Browsing by Author "Mushanyu, J."
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- ItemModelling the role of correctional services on gangs : insights through a mathematical model(Royal Society, 2017) Nyabadza, F.; Ogbogbo, C. P.; Mushanyu, J.Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ordinary differential equations to investigate the role of correctional services on the dynamics of gangs. The recruitment into gang membership is assumed to happen through an imitation process. An epidemic threshold value, Rg, termed the gang reproduction number, is proposed and defined herein in the gangs’ context. The model is shown to exhibit the phenomenon of backward bifurcation. This means that gangs may persist in the population even if Rg is less than one. Sensitivity analysis of Rg was performed to determine the relative importance of different parameters in gang initiation. The critical efficacy ε* is evaluated and the implications of having functional correctional services are discussed.
- ItemModelling the trends of inpatient and outpatient rehabilitation for methamphetamine in the Western Cape province of South Africa(BioMed Central, 2015-12-18) Mushanyu, J.; Nyabadza, F.; Stewart, A. G. R.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 Ra < 1 and Ra > 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. Conclusion: The results suggest that inpatient rehabilitation programs have an increased potential of enhancing the chances of recovery for methamphetamine addicts.