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

[摘要] ENGLISH SUMMARY: The substance abuse problem has escalated in the Western Cape province ofSouth Africa. This has resulted in high rates of gangsterism and other prob-lems associated with substance abuse. The problem has evolved as gangstershave aggressively extended their turf by recruiting school learners to sell drugswithin school premises. The e ect is that more age groups are being recruitedinto abusing substance. In order to reverse the current trends of substanceabuse it is imperative that the dynamics of the problem are fully understood.More insight can be gained if age structure was incorporated into the substanceabuse models as the processes like initiation, escalation into problematic sub-stance abuse and quitting are in uenced by age. Thus we propose an agestructured model of substance abuse. A form of the reproduction number R0is calculated and the model is shown to be well posed. A suitablenite di er-ence scheme is discussed for the numerical solution of our partial di erentialequations. Sensitivity analysis is undertaken using the Latin Hypercube Sam-pling and Partial Rank Correlation Coe cient. Parameters for the model areobtained bytting the model to the age structured data for individuals in therehabilitation centres. The dynamics of the model are described by the resultsfrom the numerical simulations. The model is used to predict the dynamics ofsubstance abuse until the year 2020. Substance abuse is predicted to increasewith time and higher incidence of substance abuse expected for the older agegroups.

[发布机构] Stellenbosch University