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Bull Math Biol. 2013 Jan;75(1):24-48. doi: 10.1007/s11538-012-9790-5. Epub 2012 Nov 29.

Modelling the dynamics of crystal meth ('tik') abuse in the presence of drug-supply chains in South Africa.

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Department of Mathematics, University of Stellenbosch, Matieland, South Africa.


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.

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