Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Kenneth Moody - Virginia Tech
Co-Author(s): Duane Seward, Norfolk State University, Norfolk, VA
Gangs have plagued communities for decades and have stifled the youths’ ability to positively contribute to society. The presence of gangs has proven to be alluring to individuals who are impoverished and have encountered academic obstacles. With 30% to 40% of gang members being under the age of 18, it’s clear that gangs must be addressed fully in order to improve the prosperity of the youth in many communities. This research project assigned emphasis to the impact of community retention programs and gang organization on gang dynamics. It was proposed that community retention programs are a vital factor in reducing gang involvement. Compartmental modeling was selected to analyze effective strategies to combat the social endemic.
Compartmental modeling implements ODEs which are optimal due to their intrinsic utility in modeling and analyzing dynamic systems. An important concept/value in understanding many of the results is the reproductive number. It yields the average number of new gang members caused by interactions with a gang member in a completely susceptible population for the duration of gang membership. A decrease in this value typically reduces the number of ‘infected’, or, in the case of this project, gang members. Employing sensitivity analysis identified that community retention is very effective in reducing gang involvement. Results also identified that the reproductive number was directly proportional to organization and incarceration of entry level gang member, while conversely inversely proportional to incarceration of upper level gang members.
Through analyzing the prevalence of gang members under different scenarios it was concluded that prevention methods, specifically by way of community retention programs, are the most effective strategy in reducing gang activity. Through numerical analysis, instances where a gang population can still exist were found when the reproductive is less than one. These scenarios require further investigation as they reveal nuances in gang dynamics that are crucial in fully understanding gangs. Additions to this project such as, gang induced mortality rate and female gang members would be vital in weaving a more complete representation of gang dynamics. Another refinement to this project would be to further investigate bifurcation and stability of the endemic equilibrium.
Key References: Abramson, P. R., Rothschild, B. (1988). Sex, drugs and matrices: mathematical prediction of HIV infection. Journal of Sex Research, 25(1), 106-122.
Anderson, Stephen A., Ronald M. Sabatelli, and Jennifer Trachtenberg. ‘Community police and youth programs as a context for positive youth development.’ Police Quarterly 10.1 (2007): 23-40.
Austin, J., Smith, E., Srinivasan, S., and Snchez, F. (2011). Social dynamics of gang involvement: A mathematical approach. Mathematical and Theoretical Biology Institute, MTBI-08-08M.
Bullock, Karen, and Nick Tilley. ‘Understanding and tackling gang violence.’ Crime Prevention and Community Safety 10.1 (2008): 36-47.
Carlie, Michael K. Into the abyss: A personal journey into the world of street gangs. M. Carlie, 2002.
Funder Acknowledgement(s): The authors wish to thank Mathematical Association of America; NREUP Grant, School for Engineering of Matter, Transport and Energy at Arizona State University and Norfolk State University. The authors also would like to thank Dr. Terry L. Alford and Dr. Aprillya Lanz for their support and guidance.
Faculty Advisor: Aprillya Lanz,