A Mathematical Model of Gang Membership and Control
Keywords:
Mathematical model, reproduction number, infectious disease, transmission dynamics, stability analysisAbstract
Communication In Physical Science, 2023, 9(1): 12-24
Authors: Anorue, Onyinyechi Favour* and Atuma, David Esther
Received: 23 November 2022/Accepted 18 January 2023
There is an increasing growth in gang membership worldwide and especially our nation Nigeria, this prompted the study as a means to contribute to the social stability of the country. We considered gang membership as an infectious disease that spreads through out a given population. We formulated a modified SEIR model to look into the transmission dynamics of gang by bringing into consideration, control techniques as measures to reduce the spread and activities of gang members. In analyzing the model, we proved that the disease free-equilibrium is locally and globally asymptotically stable when the reproduction number and unstable when The transmission pattern shows that investments in job provisions, technical crafts and programs geared towards recreation and other after-school activities factored into a compartment continues to be the best resource in curbing gang membership and its activities considering from rehabilitation point of view in the numerical simulation.
Downloads
References
Austin, J., Smith, E., Srinivasan, S.& Sanchez F. (2014). Socila Dynamics of Gang Involvement:A Mathematical Dynamics of Gang Involvement. 9, 3, pp. 360-369.
Avelardo, V. (2007). Mexican American Girls and Gang Violence: Beyond Risk, Palgrave Macmillion.eBook ISBN 978-0-230-60183-3.
Bewick S., Fagan W. F., Calabrese J. M. & Agusto F. (2016): Zika virus: endemic versus epidemic dynamics and implications for disease spread in the americas. BioRxiv, doi: https://doi.org/10.1101/041897.
Brauer F.,Van Den Driessche P., Wu J.& Allen L. J. S. (2008). Mathematical epidemiology in mathematical biosciences sub-series. Springer, https://doi.org/10.1007/978-3-540-78911-6.
Camacho E. T. (2013): The Development and Interaction of Terrorist and Fanatic Groups. Communication in Nonlinear Science and Numerical Simulation, 18, 11, pp. 3086-3097, https://doi.org/10.1016/j.cnsns.2013.04.006
Campbell, M. & Ormerod, P. (1997). Social interaction and the dynamics of crime. Technical report. Volterra Consulting Ltd. https://www.researchgate.net.
.Goffman W. (1966). Mathematical approach to the spread of scientific ideas-the history of mast cell research. Nature, 212, pp. 449–452.
Goffman W. & Newhill V. A. (1964): Generalization of epidemic theory: an application to the transmission of ideas. Nature, 204, pp. 225–228.
Hayward J (2005) A general model of church growth and decline. J Math Sociol , 29, 3, pp. 177–207.
Hayward J. (1999): Mathematical modeling of church growth. J Math Sociol 23, 4, pp. 255–292 53.
Hegemann, R. A., Smith, L. M., Barbaro, A. B. I., Bertozzi, A. L., Reid, S. E. & Tita, G. E. (2011). Geographical influences of an emerging network of gang rivalries. Physica Statistical Mechanics and its Applications,390, 21-22, pp. 3894-3914, https://doi.org/10.1016/j.physa.2011.05.040
Hethcote H. W. (2000). The Mathematics of Infectious Diseases. SIAM Rev., 42, 4, pp. 599–653.
Jeffs R. A., Hayward J., Roach P. A. & Wyburn, J. (2016). Activist model of political party growth. Phys A Stat MechAppl, 442, pp. 359–372.
Jin F., Dougherty E., Sara F. P. & Ramakrishnan N. (2013): Epidemiological modeling of news and rumors on twitter. In: Proceedings of the 7th workshop on social network mining and analysis, (article number 8), ACM Digital Library.
Kucharski, A. J., Funk, S., Eggo, R. M., Mallet, H., Edmunds W. J. & Nilles E. J. (2016). Transmission dynamics of Zika ivrus in island populations: a modelling analysis of the 2013–14 French Polynesia outbreak. PLoSNegl Trop Dis.
Young, L & Do. (2011). A modelling perspective of juvenile crimes. International Journal of Numerical
Analysis and Modeling, B, 2,4, pp. 369-378.
[Nishiura H., Kinoshita R., Mizumoto K., Yasuda Y. & Nah K. (2016). Transmission potential of Zika virus infection in the South Pacific. International Journal of Infectious Diseases, 45, pp. :95–97, doi: 10.1016/j.ijid.2016.02.017.
Ormerod P., Mounfield C. & Smith L. (2001). Non-linear modelling of burglary and violent crime in the UK. In: Lewis C (ed) Modelling crime and offending: recent developments in England and Wales, Research, Development and Statistics Directorate, London.
Papachristo, A. V. (2009). Murder by structure: dominance relations and social structure og gang homicide. American Journal of Sociology. 115, 1, pp. 74-128.
Radil, S., Flint, C. & Tita, G. (2010). Spatializing social networks: Using social network to investigate geographies of gang rivalry, territoriality and violence in Los Angeles. Annals of Association of Americal Geographers, . 100, 2, pp. 307-326.
Rivera-Castro, M., Padmanabhan, P., Caiseda, C., Seshaiyer, P. & Borai-Guanill, C. (2019). Mathematical modeling, analysis and simulation of the spread of gangs in interacting youth and adult populations. Letters in Biomathematics. 6, 2, https://doi.org/10.30707/LiB6.2Caiseda
Romero, D. M., Kribs, Zaleta, C. M., Mubayi, A. & Orbe, C. (2011): An epidemiological approach to the spread of political third parties. Discrete and Continuous Dynamical Systems - B, 15, 3, pp. 707-738, doi:10.3934/dcdsb.2011.15.707
Short, M. B., Mohler, G. O., Brantingham, P. J. & Tita, G. E. (2014). Gang rivalry dynamics via coupled point process networks. AIMS Journals. http:// AIM Sciences.org. 19, 5, pp 1459-1477. Doi: 10.3934/dcdsb.2014.19.1459
Sooknanan, J., Bhatt, B. & Comissiong, D. M. G. (2012). Life and death in a Gang – A Mathematical Model of Gang Membership. Journal of Mathematical Research, 4, 4, doi: 10.5539/jmr.v4n4p10
Sooknanan, J., Bhatt, B. & Comissiong, D. M. G. (2013). Catching A Gang- A mathematical model of the spread of gangs in a population, treated as an infectious Disease. International Journal of Pure and Applied Mathematics, 83, 1, pp. 25-43.
Tita, G., Ohen, J. & Engberg, J. (2005). An ecological study of the location of gang space. Socal Problem, . 52, 2, pp. 272-299.
Tita, G., Ridgeway, K. G., Grammich, C., Abraham, A. & Green wood P. (2003). Reducing gun violence: Results from an intervention in East Los Angeles, Natt. Inst. Justice, RAND.
Woo, J., Son J. & Chen, H. (2011). An SIR model for violent topic diffusion in social media. Proceedings of 2011 IEEE International Conference on Intelligence and Security Informatics
doi: 10.1109/ISI.2011.5984043
Downloads
Published
Issue
Section
License
Copyright (c) 2023 The Journal and the author
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
