Life and Death in a Gang-A Mathematical Model of Gang Membership

Abstract

There is increasing gang membership worldwide, but few mathematical models are available describing the growth of gangs in a population. A mathematical model consisting of a system of four coupled, nonlinear ordinary differential equations is used to divide a population into four groups based on gang affiliation. Demographics and vertical transmission are included in the model. One of the main findings of this research is the conditions under which the gang members become extinct. Bifurcation analyses shows the existence of "tipping points" in the murder rates, gang recruitment rates and the imprisonment and deterrence rates.

Mathematical analysis of crime dynamics in and out of prisons

“…16,17 The second rule (transition by contact) is based on the assumption that the population is homogeneously mixed and should be dealt in our model with care. While the models for organized gang crimes [13][14][15] treat the transition between gang members as contagion by frequent contact, such analogy with epidemic process may be not adequate for daily contacts occurring in a general society. Considering the nature of criminals that hide their true intention from others, we can presume that assimilation with criminals occurring by random contact is rare and negligible compared to other factors that we will consider in the following sections.…”

“…Some other models have adapted their basis from population biology, such as infectious disease models [7][8][9] and predator-prey models. [10][11][12] A similar approach was used for modeling organized crimes, [13][14][15] where gang membership is treated as an infection that multiplies through peer contagion.…”