Dynamics of drug trafficking: Results from a simple compartmental model

Abstract

In this work we propose a simple model for the emergence of drug dealers. For this purpose, we built a compartmental model considering four subpopulations, namely susceptibles, passive supporters, drug dealers and arrested drug dealers. The target is to study the influence of the passive supporters on the long-time prevalence of drug dealers. Passive supporters are people who are passively consenting to the drug trafficking cause. First we consider the model on a fully connected network, in such a way that we can write a rate equation for each subpopulation. Our analytical and numerical results show that the emergence of drug dealers is a consequence of the rapid increase in the number of passive supporters. Such increase is associated with a nonequilibrium active-absorbing phase transition. After that, we consider the model on a two-dimensional square lattice, in order to compare the results in the presence of a simple social network with the previous results. The Monte Carlo simulation results suggest a similar behavior in comparison with the fully connected network case, but the location of the critical point of the transition is distinct, due to the neighbors’ correlations introduced by the presence of the lattice.