Social influences among drug users and mean field approximation of cellular automata

Street-involved youth have a propensity for illicit drug use and trade. There are approximately one million street-involved youth in the United States and about 150,000 in Canada. The need for a proper intervention and follow-up strategy seems remarkably clear. A stochastic cellular automata (CA) model of the influences among current and potential illegal drug users and traffickers is presented. Simulation and mean field analysis are used to study the model. The mean field approximation (MFA) and compartmental representation of the model are also studied. The phase plane of the mean field and possible bifurcations of the system are explored. MFA typically provides a good picture of a CA model near a bifurcation. The model allows us to compare the potential effectiveness of different types of responses to the drug epidemic. Both indirect and direct strategies are found effective on their own, but combined strategies proved to be most effective.