# The geographic spread of COVID-19 correlates with the structure of social
networks as measured by Facebook††thanks: Date: . Public versions of the
social connectedness data used in this paper, as well as similar data for a
wide range of other geographies, are accessible at
https://data.humdata.org/dataset/social-connectedness-index. The full
replication code is available at https://github.com/social-connectedness-
index/example-scripts. The authors have a research consulting relationship
with Facebook. Since this project only uses data that is available to the
broader research community, nobody at Facebook reviewed the contents of this
paper.

Theresa Kuchler New York University, Stern School of Business. Email:
<EMAIL_ADDRESS>Dominic Russel New York University, Stern School of
Business. Email<EMAIL_ADDRESS>Johannes Stroebel New York University,
Stern School of Business. Email<EMAIL_ADDRESS>(Corresponding)

We use aggregated data from Facebook to show that COVID-19 is more likely to
spread between regions with stronger social network connections. Areas with
more social ties to two early COVID-19 “hotspots” (Westchester County, NY, in
the U.S. and Lodi province in Italy) generally had more confirmed COVID-19
cases by the end of March. These relationships hold after controlling for
geographic distance to the hotspots as well as the population density and
demographics of the regions. As the pandemic progressed in the U.S., a
county’s social proximity to recent COVID-19 cases and deaths predicts future
outbreaks over and above physical proximity and demographics. In part due to
its broad coverage, social connectedness data provides additional predictive
power to measures based on smartphone location or online search data. These
results suggest that data from online social networks can be useful to
epidemiologists and others hoping to forecast the spread of communicable
diseases such as COVID-19.

To forecast the geographic spread of communicable diseases such as COVID-19,
it is valuable to know which individuals are likely to physically interact
(Piontti et al., 2018). In particular, since social ties shape patterns of
physical interaction, observing the strength of social connections between
cities and regions can be useful for determining a locality’s risk of future
disease outbreaks. Yet, the geographic structure of social networks is usually
difficult to measure on a national or global scale. In this paper, we overcome
this challenge by using aggregated data from Facebook to measure social
connections between regions. We then show that these connectedness measures
can help forcecast the geographic spread of communicable diseases such as
COVID-19.

We construct a measure of the social connectedness between U.S. counties and
between Italian provinces. This _Social Connectedness Index_ captures the
probability that Facebook users in a pair of these regions are Facebook
friends with each other (Bailey et al., 2018b). We hypothesize that regions
connected through many friendship links are likely to have more physical
interactions between their residents, providing opportunities for the spread
of communicable diseases. Indeed, our measure has been shown to be predictive
of travel patterns across Europe (Bailey et al., 2020d) and within urban areas
(Bailey et al., 2020a), suggesting it contains important information about
real-world interactions. Most directly, Coven et al. (2020) use our _Social
Connectedness Index_ to show that counties with higher levels of social
connectedness to New York City were more likely to be destinations for those
fleeing the city during the pandemic, providing direct evidence for our
propopsed mechanism.

After introducing our _Social Connectedness Index_ , we show that regions with
stronger social ties to early COVID-19 “hotspots” — Westchester County, NY, in
the U.S., and Lodi province in Italy — had more documented COVID-19 cases per
resident as of March 30, 2020. These relationships are robust to controlling
for the geographic distance to these early hotspots, as well as demographic
characteristics of the regions. Social connectedness to Westchester has more
predictive power for forecasting county-level COVID-19 cases than social
connectedness to any other county outside the New York-Newark CSA. These case
studies provide initial evidence that social connectedness might serve as a
valuable predictive measure in addition to physical distance and other inputs
to current epidemiological models.

We then exploit the changing geography of the pandemic in the U.S. to conduct
a more systematic in-sample analysis. We construct regional measures of
COVID-19 exposure through social connections (“social proximity to cases”) and
physical distance (“physical proximity to cases”). We find that changes in a
county’s social proximity to cases in one time period are strongly correlated
with the county’s subsequent growth in own local cases. Even after controlling
for physical proximity to cases and other regional demographics, a doubling in
social proximity to cases in one two-week period corresponds to a 24.9%
increase in own cases in the next two-week period. These results are unlikely
to be explained by differential testing between regions, as an increase in
social proximity to deaths in one period also corresponds to an increase in
actual deaths in the next period.

To mimic a real-world epidemiological use case, we also conduct a simple out-
of-sample prediction exercise. We find that models that include our measure of
social proximity to cases are better able to predict a region’s future case
growth than alternative models that rely only on geographic distance and other
demographics. We also compare the predictive value of social proximity to
cases to measures from Google searches related to COVID-19 symptoms and the
smartphone-based Location Exposure Index (LEX) introduced by Couture et al.
(2020). In counties with both LEX and Google search data, social proximity to
cases provides only small additional predictive value — perhaps not
surprisingly, given that the real-world movement of people captured by the LEX
is precisely the mechanism we conjecture explains the predictive power of
social proximity to cases. However, when using the best available model to
make predictions for _all_ U.S. counties (for many of which no LEX data or
Google search information is available), models that include social proximity
to cases sizably improve accuracy. This highlights one important advantage of
social connectedness data: its broad coverage and global availability.

Our use of the _Social Connectedness Index_ to forecast COVID-19 spread adds
to an active body of research that studies how aspects of social media and
internet-usage patterns can be used for tracking and preventing disease (for
an overview, see Aiello et al., 2020). One strand of this literature uses the
content of individuals’ internet searches or social media posts; most
famously, Google Flu Trends used search queries related to influenza for early
outbreak detection (Ginsberg et al., 2009). Other researchers have also used
content from Twitter posts (Rodríguez-Martínez and Garzón-Alfonso, 2018,
Jahanbin and Rahmanian, 2020), Facebook likes (Gittelman et al., 2015),
Wikipedia searches (Generous et al., 2014), and Instagram posts (Correia et
al., 2016) to predict public health outcomes. A second strand of research,
which has received much attention during the COVID-19 pandemic, uses
geolocation data to track individuals’ movement patterns. These data have been
used to explore the determinants and effects of social distancing behavior
(for an overview, see Giuliano and Rasul, 2020), as well as forecast disease
spread (e.g., Jia et al., 2020, Bengtsson et al., 2015, Wesolowski et al.,
2012, 2015, Peixoto et al., 2020). A third strand of that work uses
crowdsourced information, including surveys, to monitor disease symptoms and
detect outbreaks (see Facebook Symptom Survey, , Smolinski et al., 2015,
Paolotti et al., 2014).

In comparison to this literature, our stable network-based measure is less
likely to suffer from changes in internet behavior or seasonality, both of
which have hampered Google Flu Trends (Olson et al., 2013). In addition, our
measures do not require individuals to have experienced symptoms, which
potentially allows us to identify at-risk localities before disease
transmission.111However, this suggests that our data might partner well with
these measures. For example, if one can detect an early outbreak using
surveys, they could then predict (and potentially prevent) the next outbreak
using information on social connectedness. Finally, because our measures are
based only on aggregated connections (instead of individual movement), they
are easily accessible to researchers and consistently available for a large
number of granular geographies around the world. For example, the _Social
Connectedness Index_ is available at the NUTS3 level in Europe, the GADM2
level in the Indian Subcontinent and Canada, and the GADM1 level throughout
much of the rest of the world.222Interested researchers may also access U.S.
ZCTA-level data by emailing<EMAIL_ADDRESS>The index not only measures
connections _within_ countries, but also _between_ countries, which may be
otherwise challenging with mobility data from different cellphone providers
(and important for tracking the international spread of communicable
diseases).

More generally, our results add to a literature that has applied aspects of
network theory to build spatial epidemiological models (for overviews, see
Keeling and Eames, 2005, Keeling and Rohani, 2011, Danon et al., 2011). Works
in this literature move beyond the basic assumption that individuals within a
population are “fully mixed,” or equally likely to interact; instead, they
better represent the dynamics of real-world connections (e.g., Newman, 2002,
Klovdahl, 1985, Klovdahl et al., 1994, Mossong et al., 2008, Yang et al.,
2020). While some of these studies parameterize models with information on
local networks, we are unaware of any that introduce a measure with comparably
high levels of coverage and granularity. Our hope is that our unique measure
of social connectedness can help parameterize future epidemiological work. In
addition, we hope that the Social Connectedness Index can advance the
literature on the determinants and effects of urban and regional social
networks (see Bailey et al., 2020a, Kim et al., 2017, Büchel and Ehrlich,
2020, Mossay and Picard, 2011, Brueckner and Largey, 2008, Glaeser et al.,
1992).

It is important to note that our objective in this paper is not to incorporate
social connectedness into a state-of-the-art epidemiological model. Instead,
we provide a unique measure to assess regions’ outbreak risk, answering the
call of Avery et al. (2020), among others, who highlight an “urgent need” for
“creative and entrepreneurial methods” of interpreting and sharing data to
model coronavirus spread. To that end, the data used in this paper, as well as
similar data for a number of other geographies, are available at
https://data.humdata.org/dataset/social-connectedness-index. We encourage
interested researchers to use them.

##  1 Data Description

To measure the intensity of social connectedness between locations, we use a
de-identified and aggregated snapshot of all active Facebook users and their
friendship networks from March 2020.333We use the data from March 2020, since
this this allows our analyses to correspond most closely to a real-time
forecasting exercise. The publicly available Social Connectedness Index data
is based on a snapshot from August 2020. Since the SCI is extremely stable
over time, results do not change across the various data sets. As of the end
of 2019, Facebook had nearly 2.5 billion monthly active users around the
world: 248 million in the U.S. and Canada, 394 million in Europe, 1.04 billion
in Asia-Pacific, and 817 million in the rest of the world (Facebook, 2020).
The data therefore has extremely wide coverage, and provides a unique
opportunity to map the geographic structure of social networks around the
world. Locations are assigned to users based on their information and activity
on Facebook, including their public profile information, and device and
connection information. Establishing a connection on Facebook requires the
consent of both individuals, and there is an upper limit of 5,000 on the
number of connections a person can have. As a result, Facebook connections are
generally more likely to be between real-world acquaintances than links on
many other social networking platforms.

Our measure of the social connectedness between two locations $i$ and $j$ is
the Social Connectedness Index (SCI) introduced by Bailey et al. (2018b):

$Social\ Connectedness_{i,j}=\frac{FB\ Connections_{i,j}}{FB\ Users_{i}*FB\
Users_{j}}.$ (1)

Here, $FB\ Connections_{i,j}$ is the total number of Facebook friendship links
between Facebook users living in location $i$ and Facebook users living in
location $j$. $FB\ Users_{i}$ and $FB\ Users_{j}$ are the number of active
users in each location. $Social\ Connectedness_{i,j}$ thus measures the
relative probability of a Facebook friendship link between a given Facebook
user in location $i$ and a given Facebook user in location $j$: if this
measure is twice as large, a given Facebook user in region $i$ is twice as
likely to be friends with a given Facebook user in region $j$.

In previous work, we have shown that this measure predicts a large number of
important economic and social interactions. For example, social connectedness
as measured through Facebook friendship links is strongly related to patterns
of sub-national and international trade (Bailey et al., 2020b), patent
citations (Bailey et al., 2018b), and investment decisions (Kuchler et al.,
2020).444A growing body of research also uses this measure to study issues
related to COVID-19. For example, Bailey et al. (2020c) use the $SCI$, along
with individual-level data from Facebook, to show that social network exposure
to COVID-19 cases shapes individuals’ social distancing behaviors. Holtz et
al. (2020) use $SCI$ data to document spillover effects in state-level
COVID-19 health policies. Charoenwong et al. (2020) and Makridis and Wang
(2020) work with the $SCI$ to study other behavioral effects of exposure to
COVID-19 through friends. More generally, we have found that information on
individuals’ Facebook friendship links can help understand their product
adoption decisions and their housing and mortgage choices (Bailey et al.,
2018a, 2019a, 2019b).

Data on COVID-19 cases in the U.S. by county come from Johns Hopkins
University Center for Systems Science and Engineering. Data on COVID-19 cases
for each Italian province come from the Italian Dipartimeno della Protezione
Civile. Because differential testing across regions may introduce bias in
case-based results, we will also use information on COVID-19 related deaths
from each source in Section 3.

##  2 Early Hotspot Analysis

In this section, we explore how the domestic spread of confirmed COVID-19
cases is related to the social connectedness to two early COVID-19 “hotspots”:
Westchester County, NY, in the U.S., and Lodi Province in Italy. Westchester
County includes New Rochelle, a community that had the first major confirmed
COVID-19 outbreak in the eastern United States (Chappell, 2020). By March
20th, the county had over 9,300 cases, second only to nearby New York City.
Additionally, a number of articles reported that wealthy residents from
Westchester and the New York area had fled to other parts of the U.S. (Tully
and Stowe, 2020), providing a vector that could potentially spread the
disease. Indeed, geneticists and epidemiologists later found that travel from
New York seeded much of the first wave of U.S. COVID-19 outbreaks (Carey and
Glanz, 2020). Social connections to Westchester may thus provide particularly
important information for tracking early COVID-19 spread, especially given
that Coven et al. (2020) find that social connectedness to New York City
predicted travel patterns from the city early in the pandemic. Lodi is an
Italian province of around 230,000 inhabitants in the heavily impacted region
of Lombardy. It contains Codogno, where the earliest cases of COVID-19 in
Italy were detected, and was at the center of Italy’s outbreak (Horowitz et
al., 2020).

Figure 1: Social Network Distributions from Westchester and COVID-19 Cases in
the U.S.

(a) Log of SCI to Westchester County, NY

(b) COVID-19 Cases per 10k Residents by County

(c) Westchester binscatter without controls (d) Westchester binscatter with
controls

Note: Panel (a) shows the social connectedness to Westchester for U.S.
counties. Panel (b) shows the number of confirmed COVID-19 cases per 10,000
residents by U.S. county on March 30, 2020. Panels (c) and (d) show binscatter
plots with counties more than 50 miles from Westchester as the unit of
observation. To generate the plot in Panel (c), we group $log(SCI)$ into 100
equal-sized bins and plot the average against the corresponding average case
density. Panel (d) is constructed in a similar manner. However, we first
regress $log(SCI)$ and cases per 10,000 residents on a set of control
variables and plot the residualized values on each axis. Red lines show
quadratic fit regressions. The controls for Panel (d) are 100 dummies for the
percentile of the county’s geographic distance to Westchester; population
density; median household income; and dummies for the six National Center for
Health Statistics Urban-Rural county classifications.

Panel (a) of Figure 1 shows a heatmap of the social connectedness of
Westchester County, NY, to other U.S. counties; darker colors correspond to
stronger social ties. Panel (b) shows the distribution of COVID-19 cases per
10,000 residents across U.S. counties on March 30, 2020, with darker colors
corresponding to higher COVID-19 prevalence. These maps show a number of
similarities. Perhaps most notably, coastal regions and urban centers appear
to have both high levels of connectedness to Westchester and larger numbers of
COVID-19 cases per resident. But a number of more subtle patterns also emerge.
Both measures are high in the communities along the Florida coast (in
particular along the southeastern coast, near Miami), in western and central
Colorado (in particular in areas with ski resorts), and in the upper
Northeast. These areas are all popular vacation destinations and second home
locations for many well-heeled residents of Westchester. Indeed, the governors
of Florida and Rhode Island publicly lamented the number of New York area
residents fleeing to their states and spreading COVID-19 (Mower, 2020,
Carlisle, 2020). By contrast, many areas that are geographically closer but
less socially connected to Westchester, such as counties in western
Pennsylvania and West Virginia, had fewer confirmed COVID-19 cases on March
30. There are also a number of patterns of COVID-19 prevalence that
connectedness to Westchester alone cannot explain. Areas around King County,
WA (Seattle), for example, have relatively low connectedness to Westchester,
but were an independent early hotspot of COVID-19.

The two bottom panels of Figure 1 explore the relationship between COVID-19
prevalence and social ties to Westchester more formally. Panel (c) shows a
binscatter plot of social connectedness to Westchester County and the number
of COVID-19 cases per 10,000 residents. We exclude those counties within 50
miles of Westchester County: while those areas have strong social links to
Westchester, they are also close enough geographically such that their
populations might interact physically with Westchester residents even in the
absence of social links (e.g., in supermarkets and houses of worship). There
is a strong positive relationship between social ties to Westchester and
COVID-19 prevalence. Quantitatively, a doubling of a county’s social
connectedness to Westchester is associated with an increase of about 0.88
COVID-19 cases per 10,000 residents. The R-squared of this relationship is
0.093, suggesting that, in a statistical sense, 9.3% of the cross-county
variation in COVID-19 cases can be explained by counties’ social connectedness
to Westchester.

One concern with interpreting these initial correlations is that they might be
primarily picking up other factors that affect the spread of COVID-19, and
that are correlated with social connectedness to Westchester. Specifically,
even after dropping counties within 50 miles of Westchester, the correlations
might be primarily picking up geographic distance to Westchester (which is
related to the number of friendship links to Westchester). As a result,
including social connectedness might not improve predictive power for models
that already control for some of these other variables. In Panel (d), we
therefore present a binscatter plot of the relationship between social
connectedness to Westchester County and COVID-19 cases that controls for a
number of these possible confounding variables (in addition to excluding
nearby counties). Most importantly, we non-parametrically control for the
geographic distance between each county and Westchester County by including
100 dummies for percentiles of that distance. We also control for median
income, population density, and a classification of how urban/rural a county
is. Even conditional on these other factors, Panel (d) shows a strong positive
relationship between COVID-19 cases as of March 30, 2020 and social
connectedness to Westchester County. With these controls, a doubling of a
county’s social connectedness to Westchester is associated with an increase of
about 0.80 COVID-19 cases per 10,000 residents. The total R-squared of the
statistical relationship is 0.190, while the incremental R-squared from
controlling for social connectedness to Westchester is 0.037.

Figure 2: Incremental $R^{2}$ from Adding Connections to Individual U.S.
Counties

(a) Excluding Counties within 50 Miles

(b) Excluding Counties within 150 Miles

Note: Panels show results from regressions to predict COVID-19 cases per 10k
people by county on March 30, 2020. The incremental $R^{2}$ is the increase in
$R^{2}$ from adding $log(SCI)$ and $log(SCI)^{2}$ to a particular U.S. county,
over and above a set of baseline control variables: 100 dummies for
percentiles of distance to the county under investigation; population density;
median household income; and dummies for the six National Center of Health
Statistics Urban-Rural county classifications. The graphs show the
distributions over the incremental $R^{2}$s for adding social connectedness to
each county with a population over 50,000 in turn. Each regression in panels
(a) and (b) excludes counties within 50 and 150 miles of the county of
interest, respectively. In each panel the 10 largest incremental $R^{2}$ are
labeled.

Another potential concern stems from the fact that the underlying social
network and the site of the initial hotspot are nonrandom. This may confound
our interpretation if, for example, counties with ties to Westchester were
also destinations for European travelers seeding the virus in the United
States. To contextualize the effect of connections to Westchester in
particular, we next run “placebo” regressions, identical to the one shown for
Westchester in panel (d) of Figure 1, for every U.S. county with a population
over 50,000. Figure 2 shows the incremental R-squared from adding social
connectedness in each of these regressions. Panel (a) excludes counties within
50 miles of the chosen county, as in Figure 1. Westchester’s 0.037 incremental
R-squared is second only to New York City, and each top 10 county is in the
New York-Newark Combined Statistical Area (CSA).555Although New York City
contains multiple counties, early NYC COVID-19 data was not disaggregated. As
such, we combine the counties in this section. NYC is disaggregated in all
analyses in Section 3. That connections to each of these counties matters so
strongly suggests that, although Westchester contained the earliest discovered
COVID-19 outbreak in the eastern U.S., community spread may have already been
present in many neighboring counties. Panel (b) shows results for regressions
excluding counties within 150 miles of the chosen county. Doing so will
exclude New York City and Westchester cases from every regression for a New
York-Newark CSA county.666The maximum distance from any county in the CSA to
New York City and Westchester is 91 miles and 104 miles, respectively.
Counties within the CSA remain as 9 of the top 10, including the top 3: New
York City, Fairfield, and Westchester.777Anecdotally, Williamson and Hussey
(2020) linked Fairfield to COVID-19 spread early in the pandemic. These
findings highlight that social connections to other counties that may have
similar demographics to Westchester, but that did not have an early COVID-19
outbreak, do not help with forecasting COVID-19 spread. In turn, this suggests
our previous results are not due to omitted variables whereby counties with
links to Westchester are more susceptible to COVID-19 outbreaks for some other
reason.

It is important to highlight that the purpose of this exercise is to
demonstrate the predictive power of social connectedness measured via online
social networks for COVID-19 prevalence. The control variables highlight that
the Social Connectedness Index has such predictive power over and above a
number of variables on which data is already easily available, and that may
partially proxy for social connections in models of communicable disease
spread. We will benchmark this predictive power against other measures, such
as smartphone location pings and Google searches for COVID-19 symptoms, in
Section 3.

Figure 3: Social Network Distributions of Lodi and COVID-19 Cases in Italy

(a) Percentile of SCI to Lodi Province, Italy

(b) COVID-19 Cases per 10k Residents by Province (c) Lodi binscatter without
controls (d) Lodi binscatter with controls

Note: Panel (a) shows the social connectedness to Lodi for Italian provinces.
Panel (b) shows the number of confirmed COVID-19 cases by Italian province on
March 30, 2020. Panels (c) and (d) show binscatter plots with provinces more
than 50 kilometers from Lodi as the unit of observation. To generate the plot
in Panel (c) we group $log(SCI)$ into 30 equal-sized bins and plot the average
against the corresponding average case density. Panel (d) is constructed in a
similar manner. However, we first regress $log(SCI)$ and cases per 10,000
residents on a set of control variables and plot the residualized values on
each axis. Red lines show quadratic fit regressions. The controls for Panel
(d) are 20 dummies for quantiles of the province’s geographic distance to
Lodi; GDP per inhabitant; and population density.

Figure 3 explores the analogous relationships for Lodi province in
Italy.888Because Italian provinces on the island of Sardinia do not align with
European NUTS3 regions (the level at which we measure social connectedness),
we include Sardinia as a single observation in our analysis. The provinces
with highest COVID-19 case densities and connectedness to Lodi are in the
surrounding Lombardy region, as well as the nearby Piemonte and Veneto
regions. There are also relatively high levels of both connectedness to Lodi
and COVID-19 cases in Rimini, a popular tourist destination along the Adriatic
sea. A number of provinces in southern Italy send workers and students to the
industrial Lombardy region, and therefore have strong social ties to that
region. While some of these areas have seen a number of COVID-19 cases, they
are not disproportionally larger, perhaps reflecting the efforts of Italian
authorities to restrict the movement of individuals (Kington, 2020). Panels
(c) and (d) repeat the binscatter exercises from Figure 1 (there are fewer
data points in Figure 3 than there are in Figure 1, since there are fewer
Italian provinces than U.S. counties). We exclude provinces within 50
kilometers of Lodi. In Panel (d) we control for geographic distance using 20
dummies for quantiles of distance from each province to Lodi, as well as GDP
per inhabitant and population density. As before, we find that the Social
Connectedness Index appears to have predictive power above these other
measures that might commonly be used to proxy for social interactions.
Quantitatively, the estimates from Panel (d) suggest that a doubling of the
$SCI$ corresponds to an increase of 16.6 COVID-19 cases per 10,000 residents.
The incremental R-squared of including social connectedness to Lodi over the
other control variables is 0.057.999In Appendix A, we conduct an additional
exercise to mimic a potential real-world use case in which U.S. public health
officials might have seeked to predict disease spread from the initial
Westchester outbreak. Since, by March 10, there was not yet enough documented
domestic COVID-19 spread to parameterize a forcecasting model based on U.S.
data, these officials might have looked to Italy to understand how social
connections to early hotspots translate into subsequent case growth. To
replicate such an analysis, we train a model using Italian provinces and their
conntectedness to Lodi to predict Italian COVID-19 cases as of March 10. We
then use that model to forecast U.S. COVID-19 cases as of March 30 based on
counties’ social connectedness to Westchester as the initial hotspot. We find
that including social connectedness as a model input in this exercise improves
out-of-sample predictions of COVID-19 cases across U.S. counties.

Taken together these case studies illustrate the potential usefulness of our
measure of social connectedness for predicting disease spread. In the next
section, we will use a time series of case growth from March through November,
as well as additional predictive measures from smartphone locations and Google
searches, to explore this potential in more detail.

##  3 Time Series Analysis

In this section, we exploit the changing geography of the pandemic in the U.S.
to more systematically investigate the predictive value of the $Social\
Connectedness\ Index$ for forecasting the spread of COVID-19. We construct two
primary time-varying metrics: “Social Proximity to Cases”, a county-level
measure of exposure to COVID-19 cases through social networks, and “Physical
Proximity to Cases”, a county-level measure of exposure through physical
proximity. While the two measures will be related (because individuals
generally have stronger social ties to those who are geographically nearby, as
documented in Bailey et al., 2018b), the examples in the previous section
illustrate that some geographically distant places — such as Westchester and
the east coast of Florida — can have strong social ties. To benchmark the
predictive power of social connectedness, we also construct measures using
data from smartphone locations and Google symptom searches.

### Key Variable Construction.

We construct our measure of social proximity to cases as:

$Social\ Proximity\ to\ Cases_{i,t}=\sum_{j}{Cases\ Per\
10k_{j,t}*\frac{Social\ Connectedness_{i,j}}{\sum_{h}{Social\
Connectedness_{i,h}}}}.$ (2)

$Cases\ Per\ 10k_{j,t}$ is the number of confirmed COVID-19 cases per 10,000
residents in county $j$ as of time $t$. The sums $j$ and $h$ are over all
counties. Analogously, we construct a measure of a county’s physical proximity
to cases as:

$Physical\ Proximity\ to\ Cases_{i,t}=\sum_{j}{Cases\ Per\
10k_{j,t}*\frac{1}{1+Distance_{i,j}}}.$ (3)

Here, $Distance_{i,j}$ is the physical distance between counties $i$ and $j$
measured in miles. We create a further related exposure measure using
smartphone location data. Specifically, Couture et al. (2020) create a
Location Exposure Index (LEX) that measures, among smartphones that pinged in
a given county $i$ today, the share that pinged in each county $j$ at least
once during the previous 14 days. We use these matricies to construct:

$LEX\ Proximity\ to\ Cases_{i,t}=\sum_{j}{Cases\ Per\
10k_{j,t}*\frac{LEX_{i,j,t}}{\sum_{h}{LEX_{i,h,t}}}}.$ (4)

We also use data from Google LLC  on searches related to COVID-19 symptoms.
The data include a county by week normalized (within county) probability that
a user will make a symptom-related search. For each county and two-week
period, we define the change in searches related to a symptom as the percent
change in this probability between the second week of the period and the
second week of the previous period. We use searches related to fever, cough,
and fatigue. We provide additional details in Appendix D. Finally, to explore
whether it is the specific bilateral patterns of connectedness or a county’s
overall level of connectedness that is most relevant for predicting the spread
of COVID-19, we include controls for the share of a county’s Facebook
connections that are within 50 and 150 miles.101010With the underlying
assumption that Facebook usage rates (as a share of the true population) are
roughly equal across counties, we construct these controls using the _Social
Connectedness Index_ as $Share\ Within\ K\ MI_{i}$ =
$[SCI_{i,j}*Pop_{j}*1(Distance_{i,j}<K)]/[\sum_{h}{SCI_{i,h}*Pop_{h}}]$, for
county $i$.

### Empirical Specification.

We first study the relationship between observed case growth and “lagged”
(i.e., in past time periods) growth in our measures. We hypothesize that if
social connectedness is an important predictor of the path of COVID-19 spread,
a lagged measure of social proximity to new cases will have a positive
relationship with new case counts in the next period. For each county $i$ and
time period $t$, our baseline specification is:

$\displaystyle log(\Delta\ Cases\ per\ 10k+1)_{i,t}$ $\displaystyle=$
$\displaystyle\beta_{1}*log(\Delta Cases\ per\ 10k+1)_{i,t-1}$ (5)
$\displaystyle+$ $\displaystyle\beta_{2}*log(\Delta Cases\ per\
10k+1)_{i,t-2}$ $\displaystyle+$ $\displaystyle\beta_{3}*log(\Delta Social\
Proximity\ to\ Cases)_{i,t-1}$ $\displaystyle+$
$\displaystyle\beta_{4}*log(\Delta Social\ Proximity\ to\ Cases)_{i,t-2}$
$\displaystyle+$ $\displaystyle\beta_{5}*Share\ Friends\ within\ 50mi_{i}$
$\displaystyle+$ $\displaystyle\beta_{6}*Share\ Friends\ within\ 150mi_{i}$
$\displaystyle+$ $\displaystyle\beta_{7}*log(\Delta Physical\ Proximity\ to\
Cases)_{i,t-1}$ $\displaystyle+$ $\displaystyle\beta_{8}*log(\Delta Physical\
Proximity\ to\ Cases)_{i,t-2}$ $\displaystyle+$ $\displaystyle
X_{i,t}+\epsilon_{i,t}$

Here, $t$ is defined as one of the eight two-week time periods between March
30 and November 2, 2020. For each time period $t$, prior two-week periods are
denoted $t-2$ and $t-1$ (for example, March 3 - 16 and March 16 - 30 for the
first period starting March 30). We always include two lags of own case
growth, and explore the effects of lagged changes of social and physical
proximity to cases. In some specifications we will add controls for
$log(\Delta LEX\ Proximity\ to\ Cases+1)_{i,t}$, lagged by one and two time
periods, and for the percent change in Google searches related to fever,
cough, and fatigue for this period or lagged by one period. $X_{i,t}$ are a
set of time-specific fixed effects, including percentiles of population
density and median household income. In our strictest specification, we also
add time $\times$ state fixed effects. To rule out differential testing across
regions driving our results, we also conduct a similar exercise replacing
COVID-19 cases with COVID-19-related deaths. For these analyses, we use four-
week time periods, beginning with April 28 - May 25, with our exposure
measures lagged by four and eight weeks.

Table 1: COVID-19 Case Growth and Prior Proximity to Cases

Note: Table shows results from regression 5. In Panel A, each observation is a
county $\times$ two-week period (between March 30 and November 2, 2020). The
dependent variable is log of one plus the number of new COVID-19 cases per
10,000 residents. In Panel B, each observation is a county $\times$ four-week
period (between April 28 and November 2, 2020). The dependent variable is log
of one plus the number of new COVID-19 deaths per 10,000 residents. Columns 1
and 2 include log of growth in social proximity to cases (deaths) lagged by
one and two periods (two and four weeks in Panel A, four and eight weeks in
Panel B). Columns 5 and 6 include analogous measures of physical proximity to
cases (deaths). Columns 3 and 4 also control for the share of a county’s
Facebook connections that are within 50 and 150 miles. Columns 7 and 8 include
all measures. All columns include controls for one and two period lagged
changes in cases (deaths), as well as time-specific fixed effects for
percentiles of county population density and median household income. Columns
2, 4, 6, and 8 include additional time $\times$ state fixed effects. Standard
errors are clustered at the time $\times$ state level. Significance levels:
*(p$<$0.10), **(p$<$0.05), ***(p$<$0.01).

### Regression Analysis.

Panel A of Table 1 shows that past growth in social proximity to COVID-19
cases in one period has a strong positive relationship with actual growth in
cases in the subsequent period. In columns 1 and 2, we document this
relationship without controlling for physical distance to cases (column 2 adds
state $\times$ time fixed effects to the specification in column 1, to control
for time-varying state-level differences in public health measures). In
contrast, columns 3 and 4 show that there is no systematic relationship
between the share of a county’s friends that are within 50 and 150 miles and
COVID-19 cases. This suggests that it is the specific bilateral patterns of
social connections that correlate with disease spread, not simply that
counties with more “open” networks experience worse outbreaks in every period.
Columns 5 and 6 show that physical proximity to cases is also strongly
correlated with subsequent case growth, a relationship which may confound the
one in columns 1 and 2. To address this, columns 7 and 8 include both the
physical proximity and social proximity measures. While the coefficient on
social proximity to cases declines somewhat — suggesting some of the
relationship is due to physical proximity — the relationship remains highly
statistically and economically significant. In our strictest specification,
which includes state $\times$ period fixed effects, a doubling of social
proximity to cases in one period corresponds to a 24.9% increase in cases per
capita in the next period.

Panel B of Table 1 presents the same specifications, using COVID-19 deaths
(instead of COVID-19 cases) as the dependent variable. The relationships are
very similar, suggesting that our results are not driven by differential
testing across counties that might have been correlated with social proximity
to cases.

In Appendix B we conduct two additional regression exercises. First, we run
regression 5 separately for each time period, allowing us to study how the
relationship between social connections and new COVID-19 cases changes over
the course of the pandemic. Table A2 shows that, in every two-week period from
March 30 to November 2, a one-period lagged measure of social proximity to
cases was a statistically significant predictor of actual case growth. In
Table A3, we add additional measures from smartphone locations and symptom
searches to our regression framework. We find that changes in Google symptom
searches — both in the current period and in the previous period — and lagged
LEX proximity to cases are strongly correlated with present case growth.
However, even in the presence of each of these other predictors, changes in
the social proximity to cases remains a significant predictor of subsequent
case growth in sample. We next benchmark the predictive power of social
connectedness to these measures using an out-of-sample prediction exercise.

### Out-of-Sample Prediction Analysis.

Building on our previous results, we next conduct a simple out-of-sample
prediction exercise. During a pandemic, local policymakers might want to
determine their localities’ risks for an outbreak in real time to inform
public health measures. With this case in mind, we build a series of simple
models that use available data at time $t$ to predict case growth in counties
at time $t+1$. We test the added predictive value of social proximity to cases
by building separate models that include and exclude this measure, as well as
other possible predictors. Because we do not use the “test” data to train the
models, a reduction in prediction error would be reflective of a true
improvement in real-world predictions of COVID-19 cases that could have been
achieved from using social connectedness data (as opposed to the increase in
in-sample $R^{2}$ in our previous analyses).

Table 2: Predicting COVID-19 cases in U.S., with and without Social Proximity
to Cases

Note: Table shows results from county-level predictions of COVID-19 case
growth. The predicted outcome is log of one plus the number of new COVID-19
cases per 10,000 residents. All columns show root mean squared errors (RMSEs)
from a random forest model trained on data from all periods prior to the
period of interest. The model inputs in column 1 are population density;
median household income; and log of growth in physical proximity to cases and
actual cases, lagged by two and four weeks (one and two time periods). Columns
4 and 7 include information on one and two period lagged measures of LEX
proximity to cases, and one period lagged percent changes in Google searches
related to fever, cough, and fatigue. Column 4 includes predictions for 3,136
counties using, for each county, a model that utilizes the most available
information possible. Column 7 limits to the 1,976 counties for which we have
both Google symptom search and LEX data. Columns 2, 5, and 8 add lagged
measures of social proximity to cases to columns 1, 4, and 7. Columns 3, 6,
and 9 show the change in RMSE from adding social proximity to cases.

Table 2 shows the results of this prediction exercise. The results in all
columns are generated using a random forest, an ensemble prediction algorithm
commonly used in data science applications. The algorithm allows us to find
non-linear relationships between variables, without overfitting, by
aggregating mean predictions from a number of regression trees generated over
sample subsets of both observations and input variables.111111In our analysis
we use 500 trees. For more information on random forests, see Breiman (2001).
In most settings, random forest out-of-sample predictions outperform those of
linear models.

Columns 1-3 describe the prediction error from a simple model that includes
the measures from columns 7 and 8 in Panel A of Table 1.121212Here, we use
non-binned measures of population density and median household income. Because
random forests are able to identify non-linear relationships between input and
outcome measures, we no longer need to split the measures into percentiles to
allow for non-linear relationships. Column 1 excludes the two lagged measures
of social proximity to cases and column 2 includes them. Columns 1 and 2 show
the root mean squared error (RMSE) from a model trained using data from all
periods before the period of interest, then tested on that next period; each
prediction period is shown as a separate row. The RMSE for both models
generally decreases as the training sample gets larger, ending at 0.667 and
0.652 log new cases per 10,000 residents. Column 3 shows the difference in
RMSE between the two models, with negative numbers indicating an improvement
in out-of-sample fit from including social proximity to cases. In every row,
the RMSE is lower when including social proximity to cases, suggesting it does
significantly improve predictions.

In columns 4-9 we add information on Google symptom searches and mobility
based on smartphone locations. Doing so allows us to benchmark the predictive
value of social proximity to cases over and above these other predictors.
Columns 4-6 include predictions for all counties included in the COVID-19 case
data. We make a prediction for each county using the “best” model (in terms of
model features) based on data availability. For example, for a county with LEX
and Google data, we will predict cases using a model trained with LEX and
Google data. For a county with only LEX data, we will predict using a model
trained without Google data, and so on.131313This requires training four
models: (1) baseline; (2) baseline + LEX; (3) baseline + Google; and (4)
baseline + LEX + Google. We train each model on every county that has the
necessary non-missing data. For example, a county with LEX and Google data
will be used to train all four models. Column 6 shows that, once again, RMSE
decreases in every period after including social proximity to cases,
highlighting its incremental predictive value over and above other measures
one might have used.

In columns 7-9 we limit to the 1,976 counties which have both LEX and Google
symptom search data. Column 9 shows that in 10 of 14 periods, predictions
using social connectedness do outperform the comparison model. However, the
differences are generally small, suggesting that when limiting to _only_
counties with LEX and Google data, social proximity to cases may provide only
a small degree of additional predictive value. This is perhaps unsurprising:
our proposed mechanism by which social connectedness helps forecast COVID-19
spread is through predicting in-person interactions, which are more directly
measured in LEX data.141414In Appendix C we repeat this exercise using
COVID-19 related deaths. We find similar results. Baseline models that include
social proximity to deaths have smaller prediction errors than models that
exclude the measure. Social proximity to deaths does not appear to add sizable
predictive value to LEX and Google measures when limiting to counties with
both sets of data; however, when using the “best available” model in any
county, social proximity to deaths _does_ sizably improve predictions.

Tthe fact that social connectedness consistently improves predictions in the
full set of U.S. counties (columns 4-6) highlights an important availability
advantage of the data. While the LEX and Google data are limited to counties
with a sufficient number of devices or searches in a period, the relatively
stable nature of social connectedness over time (combined with Facebook’s
large user base) allows the $SCI$ to be available in more counties, and
potentially also at finer levels, such as zip codes.151515The SCI data used
for this paper include 3,141 counties, the Google data include 2,572 counties,
and the LEX data include 2,018 counties. Furthermore, Facebook’s global reach
allows for $SCI$ measures _within and between_ most parts of the world. We are
unaware of smartphone location data that can similarly measure, for example,
connections between GADM1 regions in Africa, NUTS3 regions in Europe, and U.S.
counties — and information on these connections may aid in forecasting the
global spread of communicable diseases.

##  4 Conclusion

In the context of threats from communicable diseases such as COVID-19, a
region’s ability to determine optimal public health responses depends on its
ability to forecast the risk of an outbreak (Reich et al., 2019). A primary
determinant of this risk is the likelihood of physical interactions between
the region’s residents and residents of other areas with severe outbreaks.
Information on the geography of social connections, which shape patterns of
physical interactions, are therefore crucially important for public health
officials. In this paper, we use de-identified and aggregated data from
Facebook to measure social connections between regions, and find those
connections to be an important predictor of outbreaks during the COVID-19
pandemic. We show that areas that are more connected to early pandemic
hotspots in the U.S. and Italy had, on average, higher case counts by March
30, 2020, even after controlling for physical distance and other demographics.
Furthermore, due to its broad geographic coverage, social connectedness data
improves out-of-sample predictions of COVID-19 spread during the U.S. pandemic
beyond smartphone location and Google symptom search data.

The methodologies we use should not be interpreted as an attempt to create a
state-of-the-art epidemiological model. However, our results strongly suggest
that our measure of social connectedness may prove useful in future
epidemiological work. In particular, its high-degree of availability — in
terms of both geographic coverage and granularity — allow social connectedness
to provide predictive power over and above other available measures.

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##  Appendix A Out-of-Sample Hotspot Analysis

In this section, we conduct a simple prediction exercise to test the value of
social connectedness in forecasting how a disease will propagate from a
hotspot early in a pandemic. To do so, we train a model using an Italian
hotspot and test it using a subsequent U.S. hotspot.

On March 10, 2020, New York state created a “containment area” around New
Rochelle, a community in Westchester County that had the first major COVID-19
outbreak in the eastern United States. At this time, U.S. local officials
around the country were likely worried about the extent of their own regions’
exposures to COVID-19. Yet, in the absence of existing data on domestic
COVID-19 spread in the U.S., it may have been difficult to calibrate a local
forecasting model. One potential solution would have been to train a model
using information from the Italian outbreak — which by mid-March had been
spreading for some time — to predict COVID-19 spread in the U.S.

We mimic this use case by first training linear regression and random forest
models using data from Italy. Specifically, for each Italian province, we
predict the number COVID-19 cases per 10,000 people on March 10 using
population density, a measure of income, and distance and social connectedness
to the Lodi hotspot. We exclude provinces within 80 km (50 miles) of Lodi. We
train versions of these models with and without including social connectedness
to Lodi as a predictor. In each model, we normalize every measure by
subtracting the mean and dividing by the standard deviation. This
normalization, which is common in machine learning prediction applications,
ensures that our predictive measures are scaled similarly in the U.S. and
Italian settings. In our prediction exercise we use, for each U.S. county, the
Italy-trained models to predict the number of COVID-19 cases per 10,000 people
on March 30 (i.e., 20 days in the future) with and without data on social
connectedness to Westchester.

Table A1: Predicting U.S. Hotspot COVID-19 spread, trained on Italian Hotspot
spread

Note: Table shows results from county-level predictions of COVID-19 cases per
10,000 residents. Columns 1-3 and 4-6 show results from linear regression and
random forest models, respectively. The models are trained using information
from Italy on March 10 and tested using information from the U.S. on March 30.
All measures are normalized by subtracting the mean then dividing by the
standard deviation. Row (1) shows the prediction root mean squared errors
(RMSEs) and row (2) shows prediction rank-rank correlation with the truth. The
model inputs in columns 1 and 4 are $log(distance)$ to the hotspot (Lodi in
Italy, Westchester in the U.S.), population density, and household income /
(GDP per inhabitant). Columns 2 and 5 add $log(SCI)$ to the hotspots. Columns
3 and 6 show the change in each measure from adding $log(SCI)$.

Table A1 shows that our predictions improve when adding social connectedness
to the hotspots as a model input. Row (1) shows that the RMSE drops from 0.99
to 0.97 (in standard deviations from the mean cases per 10,000 residents) for
the linear regression model and from 1.04 to 1.01 for the random forest model.
Row (2) compares the rank of counties’ predictions with the true rank. For
both models the rank-rank correlations increase when including social
connectedness to the hotspot as a predictor.

##  Appendix B Additional Time Series Regressions

Table A2 shows the results from running the regression in Table 1’s column 8
separately for every two-week period betwen March 30 and November 2. In every
period, a two week lagged measure of social proximity to cases was a
statistically significant predictor of actual case growth. The magnitudes of
the coefficients suggest a doubling in social proximity to cases in one two-
week period corresponds to between a 10.9% and 66.4% increase in actual cases
in the next period, after controlling for physical proximity to cases and
other controls.

Table A3 shows the results from adding additional predictive measures to Table
1. Columns 1 and 2 are the same as columns 7 and 8 in Table 1. Columns 3 and 4
show that a “nowcast” of changes in Google symptom search trends is strongly
correlated with changes in case growth. Columns 5 and 6 show that this
relationship persists, though somewhat less strongly, for a one-period lagged
measure of changes in symptom searches. The latter measure, unlike the former,
could be used to predict _future_ case growth. Columns 7 and 8 show that the
change in LEX proximity to cases in one period also has a strong positive
relationship with actual case growth in the next. Even in the presence of each
of these other measures, social proximity to cases remains a significant
predictor of future case growth.

Table A2: COVID-19 Case Growth and Prior Proximity to Cases, by Two-Week
Period

Note: Table shows time-specific results from regression 5. Each observation is
a county. The dependent variable is log of one plus the number of new COVID-19
cases per 10,000 residents in one two-week period between March 30 and
November 2, 2020. All columns include log of growth in social and physical
proximity to cases, as well as log of growth in actual cases, lagged by two
and four weeks (one and two time periods). All columns include time-specific
fixed effects for percentiles of population density and median household
income, time-specific fixed effects for state, and estimations of the share of
a county’s Facebook connections that are within 50 and 150 miles Significance
levels: *(p$<$0.10), **(p$<$0.05), ***(p$<$0.01).

Table A3: COVID-19 Case Growth, Prior Proximity to Cases, and Other Predictive
Measures

Note: Table shows results from regression 5. Each observation is a county
$\times$ two-week period (between March 30 and November 2, 2020). The
dependent variable is log of one plus the number of new COVID-19 cases per
10,000 residents. Columns 1 and 2 are the same as columns 7 and 8 in Table 1.
Columns 3 and 4 add the percent growth in Google searches related to fever,
cough, and fatigue from the week prior to the period to the second week of the
period. Columns 5 and 6 includes analogous measures lagged by one period.
Columns 7 and 8 add LEX-based proximity to cases. Standard errors are
clustered at the time $\times$ state level. Significance levels: *(p$<$0.10),
**(p$<$0.05), ***(p$<$0.01).

##  Appendix C Out-Of-Sample Prediction: COVID-19 Deaths

Table A4 show the prediction error from a simple out-of-sample forecasting
exercise analogous to that in Table 2, but for COVID-19 deaths instead of
COVID-19 cases. Columns 1-3 use the variables in columns 7 and 8 of Table 1,
Panel B as predictors. The model presented in column 2 includes the two lagged
measures of social proximity to COVID-19 deaths, while the model presented in
column 1 does not include them. The RMSE is lower in every period in the model
that includes social proximity to deaths as a predictor. Columns 4-6 include
predictions for all counties included in the COVID-19 case data. We make a
prediction using the “best” model available (in terms of number of model
features), as described in Section 3. Column 6 shows that the RMSE decreases
again in every period when including social proximity to deaths as a
predictor. Columns 7-9 limit to counties with Google and LEX data. Similar to
our findings for county-level COVID-19 cases, social connectedness does not
appear to provide substantial additional predictive value in this particular
setting.

Table A4: Predicting COVID-19 deaths in U.S., with and without Social
Proximity to Deaths

Note: Table shows results from county-level predictions of COVID-19 deaths.
The predicted outcome is log of one plus the number of new COVID-19 deaths per
10,000 residents. All columns show root mean squared errors (RMSEs) from a
random forest model trained on data from all periods prior to the period of
interest. The model inputs in column 1 are population density; median
household income; and log of growth in physical proximity to deaths and actual
deaths, lagged by four and eight weeks (one and two time periods). Columns 4
and 7 include information on one and two period lagged measures of LEX
proximity to deaths, and one period lagged percent changes in Google searches
related to fever, cough, and fatigue. Column 4 includes predictions for 3,156
counties using, for each county, a model that utilizes the most available
information possible. Column 7 limits to 1,976 counties for which we have both
Google symptom search and LEX data. Columns 2, 5, and 8 add lagged measures of
social proximity to deaths to columns 1, 4, and 7. Columns 3, 6, and 9 show
the change in RMSE from adding social proximity to deaths.

##  Appendix D Additional Details on Google Symptom Search Data

In Section 3, Appendix B, and Appendix C we use data on Google searches
related to COVID-19 symptoms from Google LLC . The data include a county by
week normalized (within county) probability a user will make a symptom-related
search. These measures come in a daily series and a weekly series. If a given
symptom in a given county does not meet certain Google quality or privacy
thresholds at the daily level, it will be provided at the weekly level. If it
cannot meet these thresholds at the weekly level, it is not provided. If a
county/symptom is provided for a period at the daily level, it is not also
provided at the weekly level. To create a time series at the county/weekly
level, we therefore average non-missing daily measures by week. We use
searches related to three common COVID-19 symptoms: fever, cough, and fatigue.

To aggregate our measure to the bi-weekly periods used in Section 3, Appendix
B, and Appendix C we define the change in searches related to a symptom as the
percent change in the probability between the second week of the period and
the second week of the previous period. For example, for the period March 31 -
April 13, the percent change is from March 23 - March 29 to April 6 - 12. In
our prediction exercise presented in Table 2, we use a one-period lagged
version of this measure. Some counties are missing data for particular weeks.
So that our final sample has a complete time series for every included county,
we exclude counties with missing data in more than half the periods in our
sample and impute zero change in any remaining missing periods. 97 percent of
counties included are missing fewer than 1 in 4 periods and 77 percent are
missing fewer than 1 in 20 periods.