title: Modelling the trends of inpatient and outpatient rehabilitation for methamphetamine in the Western Cape province of South Africa.
abstract: BACKGROUND
  Dependence on methamphetamine remains one of the major health and social problem in the Western Cape province of South Africa. We consider a mathematical model that takes into account two forms of rehabilitation, namely; inpatient and outpatient. We examine the trends of these two types of rehabilitation. We also seek to investigate the global dynamics of the developed methamphetamine epidemic model.
  
  
  METHODS
  The model is designed by likening the initiation process to an infection that spreads in a community through interactions between methamphetamine users and non-users. We make use of Lyapunov functions obtained from a suitable combination of common quadratic and Volterra-type functions to establish the global stability of the methamphetamine-persistent steady state. The least squares curve fit routine (lsqcurvefit) in Matlab with optimization is used to estimate the parameter values.
  
  
  RESULTS
  The model analysis shows that the model has two equilibria, the methamphetamine free equilibrium and the methamphetamine persistent equilibrium, that are both globally stable when the threshold R(a) < 1 and R(a) > 1, respectively. Upon fitting the model to data on drug users under rehabilitation, parameter values that give the best fit were obtained. The projections carried out the long term trends of these forms of rehabilitation.
  
  
  CONCLUSIONS
  The results suggest that inpatient rehabilitation programs have an increased potential of enhancing the chances of recovery for methamphetamine addicts.
authors.affiliation: Department of Mathematics, University of Zimbabwe, Box MP 167, Mount Pleasant, Harare, Zimbabwe. mushanyuj@gmail.com.
authors.forename: J
authors.initials: J
authors.lastname: Mushanyu
authors.affiliation: Department of Mathematical Sciences, Stellenbosch University, P. Bag X1, Matieland, 7602, South Africa. nyabadzaf@sun.ac.za.
authors.forename: F
authors.initials: F
authors.lastname: Nyabadza
authors.affiliation: Department of Mathematics, University of Zimbabwe, Box MP 167, Mount Pleasant, Harare, Zimbabwe. agrstewartzw@gmail.com.
authors.forename: A G R
authors.initials: AG
authors.lastname: Stewart
mesh_terms: D019969:Amphetamine-Related Disorders / Q000534:rehabilitation*; D000697:Central Nervous System Stimulants / Q000009:adverse effects*; D007297:Inpatients / Q000706:statistics & numerical data*; D008694:Methamphetamine / Q000009:adverse effects*; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data*; D010045:Outpatients / Q000706:statistics & numerical data*; D013019:South Africa
chemical_list: D000697:Central Nervous System Stimulants; D008694:Methamphetamine