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.
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Acknowledgements
F. Nyabadza and J.B.H. Njagarah acknowledge, with thanks, the support of the University of Stellenbosch. J.B.H. Njagarah appreciates with gratitude the support from the African Institute for Mathematical Sciences (AIMS) South Africa. R.J. Smith? is supported by an NSERC Discovery Grant, an Early Researcher Award and funding from MITACS. For citation purposes, please note that the question mark in “Smith?” is part of his name.
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Nyabadza, F., Njagarah, J.B.H. & Smith, R.J. Modelling the Dynamics of Crystal Meth (‘Tik’) Abuse in the Presence of Drug-Supply Chains in South Africa. Bull Math Biol 75, 24–48 (2013). https://doi.org/10.1007/s11538-012-9790-5
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DOI: https://doi.org/10.1007/s11538-012-9790-5