title: Modelling the dynamics of crystal meth ('tik') abuse in the presence of drug-supply chains in South Africa.
abstract: Substance abuse remains a global problem, with immense health and social consequences. Crystal meth, known as 'tik' in South Africa, is a growing problem, and its supply chains have equally grown due to increased numbers of 'tik' users, especially in the Western Cape province of South Africa. We consider a model for 'tik' use that tracks drug-supply chains, and accounts for rehabilitation and amelioration for the addicted. We analyse the model and show that it has a unique drug-free equilibrium. We prove that the drug-free equilibrium is globally stable when the reproduction number is less than one. We also consider both slow and fast dynamics, and show that there is a unique drug-persistent equilibrium when the reproduction number exceeds one. The model is fitted to data on 'tik' users in rehabilitation in the Western Cape province. A sensitivity analysis reveals that the parameters with the most control over the epidemic are the quitting rate of light-drug users and the person-to-person contact rate between susceptible individuals and 'tik' users. This suggests that programs aimed at light-drug users that encourage them to quit will be significantly more effective than targeting hard-drug users, either in quitting or in rehabilitation. Similarly, the person-to-person contact rate may be reduced by social programs that raise awareness of the dangers of 'tik' use and discourage light users from recruiting others.
authors.affiliation: Department of Mathematics, University of Stellenbosch, Matieland, South Africa. nyabadzaf@sun.ac.za
authors.forename: Farai
authors.initials: F
authors.lastname: Nyabadza
authors.forename: John B H
authors.initials: JB
authors.lastname: Njagarah
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Smith
mesh_terms: D019969:Amphetamine-Related Disorders / Q000453:epidemiology; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000517:prevention & control*; D055030:Drug Users; D006801:Humans; D008694:Methamphetamine / Q000008:administration & dosage*; D008962:Models, Theoretical; D013019:South Africa / Q000453:epidemiology; D015819:Substance Abuse, Intravenous / Q000453:epidemiology*
chemical_list: D008694:Methamphetamine