Modelling multiple relapses in drug epidemics

J. Mushanyu, F. Nyabadza, G. Muchatibaya, A. G.R. Stewart

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Drug dependence is a ‘chronic disease’ treatable through rehabilitation. Many drug addicts progress through a series of rehabilitation and relapsing episodes. In this paper, we formulate a mathematical model with n-alternate stages of rehabilitation and relapsing. The dynamics of drug abuse are treated as an infectious disease that spreads through a population. The model analysis shows that the model has two equilibria, the drug free equilibrium and the drug persistent equilibrium, that are both globally stable when the threshold R0< 1 and R0> 1 respectively. The model is fitted to data on individuals under repeated rehabilitation and parameter values that give the best fit chosen. The projections carried out the long term trends of proportions for repeated rehabilitants. The relative impact for each subgroup is determined to find out which population subgroup is responsible for a disproportionate number of initiations. The results have huge implications to designing policies aligned to rehabilitation processes.

Original languageEnglish
Pages (from-to)37-63
Number of pages27
JournalRicerche di Matematica
Issue number1
Publication statusPublished - 1 Jun 2016
Externally publishedYes


  • Drug abuse
  • Least squares curve fitting
  • Rehabilitation
  • Relapse
  • Reproduction number

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Modelling multiple relapses in drug epidemics'. Together they form a unique fingerprint.

Cite this