An SIR-type compartment model is used to explain the spread of substance abuse among individuals within a community with respect to the prevalence of drug Barons. The five part model given by Njagarah & Nyabadza (2013) has been extensively analysed and briefly extended to a six part model. We are able to determine the basic reproduction number (R0 ) through the use of the Next Generation Method. We show that when R0 ≤ 1 there is a drug free equilibrium (DFE) and show that there is a drug persistent equilibrium when R0 > 1. The parameters that influence the value of R0 are then determined by applying sensitivity analysis. Latin Hypercube sampling, Partial Ranking Correlation Coefficients and Monte Carlos simulations are all methods used to achieve accurate sensitivity analysis on the model. The long-term behaviour of the model is then plotted and evaluated with different parameters to find an optimal solution and significantly reduce drug use.
Keywords: Susceptibles, drugs, drug users, drug barons, rehabilitation, law enforcement, the next generation method, Latin Hypercube sampling, partial ranking correlation coefficients.