Affiliation Arizona Point out University, Tempe, AZ, UNITED STATES

Affiliation Arizona ( az ) State College or university, Tempe, AZ, USA

Holding Northeastern The state of illinois University, Chi town, IL, USA

Affiliations Az State University or college, Tempe, AZ, USA, Northeastern Illinois School, Chicago, ARIANNE, USA

Holding Arizona State University, Tempe, AZ, USA

Contagion in Mass Killings and Institution Shootings

  • Sherry Towers
  • Andres Gomez-Lievano
  • Maryam Khan
  • Anuj Mubayi
  • Carlos Castillo-Chavez
  • Published: July 2, 2015




Several past studies have found that media information of suicides and exécution appear to subsequently increase the occurrence of similar events in the community, apparently as a result of coverage planting the seed of ideation in at-risk individuals to make similar works.


In this article we check out whether or not contagion is evident in more high-profile incidents, such as school shootings and mass killings (incidents with four or more persons killed). We fit a contagion version to new data models related to this sort of incidents in the usa, with terms that take into account the fact that a school shooting or mass murder may well temporarily boost the probability of any similar event in the quick future, by simply assuming a great exponential rot in contagiousness after a meeting.


We discover significant ev >

Citation:Towers S i9000, Gomez-Lievano A, Khan Meters, Mubayi A, Castillo-Chavez C (2015) Contamination in Mass Killings and School Shootings. PLoS ONE 10(7): e0117259.

Academic Manager:Joshua Yukich, Tulane University Institution of Public Health and Exotic Medicine, UNITED STATES OF AMERICA

Received:May 16, 2014;Approved:12 , 19, 2014;Posted:September 2, 2015

Copyright laws:© 2015 Towers et approach. This is a access article distributed beneath the terms of the Innovative Commons Remise License, which permits unrestricted use, syndication, and processing in any medium, provided the initial author and source will be credited

Data Availableness:The united states Today mass killings data are widely available by masskillings. usatoday. com. The Brady Marketing campaign data on school shootings and mass shootings happen to be freely on request from that organization, that can be contacted at (202) 370-8101. Data have also been as part of the paper and its particular Supporting Data files.

Funding:The experts have no support or financing to survey.

Competing interests:The authors have reported that simply no competing hobbies exist.


In recent years, tragedies involving mass killings in the usa, such as the Amanecer, CO movie theatre shooting in July 2012, and the Newtown, CT university shooting in December 2012, have become more intense societal concentrate on trying to understand the dynamics and contributing factors that underlie such situations, particularly since the per capita incidence of such situations and other gun related mortality is significantly higher in america than in any other industrialized region [1※4].

Statistics are not readily available within the incidence of mass killings and school shootings consist of industrialized countries, however studies have shown that the firearm murder and committing suicide rates in the usa are several occasions higher than that of any other developing country [4], plus the patterns appear to be due to bigger rates of firearm title in the US compared to other developing countries [5]. Overall, the pediatric firearm fatality rate is usually five times bigger in the United States in contrast to any other industrialized country [3], and 87% of all children age 0 to 14 around the world killed simply by firearms happen to be children residing in the US [4], even though less than five per cent of the planet’s children reside in the US [6]. In September, 2014, the Federal Bureau of Investigation (FBI) unveiled a report «A Study of Active Present shooter Incidents in the usa Between 2k and 2013» [7]. In their survey, they be aware that the incidence of mass shooting incidents has been growing over the past 14 years.

Ready entry to weaponry continues to be implicated during these trends. For instance, it has been discovered that 2/3 of school photographers obtained their very own firearms off their own home, or the home of a relative [8], and youths will be significantly more very likely to die by simply firearm murder or committing suicide in says where firearm ownership is more prevalent. Additionally , household gun ownership has been shown to significantly raise the risk for homicide in the home [9], and murder rates generally [10]. Studies have also shown the more access people have to firearms, the reduced the levels of social trust, and the higher the levels of homicide [11, 12]. A strong connection has also been located between general state suicide rates and firearm control rates [13, 14]

Access to mental healthcare has also been considered as a factor in at least some types of incidents. For example , it is often shown that access to medical and the state rates of federal help for mental health solutions are strongly associated with reduced state suicide rates [15].

Over and above the exongenous factors just like mental health issues and ease of access to weaponry that may be causing the frequency of situations, there is also the chance that the pressured individuals may have, knowingly or sub-consciously, been motivated to act in previously under control urges simply by exposure to information on similar situations. Such contagious ideation is definitely not implausible; for example , vulnerable youth have been found to be susceptible to committing suicide ideation caused by influence of reports and portrayal of suicide in mass media [16※18], and media information on suicides and exécution have been identified to apparently subsequently increase the incidence of similar occurrences in the community [19, 20]. In addtion, in a larger public health framework, the eventual and geospatial clustering of numerous types of violence and crime have been shown to be similar to the patterns observed in the pass on of infectious disease [21].

To study this issue, we all 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 that involved firearms), data about school shootings from 1998 to 2013 inclusive through the Brady Advertising campaign to Prevent Gun Violence (Dsama dengan 188), and data upon mass shootings (at least three persons shot, not really killed) coming from February june 2006 to January 2013, as well from the Brady Campaign (Nsama dengan 477).

We fit a mathematical prophylaxie model to the data sets, with style terms that take into account provisional, provisory trends because of possible exogenous non-contagion elements, and a contagion term that takes into account the fact that a school taking pictures or mass murder may briefly increase the likelihood of a similar event inside the immediate foreseeable future. We version the contamination process assuming an exponential decay in contagiousness following an event. Contagion models have been applied to monetary markets [22], propagate of YouTube videos in social networks [23], theft [24※27], civilian fatalities in Iraq [28], and terrorist attacks [29, 30], but this is actually the first illustration in which these types of models had been applied in the context of mass murders and university shootings.

Mainly because contagion is merely one potential aspect leading to these occasions, we as well examine the partnership between the incidence of these tragedies, and express prevalence of mental health issues and gun ownership, and the rankings in the strength of state gun legislation.

In the following sections we describe the options for data utilized in this evaluation, and the modeling and record data analysis methods applied. We after that present benefits, with debate and brief summary.


Here we describe the mass killing and school firing sources of info used in this analysis, and also a description from the data resources use to analyze the relationship of such occasions to state prevalence of mental illness and firearm possession, and quotes of the strength of state gun laws. There are at the moment no extensive federal repositories of data in mass killings and school shootings in america, thus for anyone studies all of us relied in data published by private agencies. Data are available at

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,, 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, apparently largely due to mistakes in transcription. For more details about the USA Today data set, see (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 transcribed incorrectly by one day. The dates were corrected for this analysis. The data are shown in Fig 1.

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.

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 inc >

This is in contrast to the 56 events involving mass killings without firearms, where only 8% of such killers committed suic >

Brady Campaign Institution Shooting Info.

Data upon school shootings in the US had been obtained from the Brady Marketing campaign to Prevent Firearm Violence, who also examined mass media reports to compile a directory of 220 college shootings in the usa between 1997 to 2013, inclusive. We all excluded out of this data set foiled plots where individuals were captured actively arranging a shooting, nevertheless had not yet carried out their particular plan, incidents that would not actually happen on a institution campus or perhaps school coach, or incidents that occurred outside of institution hours or outside the framework of school-related events (such as sports games), leaving 188 events. Of these one-hundred and eighty-eight events, after review of the media information the experts found several incidents for which the time was apparently mis-transcribed by one day, and the dates were corrected just for this analysis. The college shootings led to an average of one individual being killed per event; only half a dozen of the institution shootings hence overlap while using USA Today mass eradicating data established, and the two data sets are nearly independent. Your data are demonstrated in Fig 1 .

The incidents were significantly more very likely to occur between September to April compared with May to August (g(1)

The result is between 0 and 1, with results close to 0 (1) indicating that a certain state has rate of such incidents significantly decrease (higher) than the national typical.

Modeling and Statistical Strategies

Self-Excitation Contamination Model.

Within a self-excitation prophylaxie model, new prior events increase the possibility of another event occurring in the near future. In this analysis, we all employ an exponential possibility distribution to simulate this method. Under the hypothesis that previous events stimulate future occasions, the improved probability of the event developing during the a day of timebig tjdue to prior event that occurred about daytiis usually thus (2) whereTmotivateis a average life long the contamination process (in this research, measured in days). This kind of yields (3)

We think about a self-excitation contagion model with an additional primary (i. e.; non-contagion related) average volume of events each day ofN0(big t). Taking into account all prior events in some stochastic data realization, the total number of expected situationsNexperience, on day timecapital tinfor that recognition is hence (4) the place that the summation is finished all previous events. The parameters with this contagion version are the common number of second events encouraged by the prophylaxie of a solitary eventNsupplementary, the duration of the contagion procedureBig texcite, and whatsoever parameters are needed to explain the temporary evolution from the baseline range of eventsN0(big t). For instance, one can assumeNzero(big t) is a continuous, or a direct line which has a slope. You can also use a non-parametric procedure whereNzero(t) is worked out using a weighted running imply of the info itself (in S1 Appendix we provide reveal description of the weighted operating mean ansatz).

The functional form ofN0(to) can incorporate additional weights if required in order to consider day-of-week or seasonal results, and indeed, we all incorporate this kind of weights in the next evident that there is significant proof of dependence on time or day-of-week in a particular data arranged.

In S1 Appendix, we describe the methods used to fit the guidelines of the type of Eq 5 to data, and the strategies we used to simulate info with a self-excitation contagion style. We also describe the methods used to confirm the modeling and installing methods, plus the methods utilized to cross-check the analysis.


Based on the USA Today test, mass killings involving guns with several or more persons killed occur on average every single 12. a few days in america. Based on the Brady Advertising campaign data, university shootings take place on average every single 31. 6 days.

The results in the fits from the parameters in the self-excitation contagion model of Frequency 4 for the various data samples happen to be shown in Fig one particular, and are tabulated in Table 1 . Proof of significant contagion is found for all those samples however the Brady Plan mass firing sample with at most 3 people killed.

Nsecondaryis the normal number of fresh incidents. The p-value is usually obtained from the chance ratio test out comparing the likelihood of the full contagion model to the likelihood of the null hypothesis model of not any contagion examples of mixtures. The numbers inside the square mounting brackets indicate the 95% self-confidence interval within the parameter.

Latitude and long, data were obtained to get the location of each incident in the data pieces used in this kind of analysis. For a lot of samples, the time between occurrences was not considerably correlated to the distance together, indicating insufficient evidence of temporal/geospatial clustering (as would happen, for instance, if an event incited the same incident within a nearby locale). Additionally , the Mantel check for temporal/geo-spatial clustering inside the samples did not return significantg-values (p>zero. 05 for all samples) [35]. This lack of temporal/geo-spatial correlation is definitely consistent with what would be expected if the contamination process is definitely potentially because of, for instance, to widespread media attention given to mass killings and school shootings.

The correlation in the state incidence of our info samples to firearm control prevalence, prevalence of mental illness, and ranking of strength of state gun legislation are summarized in Fig 2 .

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