Modelling Gender Differences in Drug Abuse Epidemics

  • J. Mushanyu
  • F. Nyabadza
  • P. Mafuta
  • E. T. Ngarakana-Gwasira
Original Paper


Drug abuse is an issue of considerable concern due to its association with numerous public health problems. Mathematical models developed to describe the spread of drug abuse have generally assumed that the dynamics of drug use and treatment are substantially the same for women as men. However, research has revealed that the dynamics of women’s drug use and treatment are different in many ways from that of men’s. Understanding gender differences in patterns of drug use is essential to identify the influences of gender on the trends of drug abuse in order to develop appropriate and effective prevention programs. We formulate a sex structured compartmental model for the spread of drug abuse using nonlinear ordinary differential equations. The least squares curve fit routine (lsqcurvefit) in Matlab with optimization is used to estimate the parameter values. The model is fitted to data on individuals under substance abuse treatment centres of the Western Cape Province of South Africa and parameter values that give the best fit chosen. The projections carried out the long term trends of proportions for male and female rehabilitants. The results show that the proportion of male drug abusers in Cape Town is expected to continue to decrease whereas that of female drug abusers shall continue to increase but steadily. The estimated proportion of female drug abusers in specialist treatment centres of Cape Town was observed to be approximately \(34\%\) by the year 2030.


Drug abuse Gender differences Abuse reproduction number Least squares curve fitting 



J. Mushanyu, P. Mafuta and E.T Nkarakana-Gwasira 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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Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  • J. Mushanyu
    • 1
  • F. Nyabadza
    • 2
  • P. Mafuta
    • 1
  • E. T. Ngarakana-Gwasira
    • 1
  1. 1.Department of MathematicsUniversity of ZimbabweMount Pleasant, HarareZimbabwe
  2. 2.Department of Mathematical SciencesStellenbosch UniversityMatielandSouth Africa

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