On the dynamics of illicit drug consumption in a given population

We present and analyse a model that describes the illicit drug usage dynamics in a population consisting of both drug users and non-users. Three categories of drug users are considered, namely, the experimental category, the recreational category and the addict category. In this model, consumption of drugs such as Cannabis is considered and the model describes the dynamics of the non (N), experimental (E), recreational (R) and addict (A) user categories, respectively, within a given population. We term it as the NERA model (N: non-users, E: experimental, R: recreational users, A: addicts). We calibrated our model using the data from Korf (2001). That is, we classified the cannabis consumers from the population of 12+ in Amsterdam, for the period 1987–1997, into the non-user, experimental, recreational and addict category, respectively, for the verification and validation of our dynamical system. We then discuss and analyse the stability of the critical points when drug consumption is (i) legal and (ii) illegal in the society. The results of our numerical experiments indicate that the solution of our model agrees quite accurately with the existing data. Our analysis also reveals the existence of a drug-free equilibrium under certain conditions. The model can eventually be used as a policy control mechanism in tackling the consumption of illicit drugs in a given society.