Modelling the Dynamics of Crystal Meth ('Tik') Abuse in the Presence of Drug-Supply Chains in South Africa

Farai Nyabadza, John B.H. Njagarah, Robert J. Smith

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)24-48
Number of pages25
JournalBulletin of Mathematical Biology
Issue number1
Publication statusPublished - Jan 2013
Externally publishedYes


  • 'Tik'
  • Crystal meth
  • Drug-supply chains
  • Latin hypercube sampling
  • Partial rank correlation coefficients
  • Reproductive number

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry,Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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