Wang, Wei, Lin, and Li

# Spatial-temporal Analysis of COVID-19’s Impact on Human Mobility: the Case
of the United States

Songhe Wang∗
University of North Carolina at Chapel Hill
<EMAIL_ADDRESS>
Kangda Wei∗
University of North Carolina at Chapel Hill
<EMAIL_ADDRESS>
Lei Lin
University of Rochester
<EMAIL_ADDRESS>
Weizi Li
University of Memphis
<EMAIL_ADDRESS>
##  1 Abstract

COVID-19 has been affecting every aspect of societal life including human
mobility since December, 2019. In this paper, we study the impact of COVID-19
on human mobility patterns at the state level within the United States. From
the temporal perspective, we find that the change of mobility patterns does
not necessarily correlate with government policies and guidelines, but is more
related to people’s awareness of the pandemic, which is reflected by the
search data from Google Trends. Our results show that it takes on average 14
days for the mobility patterns to adjust to the new situation. From the
spatial perspective, we conduct a state-level network analysis and clustering
using the mobility data from Multiscale Dynamic Human Mobility Flow Dataset.
As a result, we find that 1) states in the same cluster have shorter
geographical distances; 2) a 14-day delay again is found between the time when
the largest number of clusters appears and the peak of Coronavirus-related
search queries on Google Trends; and 3) a major reduction in other network
flow properties, namely degree, closeness, and betweenness, of all states from
the week of March 2 to the week of April 6 (the week of the largest number of
clusters).

Keywords: COVID-19, Human Mobility, Spatial-temporal Analysis, Network
Analysis, Clustering

##  2 Introduction

The COVID-19 pandemic has been affecting the world since December, 2019 [1].
As for the United States, the government announced a national emergency on
March 13 and attempted to slow down the spread of the virus by issuing social
distancing guidelines. Many societal aspects are subsequently affected
including human mobility—the driven force for social-economic development.
According to Apple COVID-19 Mobility Trends Reports [2], after declaring
national emergency, the traffic flow, including driving and walking, has
decreased over 50%.

The impact of COVID-19 on the mobility of various social-demographic groups
within the United States has been assessed by several studies [3, 4, 5, 6, 7,
8, 9, 10, 11, 12]. To provide some examples, Kabiri et al. [3] study the
difference of mobility changes of younger and senior communities. They find
that both younger and senior communities have been performing social
distancing after the national emergency declaration. The percentage of people
staying at home and the social distancing index, a measurement based on the
change of a community’s daily work trips, show a trend of decreasing until
mid-April and then gradual increasing. In addition, they find that people need
a certain period of time to react to government guidelines and term this
phenomenon _social distancing inertia_ [4]. Engle et al. [5] evaluate how
local infection rate would lead to mobility reduction. They show that the
region with a higher percentage of residents older than 65 has a higher
mobility reduction rate. Lee et al. [6] analyze the relationship between
mobility and various socio-demographic factors and find that 1) the community
with higher income has a higher stay-at-home percentage compared to the
community with lower income after the outbreak, and 2) the community with
higher population density has shorter travel distance compared to the
community with lower population density. Fellows et al. [7] conclude that even
though many factors, such as perceived risk, community guidance, and media
coverage, could affect people’s mobility patterns, the factor that has the
most effect is the governmental non-pharmaceutical intervention, e.g., the
staying-at-home order. Similar studies have also been conducted in other
countries in analyzing the impact of COVID-19 on human mobility patterns [10,
11, 12].

Five months after the declaration of national emergency, many states have
moved to various phases of reopening. Some studies have examined this process.
For example, Huang et al. [13] study the impact of reopening on mortality,
infections, and hospitalizations in Harris county, Texas, United States. As
another example, Soltani and Rezazadeh [14] suggest that releasing a small
portion of the population may cause a significant increase in confirmed cases.
Most previous work focused on different responses from various social-
demographic communities and the local factors associated with the mobility
patterns. Others study the effect of reopening on the pandemic’s evolution.
However, these studies do not study the relationship between people’s
awareness of the situation and the change of mobility patterns, and do not
explore the mobility patterns between different states. Our work not only
explores the correlation between people’s awareness of the pandemic and the
mobility patterns, but also uses network analysis and clustering to reveal the
underlying mobility structures between different states.

To be specific, from the temporal aspect, we analyze the correlation between
human mobility and the amount of search queries from Google Trends at the
state level. As a result, we find that, on average, people adjust their
mobility two weeks after their awareness of the situation. From the spatial
aspect, we perform network clustering to reveal hidden mobility structures
among all states. The result shows that the connections among states at first
decreased and then gradually restored after mid-April. Meanwhile, the states
in the same cluster tend to have shorter geographically distances. In
addition, we find, again, a two-week delay between the point when the largest
number of clusters appears and the point when the peak of the Google search
trend regarding Coronavirus occurs, which confirms our temporal analysis
results. Lastly, the network analysis shows a reduction of degree, closeness,
and betweenness—the properties that describe mobility flows of a state—for all
states.

In the rest of the paper, we first discuss the data sources used in our
analysis. Then, we explain our methodology for this research. Next, we present
temporal and spatial analysis results and explain our findings. Finally, we
conclude and discuss potential future work.

##  3 Datasets

In this section, we provide details of our data sources.

Regarding the mobility data, the first dataset that we use is Apple COVID-19
Mobility Trends Report [2]. The dataset contains traffic flows measured by the
number of route changing queries via Apple Map of all states of the U.S., from
January 13 to July 20, 2020. The flow of January 13 is set to 100, and the
flow of other days is computed relatively to the flow data of January 13. For
example, if the traffic flow of a certain day is increased by 20% compared to
the traffic flow of January 13, the flow of that day is marked as 120. Some
sample data are shown in Table 1.

State | 1/13/20 | 1/14/20 | 1/15/20 | … | 3/14/20 | 3/15/20 | 3/16/20 | … | 7/18/20 | 7/19/20 | 7/20/20
---|---|---|---|---|---|---|---|---|---|---|---
Alabama | 100 | 102.9 | 103.51 | … | 139.87 | 94.6 | 101.37 | … | 204.26 | 142.92 | 151.62
Arizona | 100 | 104.06 | 106.9 | … | 113.76 | 85.38 | 94.73 | … | 112.83 | 91.34 | 101.85
Arkansas | 100 | 102.55 | 101.93 | … | 113.61 | 83.41 | 90.28 | … | 181.21 | 138.92 | 151.08
California | 100 | 104.39 | 109.34 | … | 86.16 | 66.24 | 77.57 | … | 119.08 | 101.23 | 107.6
Colorado | 100 | 103.46 | 105.66 | … | 98.41 | 75.88 | 81.94 | … | 160.1 | 138.23 | 143.85

Table 1: Samples of daily traffic data of the U.S. from Apple COVID-19
Mobility Trends Report [2]. The flow of January 13 is set to 100 and the flows
of other days are computed relatively to the flow of January 13. The national
emergency is declared on March 13 in the U.S.

The second dataset is from Google Trends [15], which we use as an indicator of
people’s awareness of the pandemic. The dataset contains both state-level and
nationwide weekly search data regarding Coronavirus. We extract the part of
the data from January 13 to July 20, 2020 for our analysis. The data are
adjusted: with 0 meaning a very small number of queries was made and 100
representing the largest number of queries made over the past year. A number
between 0 and 100 indicates that a week has a specific higher search
percentile than all other weeks over the past year. Some sample data are shown
in Table 2. Furthermore, in order to conduct daily analysis, we linearly
interpolate the weekly data so that each day in the study period also has the
search data metric.

Region | 1/12/20 | 1/19/20 | 1/26/20 | … | 3/8/20 | 3/15/20 | 3/22/20 | … | 7/12/2020 | 7/19/2020 | 7/26/2020
---|---|---|---|---|---|---|---|---|---|---|---
Alabama | $<1$ | 3 | 8 | … | 67 | 100 | 81 | … | 10 | 7 | 7
Arizona | $<1$ | 4 | 19 | … | 62 | 100 | 83 | … | 14 | 11 | 9
Arkansas | $<1$ | 4 | 13 | … | 74 | 100 | 79 | … | 11 | 8 | 7
California | $<1$ | 5 | 21 | … | 74 | 100 | 75 | … | 13 | 10 | 9
Colorado | $<1$ | 5 | 12 | … | 87 | 100 | 75 | … | 11 | 9 | 8
Nationwide | <1 | 4 | 13 | … | 73 | 100 | 74 | … | 11 | 9 | 8

Table 2: Samples of weekly search data from Google Trends regarding
Coronavirus [15]. 0 meaning the lowest search amount over the past year and
100 meaning the highest search amount over the past year. As a reference, the
national emergency is declared on March 13 in the U.S.

The third dataset is the Multiscale Dynamic Human Mobility Flow Dataset [16],
which contains weekly mobility flow data, provided by SafeGraph [17], from the
week of March 2 to the week of May 11, 2020. Each week’s data contain the
origin and destination of visitor and population flow, and the longitudes and
latitudes of the origin states and destination states. The visitor flow is
measured by recording the geographical locations of mobile devices, and the
population flow is calculated based on the visitor flow and the population of
each state.

Regarding the pandemic data, we use the daily reports of COVID-19 state-level
confirmed cases from New York Times [18]. We have pre-processed all the data
by conducting min-max feature scaling. This operation ensures that the data
are on the same scale, providing convenience for our modeling, analysis, and
visualization.

##  4 Spatial-temporal Analysis

###  4.1 Mobility Adjustment

We hypothesize that there exists a time difference between the change of
mobility and people’s awareness of the pandemic—which is assumed to be
reflected by Google Trends data. In other words, we suspect that the point of
people realizing the seriousness of a situation and the point of people taking
actions to reflect their awareness may not be well synchronized.

To test our hypothesis, we study the correlation between the two time series:
the mobility data from Apple [2] and the search trend data of COVID-19 from
Google [15]. To be specific, we compute the Pearson’s correlation coefficients
by fixing the mobility data and shifting the search trend data one day at a
time. The study period is from January 13 to July 20, 2020. As a result, the
highest correlation coefficients (absolute values) all occur after shifting
the search trend data forward in time. The number of days of delay corresponds
to the highest correlation coefficients of different states is shown in Figure
1. The minimum delay of people adjusting their mobility to reflect their
awareness of the pandemic is 11 days, the maximum delay is 18 days, and the
average delay is 14 days. These observations coincide with the previous
finding from Soltani and Rezazadeh [14], which states that people need a
certain amount of time to adjust their mobility to the posed government
guidelines.

Figure 1: The number of days of delay reflected by Apple mobility data [2] to
Google search data [15] for all states. The average delay of people’s mobility
adjustment to their awareness of the pandemic is 14 days.

###  4.2 Network Analysis and Clustering

In order to explore possible hidden structures embedded in the mobility flow
network among all states [19], we perform network clustering using the Label
Propagation algorithm implemented in the Python library NetworkX [20] on the
Multiscale Dynamic Human Mobility Flow Dataset [16]. The graph we study
contains 50 states as its nodes and the traffic flows among the states as its
edges. The algorithm works as follows: first the algorithm assigns each node a
distinct label and then recursively assigns the label of each node to be the
label that appears most frequently among the labels of the node’s neighbors.
In the case of multiple labels sharing the highest frequency, one of the
labels will be randomly chosen for the node. The algorithm stops when all
nodes have the labels that appear most frequently among the labels of their
neighbors.

Since the Multiscale Dynamic Human Mobility Flow Dataset contains weekly
inter-state mobility flows over 11 weeks (from the week of March 2 to the week
of May 11, 2020), we have 11 mobility flow networks to analyze. For each week,
we run the Label Propagation algorithm 100 times to reveal hidden clusters.
During that process, we record the mode, mean, and standard deviation of the
number of the clusters of the 11 weeks. These statistics are shown in Table 3.
We take the mode of the number of clusters of each week as the final number of
clusters to conduct further analysis.

Statistics | Week 1 | Week 2 | Week 3 | Week 4 | Week 5 | Week 6 | Week 7 | Week 8 | Week 9 | Week 10 | Week 11
---|---|---|---|---|---|---|---|---|---|---|---
Mode | 1 | 1 | 2 | 5 | 6 | 8 | 7 | 6 | 5 | 5 | 4
Mean | 1 | 1 | 2.44 | 4.85 | 6.49 | 7.66 | 7.34 | 6.66 | 5.45 | 4.36 | 3.96
Std | 0 | 0 | 1.12 | 0.89 | 1.28 | 1.11 | 1.25 | 1.21 | 1.14 | 0.99 | 1.19

Table 3: Statistics of the clustering results using weekly mobility flow data
from the Multiscale Dynamic Human Mobility Flow Dataset [16]. The larger the
number of clusters, the more isolated the states are. The largest number of
clusters appears at week 6, i.e., the week of April 6.

From the clustering result, we observe that the number of clusters tend to
increase and then decrease over the study period of 11 weeks. To be specific,
in the first two weeks (before the national emergency declaration on March
13), all states are identified as one cluster. We suspect the reason being
that people’s awareness of COVID-19 remained low and the staying-at-home order
was not implemented. As the pandemic evolves and people become more aware of
the situation, the number of clusters increases, which implies people have
restricted their travel and the states are more isolated. The maximum number
of clusters appeared at week 6 (the week of April 6). This result may
correlate with some major events occurred between March 13 and April 6,
including the declaration of national emergency, the issuing of stay-at-home
orders in all 50 states, and the cancellation of events with crowds.
Afterwards, the number of clusters starts to decrease, which implies that
people gradually resume their prior-pandemic travel behaviors. Figure 2 TOP
showcases the clustering results. To provide some examples, Week 3 (the week
of March 16) shows that in the beginning of the pandemic, we only have two
clusters, which indicates that mobility flows are more uniformly distributed
across the country. Week 6 (the week of April 6) presents the largest number
of clusters, i.e., eight clusters, indicating that the mobility flows among
states reach the lowest point. Week 11 (the week of May 11) shows that the
number of clusters reduces to four, showing that the states are less isolated
and the mobility flows start to recover.

In order to quantify our results, we further compute two types of distances:
_cluster average distance_ and _country average distance_. Both distances are
calculated using the coordinates of the geometric centroids of the states. For
computing the cluster average distance, we first empirically pick a state in
the cluster as the centroid and then take the average of the distances from
the rest of the states in that cluster to the centroid. Next, we compute the
country average distance by taking the distances from all states to the
centroid. The relative reduction in percentage of cluster average distance
compared to the country average distance of all clusters over nine weeks,
starting from the week of March 16 and ending at the week of May 11, are shown
in Figure 2. The first two weeks, i.e., the weeks of March 2 and March 9 are
exclude since for these two weeks the algorithm reports the whole country as
one cluster. As a result, all cluster average distances are much shorter than
their corresponding country average distances, which suggests that the states
in the same cluster are geographically close to each other. This result
confirms that the increase of the number of clusters indeed reflects the
isolation of the states and reductions in inter-state mobility flows.

Figure 2: Clustering results starting from the week of March 16 and ending at
the week of May 11. The visualization results, as well as the relative
reduction in percentage of cluster average distance compared to the country
average distance are shown. The cluster average distances are much shorter
than the country average distances, indicating the states in the same cluster
are closer to each other, which may be the results of shortened travel
distances of people due to the pandemic.

Table 4 shows the change of the number of clusters and nationwide weekly
Google Trends data over the 11 weeks. A two-week delay between the peak of
search trends on Google and the largest number of clusters is again spotted.
It is worth noticing that even though we use different mobility data in our
mobility adjustment analysis and network analysis, both analyses find the same
amount of delay in time between the mobility change and people’s awareness of
the pandemic.

| Week 1 | Week 2 | Week 3 | Week 4 | Week 5 | Week 6 | Week 7 | Week 8 | Week 9 | Week 10 | Week 11
---|---|---|---|---|---|---|---|---|---|---|---
Num. of Cluster(s) | 1 | 1 | 2 | 5 | 6 | 8 | 7 | 6 | 5 | 5 | 4
Google Trends | 16 | 31 | 73 | 100 | 74 | 59 | 57 | 43 | 34 | 20 | 18

Table 4: The change of the number of clusters and weekly Google Trends data
over the 11 weeks. We observe a two-week delay between the peak of Google
Trends data and the largest number of clusters. This result coincides with our
previous finding, which, on average, it takes 14 days for people to adjust
their mobility to reflect their awareness of the pandemic (indicated by the
Google Trends data).

Because the pandemic may affect different states unequally, we have examined
other network flow properties, namely the degree, closeness, and betweenness
of each state as a node in the traffic flow network. In particular, the degree
of a node is defined as the sum of edge weights to all its neighbors. The
change of the degree can inform the change of the flow of a state. The
closeness of a node is defined as the average length of the shortest path
(computed using the edge weights) from the node to all other nodes in the
graph, which can reflect the accessibility of a state. Having the closeness
calculated for all nodes, we could study which states tend to be less
“attractive” during the pandemic. Lastly, betweenness quantifies the number of
times a node that acts as the “bridge” along the shortest path between two
other nodes. The betweenness of a node can be used to identify which state is
serving as a domestic transportation “hub”. The higher the value the more
influence the state has on the domestic mobility.

As part of our quantitative analysis, Table 5 lists top 10 states with most
reductions in degree, closeness, and betweenness of the week of April 6 (the
week has the largest number of clusters and most isolated) compared to the
week of March 2 (the beginning of the pandemic). We can see that the average
reductions in degree, closeness, and betweenness are 7.7%, 6.9%, and 21.6%
respectively.

As part of our qualitative analysis, Figure 3 visualizes the change of inter-
state flow connections of the week of March 2 and the week of April 6. The
size of a node represents the total mobility flow through that state during
the week, while each edge indicates 10,000+ mobility flow connecting two
states. A significant reduction of the edges (i.e., mobility flow) is
observed.

State | Degree Reduction | State | Closeness Reduction | State | Betweenness Reduction
---|---|---|---|---|---
Nevada | 32.5% | New Hampshire | 19.3% | Nevada | 97.8%
Massachusetts | 25.5% | Maine | 19.0% | Wisconsin | 57.1%
District of Columbia | 24.3% | Rhode Island | 15.4% | New Jersey | 53.7%
New York | 22.7% | Massachusetts | 14.8% | North Dakota | 44.3%
Maine | 22.5% | Nevada | 12.0% | New Hampshire | 43.2%
New Hampshire | 21.6% | California | 10.9% | Colorado | 32.4%
Arizona | 20.9% | Arizona | 10.7% | Arizona | 30.1%
Colorado | 18.5% | District of Columbia | 10.3% | Utah | 29.9%
Wisconsin | 16.0% | North Dakota | 9.6% | Michigan | 22.3%
Vermont | 15.4% | New Jersey | 9.1% | Idaho | 20.4%
Mean | 7.7% | Mean | 6.9% | Mean | 21.6%
Std | 9.7% | Std | 4.0% | Std | 27.3%

Table 5: Top 10 states with most reductions in degree, closeness, and
betweenness of the week of April 6 (the most isolated week in terms of
mobility flow) compared to the week of March 2. Figure 3: The inter-state flow
connections of the week of March 2 (LEFT) and the week of April 6 (RIGHT).
Each edge represents 10,000+ flow connecting two states. A significant
reduction of the mobility flow is observed comparing the two weeks.

##  5 Conclusion

The outbreak of COVID-19 has significantly impacted our society and
dramatically changed our mobility patterns. We conduct spatial-temporal
analysis of the influence of COVID-19 on human mobility in the United States.
From the temporal perspective, we find that there exists a delay of, on
average, 14 days between people’s awareness of the pandemic and the change of
mobility patterns. From the spatial perspective, we discover that the states
within the same cluster tend to have shorter geographical distances. There
also exists a two-week delay between the appearing of the largest number of
clusters and the occurrence of the peak of the Google search trend regarding
Coronavirus. Lastly, we perform a network analysis and find that there is a
reduction of the network flow properties, namely degree, closeness, and
betweenness, for all states.

For the future research, we are mainly interested in two directions. The first
direction concerns a more detailed mobility analysis at the city level. We can
first use existing techniques such as Compressed Sensing [21, 22] to
interpolate the sparse mobile data used in this work. In combination with
other COVID-19 tracker data, we can then potentially estimate the impact of
COVID-19 on city-level traffic states and simulate the dynamics of the virus
spread using some existing techniques [23, 24, 25]. Another interesting topic
in this direction is to study the change of shared mobility such as bikes [26,
27]. The second research direction concerns future mobility, as the future
traffic system is projected to be connected and autonomous [28], we would like
to study when mobility patterns have a drastic change, to what extent the
connected and autonomous vehicles can be used to supplement the traffic system
and fulfill various societal needs. We can leverage recent advances in
autonomous driving modeling and simulation to facilitate this research
direction [29, 30, 31].

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n}\middle\|\sigma_{B^{n}}\otimes\left(\frac{I_{R}}{d}\right)^{\otimes
n}\right)$ (194)
$\displaystyle\leq\frac{1}{2}D^{\varepsilon^{2}}_{h}\left(\left(\left(\mathcal{N}\otimes\mathcal{I}_{R}\right)(|\phi\rangle\\!\langle\phi|_{A^{\prime}R})\right)^{\otimes
n}\middle\|(\mathcal{N}(\rho_{A^{\prime}}))^{\otimes
n}\otimes\left(\frac{I_{R}}{d}\right)^{\otimes n}\right)\,.$ (195)

For the particular case where the error is chosen to be
$1-\varepsilon_{n}=1-e^{-na_{n}^{2}}$ and using the AEP for the hypothesis
testing relative entropy (Proposition III.10), we get that for $\eta>0$, there
exists $n^{\star}\in\mathbb{N}$ such that for $n\geq n^{\star}$ we have

$\displaystyle\frac{1}{n}r^{\star}_{1-\varepsilon}(\mathcal{N}^{\otimes n})$
$\displaystyle\leq\frac{1}{2n}D^{(1-2\varepsilon_{n}+\varepsilon_{n}^{2})}_{h}\left(\left(\left(\mathcal{N}\otimes\mathcal{I}_{R}\right)(|\phi\rangle\\!\langle\phi|_{A^{\prime}R})\right)^{\otimes
n}\middle\|(\mathcal{N}(\rho_{A^{\prime}}))^{\otimes
n}\otimes\left(\frac{I_{R}}{d}\right)^{\otimes n}\right)$ (196)
$\displaystyle\leq\frac{1}{2}\left(I(R:B)_{(\mathcal{N}\otimes
I)(|\phi\rangle\\!\langle\phi|)}+\sqrt{2V(R:B)_{(\mathcal{N}\otimes
I)(|\phi\rangle\\!\langle\phi|)}}a_{n}+\eta a_{n}\right)$ (197)
$\displaystyle\leq
C(\mathcal{N})+\frac{a_{n}}{\sqrt{2}}\sqrt{V_{\max}(B:R)_{\mathcal{N}}}+o(a_{n}\,,$
(198)

which matches the converse statement for channel coding in the moderate
deviation regime (Proposition VI.4).