Mathematical Modeling and Analysis of Cannabis Epidemic in a South Africa Province


  • Lezanie Coetze University of Stellenbosch
  • Siphokazi Gatyeni
  • Heike Lutermann University of Pretoria
  • Americo Matusse* University of Pretoria
  • Farai Nyabadza University of Stellenbosch
  • Yibeltal Adane Terefe (Late Submission) PhD student, University of Pretoria, Department of Mathematics and Applied Mathematics.



The use of illegal drugs is associated with considerable morbidity and mortality but also costs to a society linked to health care and drug-related crimes. Cannabis is frequently considered a `soft` drug for first-time illegal drug users that is considered a gateway to so-called `harder` drugs. Hence, understanding the initiation of cannabis use and addiction may provide insights that can inform policies aiming to reduce the consumption of cannabis. We develop a mathematical model to analysis the dynamics of cannabis use in a South Africa metropolis (i.e. Durban) for which empirical data of cannabis use has been collected since 1996. The threshold parameter $\mathcal{R}_0$, the basic reproduction number, is determined andВ  used in the analysis of the model. It is shown that the model has multiple cannabis persistent equilibria. For a certain range of $\mathcal{R}_0$, the locally asymptotically stable cannabis-free equilibrium co-exists with the locally asymptotically stable cannabis persistent equilibrium which indicates the model may exhibit backward bifurcation phenomenon. In this case, the cannabis consumptionВ  will remain endemic in the population even though the basic reproduction number is less than unity. Numerical experiments are given to support the theoretical analysis of the model.

Author Biography

Yibeltal Adane Terefe (Late Submission), PhD student, University of Pretoria, Department of Mathematics and Applied Mathematics.

PhD student at department of Mathematics and Applied mathematics, UP, South Africa.






Conference Contributions (Pretoria)