Using a mathematical model and likelihood methods to assess contagion in mass killings and school shootingsSherry TowersSimon A. Levin Mathematical, Computational and Modeling Sciences CenterArizona State University

OutlineBackgroundSources of dataPoint process model of contagionLikelihood methods for optimising model to dataResults

Guns in America

Gun violence in AmericaOn an average day, 88 people are killed by a firearm in the US, 40% of which are homicides (CDC and www.pewresearch.org)Nine children shot unintentionally each day

Data sources for mass killings and school shootings

Model

Model optimisationUsing Negative Binomial likelihood to account for over-dispersion, we fit the model to the observed number of shootings per dayWe first fit the null model, with N_0(t), but no self-excitation componentWe then fit the full model with added self-excitation, with parameters Texcite and Nsecondary.The likelihood ratio test was used to determine if the self-excitation model was significantly better than the null model

Model validationIt is important to ensure that model has good predictive power for independent data sets, and that the fitting procedure yields unbiased parameter estimates!We did 100 iterations, bootstrapping 50% of the data, fitting the null and full models to the data, and testing the fitted model on the remaining dataAlso tested fitting procedure using simulated data sets that include self-excitation to ensure the procedure yielded unbiased and efficient estimates of Texcite and Nsecondary

Differing media attention may explain differences between data sourcesSchool shootings and mass killings usually receive national (or even international) media attentionIn contrast, mass shootings with low casualty counts happen so often in the US, they rarely make it past the local news

Stages of a contagious processIndividual needs to be susceptible. ”Health status” can affect susceptibilityNeeds to be exposed to another infectious individual. Interventions like quarantine or isolation can help hereEven upon exposure, interventions like treatment can reduce or prevent moving on to the infectious stage

Five stages of an active shooterFantasyMedia controlMental healthcare access PlanningPreparationGun controlApproachImplementationArmed citizens (“good guys with guns”)www.lawenforcementtoday.com/tag/five-stages-of-the-active-shooter/

Need more researchSince 1996, there has been a Congressional moratorium on federal funding for most gun violence research, under the premise that gun violence research a priori “advocates and promotes gun control”

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