Dynamics of drug trafficking: Results from a simple compartmental model

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 newtork, 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 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.