An age structured model for substance abuse dynamics in the Western Cape Province of South Africa.

Chinake, Filister (2017-03)

Thesis (MSc)--Stellenbosch University, 2017.

Thesis

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.

AFRIKAANSE OPSOMMING: In die Wes-Kaapse Provinsie van Suid-Afrika het die misbruik van dwelms vererger. Dit het groot skaalse probleme en rampokkery wat geassosieer word met dwelms veroorsaak. Die probleem het gergroei toe rampokkers met ag- gressie hul turf vergroot het deur skoolkinders te rekruut om dwelms op die skoolgrand te verkoop. Die e ek is dat meer ouderdomsgroepe epgelei word om dwelms te misbruik. Om die huidige koers van dwelm misbruik om te keer, is dit noodsaaklik om die dinamika van die probleem volledig te verstaan. Meer insig kan herwin word as 'n ouderdomsstruktuur opgerig word in dwelm misbruik-modelle sodat die prosesse soos inisiasies,die escaleer in problematiese dwelmmisbruik en opgee gein vloed word deur ouderdom. Dus stel ons voor in ouderdomstruktuur model van dwelmimisbruik vorm van die reproduksie nommer R0 is bereken en die model is goed gestel. 'n verkose niet verskil skema is bespreek vir die numerieke oplossing van ons partydige di erensiale gelyke. Sensitiewe analise is onderneem deur die Latin Hypercube Sampling en Partial Rank Correlation Coe cient te gebruik. Die paramaters vir die model is verwerf deur pas die model by ouderdomstruktuur data vir individuele in die rehabilitasie sentrums aan te pas. Die dinamika vir die kompartemente van die model is beskryf deur die resultate van die numerieke simulasies. Die model word gebruik om die dinamika van dwelmmisbruik tot in die jaar 2020 te voorspel. Dit word voorspel dat dwelmmisbruik met tyd gaan verhoog en hoer insidente van dwelmmisbruik verwag word in ouer ouderdomsgroepe.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/101422
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