The Social Dynamics of Gang Involvement: A Mathematical Approach

Gangs have played a significant role in Chicago's social and political history, and continue to impact the city today, as gang violence rates continue to grow despite drops in overall crime. In this paper, we model the dynamics between at-risk members, gang members, and temporarily removed (reformed) gang members using an epidemiological approach. A system of nonlinear differential equations is used to model the interaction between the at-risk population and the gang population. Particularly, we focus on the effect that former gang members have on the rate at which the at-risk population enters gangs. Our model exhibits a bifurcation with forward and backward behavior. From this we deduce that keeping recidivism rates low is crucial to controlling gang population. Furthermore, we find that the temporarily removed population has some impact on gang population size, though other factors such as cost and recidivism rates seem to play a more substantial role in gang population dynamics.