An analysis of the dynamical evolution of experimental, recreative and abusive marijuana consumption in the states of Colorado and Washington beyond the implementation of I-502 (2015)

We analyze the NERA model (N: Nonuser, E: Experimental Users, R: Recreational Users, A: Addicts), which describes the illicit drug usage dynamics in a population consisting of both drug users and nonusers. The model considers three categories of drug users: the experimental (E) category, the recreational (R) category and the addict(A) category. We prove the uniqueness and positivity of the solution to the model in time.We extend the model by taking into account the unpredictability of person-to-person contacts and consider individuals susceptible to experience an illicit drug being subjected to a continuous spectrum of random factors. Based on the existence of such a randomness in the movement from nonuser to experimental users, we modify the model to set up a stochastic one. The latter model is also analyzed in the current work. We verify and validate our results by using the data available in Hanley (2013), on the prevalence of marijuana in the population of 21+ in the states of Colorado and Washington. We simulate the evolution of the above mentioned categories of drug users within those two states from 2002, beyond the implementation of I-502 and until 2040. Our results show that the model can used as a policy decision mechanism in the problematic of illicit drug consumption by monitoring the respond of the different categories of drug users when subject to drug control interventions.