From heroin epidemics to methamphetamine epidemics: Modelling substance abuse in a South African province

Farai Nyabadza, Senelani D. Hove-Musekwa

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


The global rise in the use of methamphetamine has been documented to have reached epidemic proportions. Researchers have focussed on the social implications of the epidemic. A typical drug use cycle consists of concealed drugs use after initiation, addiction, treatment-recovery-relapse cycle, whose dynamics are not well understood. The model by White and Comiskey [41], on heroin epidemics, treatment and ODE modelling, is modified to model the dynamics of methamphetamine use in a South African province. The analysis of the model is presented in terms of the methamphetamine epidemic threshold R0. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable drug free equilibrium co-exists with a stable drug persistent equilibrium for a certain defined range of R0. The stabilities of the model equilibria are ascertained and persistence conditions established. Furthermore, numerical simulations are performed; these include fitting the model to the available data on the number of patients with methamphetamine problems. The implications of the results to drug policy, treatment and prevention are discussed.

Original languageEnglish
Pages (from-to)132-140
Number of pages9
JournalMathematical Biosciences
Issue number2
Publication statusPublished - Jun 2010
Externally publishedYes


  • Epidemics
  • Methamphetamine
  • Projections
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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