A Model of Chaotic Drug Markets and Their Control

Drug markets are often described informally as being chaotic, and there is a tendency to believe that control efforts can make things worse, not better, at least in some circumstances. This paper explores the idea that such statements might be literally true in a mathematical sense by considering a discrete-time model of populations of drug users and drug sellers for which initiation into either population is a function of relative numbers of both populations. The structure of the system follows that considered in an arms control context by Behrens et al. (1997). In this context, the model suggests that depending on the market parameter values, the uncontrolled system may or may not be chaotic. Static application of either treatment or enforcement applied to a system that is not initially chaotic can make it chaotic and vice versa, but even if static control would create chaos, dynamic controls can be crafted that avoid it. Socalled OGY controls seem to work well for this example.