Predator-Prey Model for Illicit Drug Consumption

Abstract

Mathematical modeling of illicit drug consumption is a very difficult and complex problem. To this aim predator-prey models have been used at the end of the nineties. Then, in 2013 a model called NERA has been built to describe the dynamics of the non (N), experimental (E), recreational (R) and addict (A) user categories, respectively, within a given population. However, the original NERA model didn’t involve limitation in drug consumption and was consequently unable to transcribe the periodic evolution of each category. So, we have modified this model by analogy with the classical predator-prey models and while considering non-users (N) as prey and users (E, R and A) as predator. Then, using data from the state of Colorado and Washington and a genetic algorithm, we calibrated our predator-prey NERA models by estimating their parameters sets. This allowed us to account for the periodic evolution of each category. Then, by considering that the population of Nonusers increases in proportion of the demography we highlighted chaotic regions within which the evolution of the variables becomes unpredictable. Thus, it appears that our validated NERA model can be a precious tool in forecasting of illicit drug consumption and can be of substantial interest to policy-makers in the problematic of illicit drug consumption.