trip rate, we infer that the travel distance of non-work trips in high-income communities reduced more than in low-income communities due to the pandemic. Different accessibility to life supplies during the pandemic probably can explain this. It might be easier for the residents living in high-income communities to satisfy their life needs without traveling so far away as low-income people do. For example, low-income people may not be that capable of paying daily food delivery and hence they have to go outside frequently to buy food. Regarding the consistency of being social distancing, being high-income reduces the daily fluctuation of all six mobility metrics during the quarantine inertia and fatigue period. High-income communities present a more stable social distancing behavior. Additionally, among the five basic mobility metrics (the others except social distancing index), being high-income has the largest causal impact on reducing the variation of the three trip rate related metrics, which is followed by the travel distance and the percentage of staying home.
This indicates that being high-income is more likely to influence those people going out regarding trips and travel distance while is less likely to change the proportion of people staying home. In addition to stay-in-home orders, policies that specifically target low-income people's daily travel demands are also needed to help contain the pandemic.
In a causal effect analysis, the two measures, Average Treatment Effect (ATE) and Average Treatment Effect on the Treated (ATET), are ideally used in randomized experiments. However, in practice, many observational studies do not have a randomization process. In this case, the systematic differences between treated and untreated subjects must be addressed to reduce the effect of confounding factors 21, 22 . Propensity Score Matching (PSM) has been popularly applied to estimating the treatment effect in various observational studies, such as policy analysis, pharmacoepidemiologic research, education, econometric studies, and accounting research 19,23-24 . In this study, a causal modeling is built using PSM to measure the causal effect of income on social distancing behavior. To strengthen the impact analysis of income, a comprehensive set of control variables is involved from aspects of age, race, gender, education, and population density. Those control variables are believed to potentially influence social distancing performance and are correlated with the income level of a community based on current studies 10, 25, 26 . All sociodemographic data used in this paper is the American Community Survey data from U.S. Census
Bureau. The first step of propensity score matching is to address the systematic biases between the two treatment groups (high-and low-income groups) by controlling the effect of confounding variables using a multivariate binomial logistic regression model. With all control variables being the independent variables, the model predicts the probability of a community to perform as a highincome community (the propensity score, the probability of being treated).
The estimated propensity score for all communities would be used as reference to pair each highincome community with its corresponding low-income community. The nearest neighbor method is applied to carry out this pairing process. Given a high-income community, the community from the low-income group with the closest propensity score value to that of this high-income community will be selected as the counterpart. After the matching process, we have a set of highand low-income community pairs and hence the counterfactual values are provided by each pair.
Then the average treatment effect and the average treatment effect on the treated can be measured using the equations below. 
To calculate the mobility metrics, the research team utilized a data panel created by integrating several mobile device data sources that represent movements of both person and vehicle. The data has been obtained through various data providers that collect anonymized movement data first hand. As the next step, we conducted thorough data cleaning procedures to ensure consistency, completeness, accuracy, and timeliness of all observations. After data cleaning, activity locations are determined based on spatial and temporal clustering of location sightings to identify home and work locations at the census block group level. Furthermore, we applied our previously developed recursive algorithm to extract trips from raw location points and produce trip information including trip origin, trip destination, departure time, arrival time, and travel distance 12, 27 . All anonymized devices that did not make any trip longer than one mile from home on a calendar day were considered as people staying home. Finally, a robust multi-level weighting algorithm was applied to expand the observed sample to the entire population at the national, state, and county levels.
The final results were extensively validated based on several independent data sources such as American Community Survey, National Household Travel Survey, and also peer-reviewed by an external expert panel 27 . A more detailed description of the methodology used for deriving the basic mobility metrics can be found in our previous work 12 .
In addition to the basic metrics produced using the aforementioned methodology, the research team introduced a social distancing index (SDI) to better portray the different aspects of human mobility patterns using a single metric. SDI has been calculated to measure the extent of social distancing practices by both residents and visitors of a geographical area as a score-based index. For each region, a score between 0 and 100 is assigned by considering the temporal changes in five basic mobility metrics, including percent of staying at home, daily work trips, daily non-work trips, trip distance, and percent of out-of-county trips in comparison to baseline days before the COVID-19
outbreak. The weighting schemes for incorporating these five metrics were designed to consider the importance of each metric based on both real-world observations and conceptual guidelines.
The theoretical basics of the formulation of the SDI metric has been described in detail in our earlier work 11 . Where is the percentage of people staying at home, is the percentage reduction in the number of total trips in comparison with the pre-pandemic benchmark, is the percentage reduction in the number of work trips in comparison with the pre-pandemic benchmark, is the percentage reduction in the number of non-work trips in comparison with the pre-pandemic benchmark, is the percentage reduction in the total daily distance traveled in comparison with the pre-pandemic benchmark, is the percentage reduction in the number of out-of-county in comparison with the pre-pandemic benchmark.