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 \textquotedblleft tipping points\textquotedblright\ in the murder rates, gang
recruitment rates and the imprisonment and deterrence rates.

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