Browsing by Author "Chinake, Filister"

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    An age structured model for substance abuse dynamics in the Western Cape Province of South Africa
    (Stellenbosch : Stellenbosch University, 2017-03) Chinake, Filister; Nyabadza, Farai; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH SUMMARY: The substance abuse problem has escalated in the Western Cape province of South Africa. This has resulted in high rates of gangsterism and other prob- lems associated with substance abuse. The problem has evolved as gangsters have aggressively extended their turf by recruiting school learners to sell drugs within school premises. The e ect is that more age groups are being recruited into abusing substance. In order to reverse the current trends of substance abuse it is imperative that the dynamics of the problem are fully understood. More insight can be gained if age structure was incorporated into the substance abuse models as the processes like initiation, escalation into problematic sub- stance abuse and quitting are in uenced by age. Thus we propose an age structured model of substance abuse. A form of the reproduction number R0 is calculated and the model is shown to be well posed. A suitable nite di er- ence scheme is discussed for the numerical solution of our partial di erential equations. Sensitivity analysis is undertaken using the Latin Hypercube Sam- pling and Partial Rank Correlation Coe cient. Parameters for the model are obtained by tting the model to the age structured data for individuals in the rehabilitation centres. The dynamics of the model are described by the results from the numerical simulations. The model is used to predict the dynamics of substance abuse until the year 2020. Substance abuse is predicted to increase with time and higher incidence of substance abuse expected for the older age groups.