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Modelling multiple relapses in drug epidemics

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Abstract

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 \({\mathcal {R}}_{0}<1\) and \({\mathcal {R}}_{0}>1\) 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.

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Acknowledgments

Two of the authors acknowledge, with thanks, the support of the Department of Mathematics, University of Zimbabwe. F. Nyabadza acknowledges with gratitude the support from National Research Foundation and Stellenbosch University for the production of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Zimbabwe, Mount Pleasant, Box MP 167, Harare, Zimbabwe

    J. Mushanyu, G. Muchatibaya & A. G. R. Stewart

  2. Department of Mathematical Sciences, Stellenbosch University, P. Bag X1, Matieland, 7602, South Africa

    F. Nyabadza

Authors
  1. J. Mushanyu
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  2. F. Nyabadza
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  3. G. Muchatibaya
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  4. A. G. R. Stewart
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Corresponding author

Correspondence to F. Nyabadza.

Additional information

Communicated by Salvatore Rionero.

This work was supported by the National Research Foundation (NRF).

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Mushanyu, J., Nyabadza, F., Muchatibaya, G. et al. Modelling multiple relapses in drug epidemics. Ricerche mat. 65, 37–63 (2016). https://doi.org/10.1007/s11587-015-0241-0

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  • DOI: https://doi.org/10.1007/s11587-015-0241-0

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