Role of imitation and limited rehabilitation capacity on the spread of drug abuse

Abstract

Objectives: We formulate a mathematical model for the spread of drug abuse using non linear ordinary differential equations. The model seeks to investigate both peer influence and limited rehabilitation effects on the dynamics of drug abuse. Peer-influence is modelled through the mechanism of imitation and limited rehabilitation is described using a special treatment function. Center manifold theory is used to show that the model exhibits the phenomenon of backward bifurcation. Matlab has been used to carry out numerical simulations to support theoretical findings. Results: The model analysis shows that the model has multiple equilibria. It has been shown that the classical R a - threshold is not the key to control drug abuse within a population. In fact drug abuse problems may persist in the population even with subthreshold values of R a. This was shown to result, in particular when ω, η 1 and η 2 are high enough such that ω > ω ∗, η 1 > η 1 ∗and η 2 > η 2 ∗. The results suggest the need for comprehensive and accessible substance abuse treatment services to curtail drug abuse.