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NIMBioS/DySoC Investigative Workshop

Mathematics of Gun Violence

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Topic: Mathematics of Gun Violence

Meeting dates: May 1-3, 2019

Location: NIMBioS at the University of Tennessee, Knoxville

Andrea L. Bertozzi, Mathematics and Mechanical and Aerospace Engineering, UCLA
Louis J. Gross, Mathematics and Ecology & Evolutionary Biology, NIMBioS, Univ. of Tennessee, Knoxville
Andrew V. Papachristos, Sociology, Institute for Policy Research, Northwestern Univ.
Shelby M. Scott, Ecology & Evolutionary Biology, Univ. of Tennessee, Knoxville
Martin B. Short, Mathematics, Georgia Tech


Gun violence is a central public concern in the United States, annually leading to the deaths of 31,000 individuals and the non-fatal injuries of 78,000 others. It has been called an epidemic and a public health crisis. For infectious disease epidemics and associated public health planning (including recent Zika and Ebola outbreaks), officials relied on mathematical models to evaluate immediate responses and develop preventative policies. The construction of policies to curb the spread of gun violence could benefit from the development of mathematical models linked with available data. This workshop brought together researchers from diverse disciplinary backgrounds to (i) review the existing approaches on the mathematics and modeling of gun violence, (ii) identify and prioritize areas in the field that require further research, (iii) develop cross-disciplinary collaborations to gain new perspectives, and (iv) suggest research and data-collection that could assist evidence-based policy recommendations. A direct outcome from this workshop: a comprehensive review of existing models on this topic with suggestions for further effort. It is expected that collaborations arising from the workshop will result in novel efforts to enhance the quantitative underpinnings of the science of gun violence.

The workshop incorporated discussions and critiques of the existing approaches to gun violence modeling and how these relate to the objectives for which models could be developed. Comparisons of various modeling approaches (including dynamical systems, agent-based, spatial, and statistical) and the parameterization of these models were considered. Through discussions of existing and future models, we also assessed the available data and suggested new data collection. The workshop considered the variety of scales at which models of this system can be developed and the associated implications at these different scales. Relationships to models for human behavior, including those from social psychology and game theory, were evaluated.

Effective approaches to building a theory of gun violence, which will then inform a science of gun violence, will require perspectives from multiple disciplines. The workshop considered a systems approach that brought together interacting factors and components operating on multiple scales of time and space. Attendees incorporated ideas from various quantitative fields (including mathematics, computer science, statistics, and informatics), social science areas (including geography, psychology, and criminology), and biological disciplines (including behavior, medicine, and ecology). The necessary research will be informed by practitioners involved in policy and law enforcement and will account for ethical issues of social justice and privacy. An objective was to consider how models might inform potential interventions, communication formats, educational initiatives, and control methods.

The workshop included presentations from participants, a poster session to indicate the diversity of methods currently being used in the field, and breakout groups on topics chosen with input from participants. Participants will contribute to a review outlining the current approaches identifying gaps in the literature, and presenting potential future directions.

Descriptive flyer

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Mathematics of Gun Violence WordPress site

Pre-workshop Webinar

A pre-workshop webinar was held from 2-3 p.m. EDT on Wednesday, April 17. The objective of the webinar was to foster a common vocabulary for all those interested in this research topic, to review the existing literature on mathematical approaches to gun violence, and respond to posted questions.

Online video of WebinarVideo icon.
  Webinar slides (pdf)
  Webinar chat (txt)

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Workshop Results

Summary Report (PDF)
Full Report (PDF)

Playlist of online Workshop videos Video icon.

NIMBioS Investigative Workshops focus on broad topics or a set of related topics, summarizing/synthesizing the state of the art and identifying future directions. Workshops have up to 35 participants. Organizers and key invited researchers make up half the participants; the remaining participants are filled through open application from the scientific community. Open applicants selected to attend are notified by NIMBioS within two weeks of the application deadline. Investigative Workshops have the potential for leading to one or more future Working Groups. Individuals with a strong interest in the topic, including post-docs and graduate students, are encouraged to apply. If needed, NIMBioS can provide support (travel, meals, lodging) for Workshop attendees, whether from a non-profit or for-profit organization.

A goal of NIMBioS is to enhance the cadre of researchers capable of interdisciplinary efforts across mathematics and biology. As part of this goal, NIMBioS is committed to promoting diversity in all its activities. Diversity is considered in all its aspects, social and scientific, including gender, ethnicity, scientific field, career stage, geography and type of home institution. Questions regarding diversity issues should be directed to You can read more about our Diversity Plan on our NIMBioS Policies web page. The NIMBioS building is fully handicapped accessible.

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From 2008 until early 2021, NIMBioS was supported by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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