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RESEARCH ARTICLE
Contagion in Mass Killings and School
Shootings
Sherry Towers
1
*, Andres Gomez-Lievano
1
, Maryam Khan
2
, Anuj Mubayi
1,2
,
Carlos Castillo-Chavez
1
1 Arizona State University, Tempe, AZ, USA, 2 Northeastern Illinois University, Chicago, IL, USA
*
smtowers@asu.edu
Abstract
Background
Several past studies have found that media reports of suicides and homicides appear to
subsequently increase the incidence of similar events in the community, apparently due to
the coverage planting the seeds of ideation in at-risk individuals to commit similar acts.
Methods
Here we explore whether or not contagion is evident in more high-profile incidents, such as
school shootings and mass killings (incidents with four or more people killed). We fit a conta-
gion model to recent data sets related to such incidents in the US, with terms that take into
account the fact that a school shooting or mass murder may temporarily increase the proba-
bility of a similar event in the immediate future, by assuming an exponential decay in con-
tagiousness after an event.
Conclusions
We find significant evidence that mass killings involving firearms are incented by similar
events in the immediate past. On average, this temporary increase in probability lasts 13
days, and each incident incites at least 0.30 new incidents (p = 0.0015). We also find signifi-
cant evidence of contagion in school shootings, for which an incident is contagious for an
average of 13 days, and incites an average of at least 0.22 new incidents (p = 0.0001). All
p-values are assessed based on a likelihood ratio test compari ng the likelihood of a conta-
gion model to that of a null model with no contagion. On average, mass killings involving
firearms occur approximately every two weeks in the US, while school shootings occur on
average monthly. We find that state prevalence of firearm ownership is significantly associ-
ated with the state incidence of mass killings with firearms, school shootings, and mass
shootings.
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 1/12
a11111
OPEN ACCESS
Citation: Towers S, Gomez-Lievano A, Khan M,
Mubayi A, Castillo-Chavez C (2015) Contagion in
Mass Killings and School Shootings. PLoS ONE 10
(7): e0117259. doi:10.1371/journal.pone.0117259
Academic Editor: Joshua Yukich, Tulane University
School of Public Health and Tropical Medicine,
UNITED STATES
Received: May 16, 2014
Accepted: December 19, 2014
Published: July 2, 2015
Copyright: © 2015 Towers et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any
medium, provided the original author and source are
credited.
Data Availability Statement: The USA Today mass
killings data are publicly available from masskillings.
usatoday.com. The Brady Campaign data on school
shootings and mass shootings are freely available on
request from that organization, who can be contacted
at (202) 370-8101. Data have also been included in
the paper and its Supporting Information files.
Funding: The authors have no support or funding to
report.
Competing Interests: The authors have declared
that no competing interests exist.
Introduction
In recent years, tragedies involving mass killings in the US, such as the Aurora, CO movie the-
ater shooting in July 2012, and the Newtown, CT school shooting in December 2012, have
intensified societal focus on trying to understand the dynamics and contributing factors that
underlie such events, particularly since the per capita incidence of such events and other fire-
arm related mortality is significantly higher in the US than in any other industrialized country
[
1–4].
Statistics are not readily available on the incidence of mass killings and school shootings in
other industrialized countries, however studies have shown that the firearm homicide and sui-
cide rates in the US are several times higher than that of any other industrialized country [
4],
and the patterns appear to be due to higher rates of firearm ownership in the US compared
with other industrialized countries [
5]. Overall, the pediatric firearm mortality rate is five times
higher in the United States compared with any other industrialized country [
3], and 87% of all
children age 0 to 14 worldwide killed by firearms are children living in the US [
4], despite the
fact that less than 5% of the world’s children live in the US [
6]. In September, 2014, the Federal
Bureau of Investigation (FBI) released a report “A Study of Active Shooter Incidents in the
United States Between 2000 and 2013” [
7]. In their report, they note that the incidence of mass
shooting incidents has been growing over the past 14 years.
Ready access to weaponry has been implicated in these trends. For instance, it ha s been
found that two thirds of school shooters obtained their firearms from their own home, or the
home of a relative [
8], and youths are significantly more likely to die by firearm homicide or
suicide in states where gun ownership is more prevalent. In addition, household gun ownership
has been shown to significantly raise the risk for homicide in the home [
9], and homicide rates
in general [
10]. Studies have also shown that the more access people have to firearms, the lower
the levels of social trust, and the higher the levels of homicide [
11, 12]. A strong association has
also been found between overall state suicide rates and firearm ownership rates [
13, 14],
Access to mental health care has also been viewed as a factor in at least some types of inci-
dents. For example, it has been shown that access to health care and the state rates of federal
aid for mental health services are strongly associated with reduced state suicide rates [
15].
Beyond the exongenous factors like mental health issues and ease of access to weaponry that
may be contributing to the frequency of events, there is also the possibility that the stressed
individuals may have, consciously or sub-consciously, been inspired to act on previously sup-
pressed urges by exposure to details of similar events. Such contagious ideation is not implausi-
ble; for example, vulnerable youth have been found to be susceptible to suicide ideation
brought on by influence of reports and portrayal of suicide in mass media [
16–18], and media
reports on suicides and homicides have been found to apparently subsequently increase the
incidence of similar incidents in the community [
19, 20]. In addtion, in a broader public health
context, the temporal and geospatial clustering of many types of violence and crime have been
shown to be similar to the patterns seen in the spread of infectious disease [
21].
To study this issue, we examine data on mass killings (four or more people murdered, by
any means) in the US between 2006 to 2013 compiled by USA Today (N = 232, 176 of which
involved firearms), data on school shootings from 1998 to 2013 inclusive from the Brady Cam-
paign to Prevent Gun Violence (N = 188), and data on mass shootings (at least three people
shot, not necessarily killed) from February 2005 to January 2013, also from the Brady Cam-
paign (N = 477).
We fit a mathematical contagion model to the data sets, with model terms that take into
account temporal trends due to possible exogenous non-contagion factors, and a contagion
term that takes into account the fact that a school shooting or mass murder may temporarily
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 2/12
increase the probability of a similar event in the immediate future. We model the contagion
process assuming an exponential decay in contagiousness after an event. Contagion models
have been applied to financial markets [
22], spread of YouTube videos on social networks [23],
burglary [
24–27], civilian deaths in Iraq [28], and terrorist attacks [29, 30], but this is the first
instance in which these models have been applied in the context of mass murders and school
shootings.
Because contagion is just one potential aspect contributing to these events, we also examine
the relationship between the incidence of these tragedies, and state prevalence of mental illness
and firearm ownership, and the rankings of the strength of state firearm legislation.
In the following sections we describe the sources of data used in this analysis, and the
modeling and statistical data analysis methods used. We then present results, with discussion
and summary.
Methods
Data
Here we describe the mass killing and school shooting sources of data used in this analysis,
along with a description of the data sources use to examine the relationship of such events to
state prevalence of mental illness and firearm ownership, and estimates of the strength of state
gun laws. There are currently no comprehensive federal repositories of data on mass killings
and school shootings in the US, thus for these studies we relied on data compiled by private
organizations. Data are available at
http://tinyurl.com/oql4lpy.
USA Today mass killing data. Data on mass killings in the US between 2006 to December
2013 were obtained from a USA Today study that examined Federal Bureau of Investigation
(FBI) data from the FBI Supplemental Homicide Reports, and hundreds of media reports and
police documents to compile a list of incidents that involved four or more people being killed,
not including the killer (data are available from, and described at,
masskillings.usatoday.com,
accessed March 2014). The USA Today study did not rely solely upon the FBI data, in part
because the FBI data are based on voluntary reports by local police agencies and are thus an
incomplete tally of mass murders in the US, and also because the data were found to only have
a 61% accuracy rate when compared with data available from local police documents, appar-
ently largely due to mistakes in transcription. For more details about the USA Today data set,
see
www.usatoday.com/story/new s/nation/2013/12/03/fbi-mass-killing-data-inaccurate/
3666953/ (accessed January 30, 2015).
The data consist of 232 events, of which firearms were involved in 176 (76%). Of these 232
incidents, the authors found only three apparent errors, where the date was accidentally tran-
scribed incorrectly by one day. The dates were corrected for this analysis. The data are shown
in
Fig 1.
Incidents showed no significant dependence on month of the year, but were significantly
more likely to occur on Saturdays (Pearson χ
2
p = 0.04). For the 176 incidents that involved
mass killings with firearms, 46% of the killers committed suicide (either by th emselves or by
“suicide by cop”). This is significantly higher than the estimated 5% to 10% suicide rate of
killers in all murders [
31]. On average, 22% more people were killed (not including the killer)
in events where the murderer committed suicide (Student-t two-sided p = 0.038).
This is in contrast to the 56 events involving mass killings without firearms, where only 8%
of such killers committed suicide, and there was no significant difference in the number killed
when the murderer committed suicide (Student-t two-sided p = 0.74).
Brady Campaign School Shooting Data. Data on school shootings in the US were
obtained from the Brady Campaign to Prevent Gun Violence, who examined media reports to
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 3/12
compile a list of 220 school shootings in the US between 1997 to 2013, inclusive. We excluded
from this data set foiled plots where individuals were caught actively planning a shooting, but
had not yet carried out their plan, incidents that did not actually occur on a school campus or
school bus, or incidents that occurred outside of school hours or outside the context of school-
related events (such as sports games), leaving 188 events. Of these 188 events, upon review of
the media reports the authors found four incidents for which the date was apparently mis-tran-
scribed by one day, and the dates were corrected for this analysis. The school shootings resulted
in an average of one person being killed per incident; only six of the school shootings thus over-
lap with the USA Today mass killing data set, and the two data sets are nearly independent.
The data are shown in
Fig 1.
Fig 1. Number of mass killings, school shootings, and mass shootings over time for the data samples used in these studies. For clarity of
presentation, all data samples are shown over the same time frame. Overlaid is the fit of the full model of
Eq 4 that also contains a contagion component
(red). The green line indicates the estimated portion of the data due to contagion. The points along the x axis for the first three samples indicate the date of
events that had number of people killed in the top 5
th
percentile for that sample.
doi:10.1371/journal.pone.0117259.g001
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 4/12
The incidents were significantly more likely to occur between September to April compared
with May to August (p < 0.001), and on weekdays compared with weekends (p < 0.001).
Of all events, 18% of the shooters committed suicide, with the fraction rising to 23% in inci-
dents in which at least one person was killed (not including the shooter). Again, this is signifi-
cantly higher than the estimated 5% to 10% suicide rate of killers in all homicides [
31]. There
was no significant difference in the number of people killed in incidents where the shooter did,
and did not, commit suicide.
Brady Campaign Mass Shooting Data. Additional data on 477 mass shootings in the US
between February 2005 to January 2013 were also obtained from the Brady Campaign. These
data include shootings where at least three people were shot or injured (but not necessarily
killed).
Incidents were excluded that did not mention a verifi able source, or were an agglome ration
of events rather than a single event (such as a mention of the total number of people killed by
firearms in particular city over a weekend), and we were unable to identify news stories con-
taining the details of the separate events. In addition, two of the entries appeared to be repeti-
tions of a previous entry and were thus excluded from the analysis. A total of 468 incidents
remained after these selections. Ten of the events had the date of the incident mis-transcribed
by a day or two, and the dates were corrected for this analysis. Of the 468 mass shootings, 92
involve 4 four or more people killed, 83 of which are also included in the 154 mass killings by
firearms in the USA Today data set that spans the same time frame. Because of this large over-
lap of the two data sets, in order to ensure that the Brady Campaign mass shooting data is inde-
pendent of the USA Today mass killing data we thus examine only the mass shootings in the
Brady Campaign data that have less than four people killed, yielding a total of 376 incidents.
The data are shown in
Fig 1.
Incidents showed no significant dependence on month of the year, but were significantly
more likely to occur on Saturday and Sunday (p < 0.001).
Of all events, 17% of the shooters committed suicide, with the fraction rising to 25% in inci-
dents in which at least one person was killed (not including the shooter). Again, this is signifi-
cantly higher than the estimated 5% to 10% suicide rate of killers in all homicides [
31]. On
average, 2.3 times more people were killed in events where the shooter committ ed suicide,
compared with events where the shooter did not (Student-t p < 0.001).
Correlation of data samples to exogenous variables. No official government statistics are
available for firearm ownership by state. In order to estimate the relative firearm ownership by
state, we thus examined the fraction of all suicides within each state that involved firearms
(past firearm suicide rates have been shown to be directly correlated to firearm ownership rates
[
13, 14], and are a good proxy for firearm ownership rates [32]). Suic ide data from 1999 to
2010 by state and cause used to calculate these estimates were obtained from the Centers for
Disease Control Web-based Injury Statistics Query and Reporting System (
http://www.cdc.
gov/injury/wisqars/index.html, accessed January 30, 2015). State populations in 2012 were
obtained from the US Census Bureau
www.census.gov (accessed January 30, 2015).
State prevalence rates of serious mental illness for all 50 states were obtained from the from
the National Alliance on Mental Illness (NAMI) [
33, 34].
The Brady Campaign to Prevent Gun Violence regularly publishes rankings of the states on
the basis of laws that can prevent gun violence, such as background checks on all gun sales, per-
mit-to-purchase requirements, limiting handgun purchases to one a month, and retention of
sales records. The most recent state rankings were obtained from
bradycampaign.org.
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 5/12
To study how the state variations in incidence of mass killings, school shootings, and mass
shootings may be related to exogenous variables such as state rates of firearm ownership, prev-
alence of mental illness, etc, we first calculated the national average rate of such incidents, μ.
For a state with observed number of incidents, k
i
, and population N
i
, we determined the signifi-
cance of the observed number of incidents by calculating the Binomial CDF
Fð k
i
jN
i
; mÞ¼
X
k
i
j¼0
N
i
j
!
m
j
ð1 mÞ
N
i
j
: ð1Þ
The result is between 0 and 1, with results close to 0 (1) indicating that a particular state has
rate of such incidents significantly lower (higher) than the national average.
Modeling and Statistical Methods
Self-Excitation Contagion Model. In a self-excitation contagion model, recent prior
events increase the probability of another event happening in the near future. In this analysis,
we employ an exponential probability distribution to simulate this process. Under the hypothe-
sis that past events incite future events, the increased probability of an event occurring during
the 24 hours of day t
j
due to prior event that occurred on day t
i
is thus
Pðt
j
jt
i
; T
excite
Þ¼
Z
t
j
t
i
t
j
t
i
1
dx
e
x=T
excite
T
excite
;
ð2Þ
where T
excite
is the average duration of the contagion process (in this analysis, measured in
days). This yields
Pðt
j
jt
i
; T
excite
Þ¼e
ðt
j
t
i
1Þ=T
excite
e
ðt
j
t
i
Þ=T
excite
:
ð3Þ
We consider a self-excitation contagion model with an additional baseline (i.e.; non-conta-
gion related) average number of events per day of N
0
(t). Taking into account all prior events in
some stochastic data realization, the total number of expected events, N
exp
, on day t
n
for that
realization is thus
N
exp
ðt
n
Þ¼N
0
ðt
n
ÞþN
secondary
X
8t
i
<t
n
Pðt
n
jt
i
; T
excite
Þ;
ð4Þ
where the summation is over all prior events. The parameters of this contagion model are the
average number of secondary events inspired by the contagion of a single event, N
secondary
, the
duration of the contagion process, T
excite
, and whatever parameters are needed to describe the
temporal evolution of the baseline number of events, N
0
(t). For instance, one can assume N
0
(t)
is a constant, or a straight line with a slope. One can also use a non-parametric approach where
N
0
(t) is calculated using a weighted running mean of the data itself (in S1 Appendix we provide
a detailed description of the weighted running mean ansatz).
The functional form of N
0
(t) can incorporate additional weights if needed in order to take
into account day-of-week or seasonal effects, and indeed, we incorporate such weights when it
is evident that there is significant evidence of dependence on season or day-of-week in a partic-
ular data set.
In
S1 Appendix, we describe the methods used to fit the parameters of the mode l of Eq 4 to
data, and the methods we used to simulate data with a self-excitation contagion model. We
also describe the methods used to validate the modeling and fitting methods, and the methods
used to cross-check the analysis.
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 6/12
Results
Based on the USA Today sample, mass killings involving firearms with four or more people
killed occur on average every 12.5 days in the US. Based on the Brady Campaign data, school
shootings occur on average every 31.6 days.
The results of the fits of the parameters of the self-excitation contagion model of
Eq 4 to the
various data samples are shown in
Fig 1, and are tabulated in Table 1. Evidence of significant
contagion is found for all samples but the Brady Campaign mass shooting sample with at most
three people killed.
Latitude and longitude data were obtained for the location of each incident in the data sets
used in this analysis. For all samples, the time between incidents was not significantly corre-
lated to the distance between them, indicating lack of evidence of temporal/geospatial cluster-
ing (as would happen, for instance, if an incident incited a similar incident in a nearby locale).
Additionally, the Mantel test for temporal/geo-spatial clustering in the samples did not return
significant p-values (p > 0.05 for all samples) [
35]. This lack of temporal/geo-spatial correla-
tion is consistent with what would be expected if the contagion process is potentially due, for
instance, to widespread media attention given to mass killings and school shootings.
The correlation of the state incidence of our data samples to firearm ownership prevalence,
prevalence of mental illness, and ranking of strength of state firearm legislation are summa-
rized in
Fig 2.
Discussion and Summary
In our analysis, we employ a self-excitation contagion model, and find significant evidence of
contagion in mass killings and school shootings. There is no significant evidence of contagion
in mass shootings that involve three or fewer people killed, possibly indicating that the much
higher frequency of such events compared with mass killings and school shootings reduces
their relative sensationalism, and thus reduces their contagiousness. This is the first analysis of
its kind to examine the potential of contagion in such incidents.
We find that state prevalence of firearm ownership is significantly associated with state inci-
dence of mass killings with firearms, school shootings, and mass shootings. Once state preva-
lence of firearm ownership has been taken into account, there is no significant association
between state incidence of these events and state prevalence of mental illness or ranking of
strength of firearm legislation. Mass killings not involving firearms are not significantly corre-
lated to any of these variables. Our noted apparent relationship of high-profile shooting inci-
dents to firearm ownership is in concordance with the results of other studies of firearm
violence, including homicide and suicide [
8–14, 36].
Table 1. Results of fits of the self-excitation contagion model in Eq 4 to the various data samples considered in these studies, using a running
mean calculation of N
0
(t). N
secondary
is the average number of new incidents. The p-value is obtained from the likelihood ratio test comparing the likelihood
of the full contagion model to the likelihood of the null hypothesis model of no contagion. The numbers in the square brackets indicate the 95% confidence
interval on the parameter.
Sample # in sample N
secondary
T
excite
p−value
USA Today full sample 232 0.28 [0.10,0.56] 13.3 [4.6,58.6] p = 0.004
USA Today w/ firearms 176 0.30 [0.12,0.56] 13.2 [4.3,46.8] p = 0.002
USA Today w/o firearms 56 0.23 [0.04,0.64] 11.9 [3.2,89.5] p = 0.037
Brady Campaign school shootings 188 0.22 [0.10,0.42] 12.9 [5.4,53.3] p < 0.001
Brady Campaign mass shootings w/ 3 killed 373 0.28 [0.00,0.62] 38 [0, 90] p = 0.18
doi:10.1371/journal.pone.0117259.t001
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 7/12
Given the significant correlation of the incidence of mass killings to firearm ownership
prevalence, it is worthwhile to explore the potential reasons for the apparent relationship. We
note that the overall effect of firearm right-to-carry laws on the prevalence of various types of
crime has been hotly debated (see, for instance, References [
37–41]). However, it has been
shown that firearm regulations that reduce overall firearm availability, such as permit and
licensing regulations, appear to have a significant deterrent effect on suicide rates [
42], and
shall-issue laws that eliminate most restrictions on carrying a concealed weapon have been
associated with increased firearm homicide rates [
43]. In addition, firearm mortality rates were
found to be significantly lower in states with stricter gun laws [
44]. Secure gun storage practices
involving safes and trigger locks have been shown to decrease the risk of youth suicides and
unintentional firearm injuries [
45].
Fig 2. Relationship of state prevalence of firearm ownership, mental illness, and state rankings of strength of firearm legislation, to the state
incidence of mass killings, school shootings, and mass shootings. Correlations with jρj0.28 are significant to p < 0.05.
doi:10.1371/journal.pone.0117259.g002
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 8/12
We found no significant association between the rate of school and mass shootings and
state prevalence of mental illness. However, we note that in all our data samples but mass kill-
ings not involving firearms, the probability that the perpetrator committed suicide was several
times higher than the overall estimated perpetrator suicide rate of 5% to 10% for all homicides
[
31]. In addition, in our mass killings with firearms and mass shootings data samples, we have
found a significant positive association between the overall number killed and perpetrator sui-
cide. Further study of the reasons behind these patterns is indicated, including an examination
of whether or not problems with access to mental health treatment at the individual level
played a partial role in such incidents.
While our analysis was initially inspired by the hypothesis that mass media attention given
to sensational violent events may promote ideation in vulnerable individuals, in practice what
our analysis tests is whether or not temporal patterns in the data indicate evidence for conta-
gion, by whatever means. In truth, and especially because so many perpetrators of these acts
commit suicide, we likely may never know on a case-by-case basis who was inspired by similar
prior acts, particu larly since the ideation may have been subconscious.
It is also unclear whether or not the patterns we have observe d in our analysis are perhaps
spuriously caused by potential unaccounted-for biases in the data samples that were compiled
by private organizations. To further the understanding of the unde rlying root causes of these
events, and to confirm whether or not contagion truly plays a role, an official comprehensive
detailed, accurate, and publicly available federal database of incidents of all mass killings and
school shootings in the US is necessary. A database that includes, at a minimum, details on the
background events, mental health status and access to mental health treatment of the perpetra-
tors, exactly what kinds of weapons were used, where the perpetrators obtained their weapons,
and whether they did so legally or illegally. Several studies of firearm violence over the past
decade have pointed out the need for such a database (see, for instance, References [
46, 47]).
For the time being, while waiting for such a database to become available, studies such as this
must use what data are available, paying attention to cross-checks of the robustness of the
modeling methodology to potential biases, as we ha ve attempted to do here.
Studies into the prevention of such tragedies are also hampered by the freeze on federal
funding for research into gun violence in the United States, put in place by Congress in 1997
[
48, 49]. In January, 2013, President Obama issued a presidential memorandum directing the
Centers for Disease Control to resume studies into firearm violence. However, at the time of
this writing in September 2014, the majority of members of Congress have vowed to continue
to block allocation of federal funding to the studies. In the near term it thus appears that federal
legislation will not be put forward to address the need for the documentation and detailed
study of such events.
Supporting Information
S1 Appendix.
(PDF)
S1 Data. A compressed directory containing the data files used in this study.
(GZ)
Acknowledgments
The authors wish to thank the Brady Campaign to Prevent Gun Violence for making their data
available for this study.
Contagion in Mass Killings and School Shootings
PLOS ONE | DOI:10.1371/journal.pone.0117259 July 2, 2015 9/12
Author Contributions
Conceived and designed the experiments: ST AGL. Performed the experiments: ST AGL MK
AM. Analyzed the data: ST AGL MK AM. Contributed reagents/materials/analysis tools: ST
AGL AM CCC. Wrote the paper: ST AGL MK AM CCC. Developed concept of study: ST AGL.
Developed software: ST AGL. Conducted data collection and analysis of self-excitation model:
ST AGL MK AM. Conducted development and analysis interpretation of deterministic model:
ST AGL AM CCC.
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