IJPAM: Volume 83, No. 1 (2013)

CATCHING A GANG - A MATHEMATICAL MODEL OF
THE SPREAD OF GANGS IN A POPULATION
TREATED AS AN INFECTIOUS DISEASE

J. Sooknanan$^1$, B. Bhatt$^2$, D.M.G. Comissiong$^3$
$^{1,2,3}$Department of Mathematics and Statistics
The University of the West Indies
TRINIDAD AND TOBAGO


Abstract. In this study, criminal gang membership is treated as an infection that spreads through a community by interactions among gang members and the population. A mathematical model consisting of a system of coupled, nonlinear ordinary differential equations is used to describe this spread and to suggest control mechanisms to minimize this infection. The analysis shows the existence of three equilibrium states - two of which contain no gang members. When parameters such as recruitment, conviction and recidivism rates and longer jail sentences are varied, the greatest reduction occurs by changing the parameters in combination. A bifurcation analysis shows transcritical bifurcations and no hopf bifurcations.

Received: April 3, 2012

AMS Subject Classification: 91D10, 37M20, 34D20

Key Words and Phrases: mathematical model, infectious disease, criminal gang membership

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DOI: 10.12732/ijpam.v83i1.4 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 1