Modelling methamphetamine abuse: Application of a simple modelwith self initiation, behaviourchange and rehabilitation

The abuse of methamphetamine remains a major problem in the South Africa, particularlyin the Western Cape province. In this study the model by Nyabadza andMusekwa [14], is modified to include a core and non-core group, fast and slow progressionto addiction and self initiation (innovators). The analysis of the model is presentedin terms of the methamphetamine abuse epidemic threshold R0. Furthermore,numerical simulations are performed, which include the fitting of the model to data onthe number of patients who enter into treatment centers for rehabilitation. The resultsuggests that the substance abuse epidemic, can be reduced by having, interventionprograms at the light drug use stage and increasing the uptake rate into treatment. Thecontribution of re-initiation is also explored. It is shown that re-initiation increases theprevalence of drug abuse. Projections are made to determine the possible long termtrends of the prevalence of methamphetamine abuse in theWestern Cape.