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 <i>N</i>₀(<i>t</i>).

<p><i>N</i>_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.</p

Contagion in Mass Killings and School Shootings

<div><p>Background</p><p>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.</p><p>Methods</p><p>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 contagion 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 probability of a similar event in the immediate future, by assuming an exponential decay in contagiousness after an event.</p><p>Conclusions</p><p>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 (<i>p</i> = 0.0015). We also find significant 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 (<i>p</i> = 0.0001). All <i>p</i>-values are assessed based on a likelihood ratio test comparing the likelihood of a contagion 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 associated with the state incidence of mass killings with firearms, school shootings, and mass shootings.</p></div

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.

<p>Correlations with ∣<i>ρ</i>∣ ≥ 0.28 are significant to <i>p</i> < 0.05.</p

The percentage of the variance, <i>R</i>², of the Ebola-related Twitter and Google search samples described by the contagion model of Eq 2 or Eq 3 (as appropriate to the sample); shown are the <i>R</i>² of the model fit to the full sample, the first half of the sample (model validation training sample), and the extrapolated model prediction for the remaining half of the sample (model validation test sample).

<p>Also shown are the <i>R</i>² for the statistical model, which linearly regresses the data samples on the daily number of Ebola-related news videos.</p><p>The percentage of the variance, <i>R</i>², of the Ebola-related Twitter and Google search samples described by the contagion model of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129179#pone.0129179.e002" target="_blank">Eq 2</a> or <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129179#pone.0129179.e003" target="_blank">Eq 3</a> (as appropriate to the sample); shown are the <i>R</i>² of the model fit to the full sample, the first half of the sample (model validation training sample), and the extrapolated model prediction for the remaining half of the sample (model validation test sample).</p

Parameters of the Ebola-related news media contagion model of Eq 2 or Eq 3 (as appropriate to the sample), fit to the Ebola-related Google searches and tweets.

<p>The parameter <i>f</i> is the initial fraction of the population susceptible to news media induced Ebola interest or panic (as manifested by the particular Ebola-related Internet searches or tweets in our samples). The parameter <i>β</i> is the transmission rate, and 1/<i>γ</i> is the average time, in days between an individual viewing an Ebola-related news video, and performing an Ebola-related Google search or tweet. The average number of particular Internet searches or tweets in our samples inspired by a single news video in the initial susceptible population is <i>fβ</i>. The numbers in the square brackets represent the 95% confidence intervals.</p><p>Parameters of the Ebola-related news media contagion model of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129179#pone.0129179.e002" target="_blank">Eq 2</a> or <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129179#pone.0129179.e003" target="_blank">Eq 3</a> (as appropriate to the sample), fit to the Ebola-related Google searches and tweets.</p

Time series of Ebola-related news media, Twitter, and Google search data used in this study.

<p>The samples consist of six weeks of data ending October 31^st, 2014. The first case of Ebola confirmed in the U. S. occurred on September 29, 2014. The temporal trends in the data samples are highly inter-correlated, with a minimum of 70% correlation between samples.</p

Fits of the news media contagion model, and a simple linear regression model, to the sources of data used in this study.

<p>The fits of the linear regression model (shown in blue) tend to be generally too low in the beginning and too high at the end. In contrast, the contagion model (red line) accounts for the boredom effect, where people become more and more disinclined to perform Ebola-related searches or tweets after an extended period of exposure to Ebola-related news-coverage. Incorporation of this dynamic in the model yields significantly better fits to the data compared to the regression model.</p

The percentage of the variance, <i>R</i>², of the data samples described by the contagion model of Eq 1, assuming that the news videos, <i>V</i>, cause the patterns seen in the data (<i>V</i> → <i>I</i>).

<p>Also shown are the <i>R</i>² under the assumption that the temporal patterns in the data samples cause the temporal patterns in the news videos (<i>I</i> → <i>V</i>). The p-values testing for Granger causality between the various time series are also shown.</p><p>The percentage of the variance, <i>R</i>², of the data samples described by the contagion model of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0129179#pone.0129179.e001" target="_blank">Eq 1</a>, assuming that the news videos, <i>V</i>, cause the patterns seen in the data (<i>V</i> → <i>I</i>).</p

Comparison of the 2014 Ebola-related Google search trends to influenza-related search trends during the 2009 A/H1N1 pandemic.

<p>The relative interest in Ebola-related searches during the month of October 2014 rivaled the flu-related searches at the beginning of the A/H1N1 pandemic.</p