Browsing by Author "Gatyeni, Siphokazi Princess"

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    Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments
    (2015-12) Gatyeni, Siphokazi Princess; Nyabadza, Farai; Stellenbosch University. Faculty of Science. Department Mathematical Sciences (Mathematics)
    ENGLISH ABSTRACT : Substance abuse is a major problem globally with immeasurable consequences to the health of users. Rehabilitation is one of the strategies that can help to fight against substance abuse. It is divided into two forms: in-patient and out-patient rehabilitation. In this study, we consider a compartmental model of substance users in rehabilitation, where a periodic function is included to illustrate seasonal oscillations of drug users entering rehabilitation. In this thesis, we derive two basic reproduction numbers R0 and [R0], where R0 is the model with periodicity and [R0] the model without periodicity. We show that the model has a drug-free equilibrium when the basic reproduction number R0 is less than one and drug persistent equilibrium when R0 is greater than one. We fit the model to data and obtained sneak preview of the future of these forms of rehabilitation. Our results indicate that when R0 is less than one, the in- and out-patient populations decrease quickly and when R0 is greater than one drugs persists and after a long period of time, individuals in rehabilitation approaches w-periodic solution. Sensitivity analysis is performed and the results show that control measures should focus on the effective contact rate between susceptibles and drug users so as to control the epidemic. These results have significant implications on the management and planning of rehabilitation programs in South Africa.