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Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments
Thesis (MSc)--Stellenbosch University, 2015
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| Format: | Thesis |
| Language: | en_ZA |
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2015
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| _version_ | 1867614115919298560 |
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| access_status_str | Open Access |
| author | Gatyeni, Siphokazi Princess |
| author2 | Nyabadza, Farai |
| author_browse | Gatyeni, Siphokazi Princess Nyabadza, Farai |
| author_facet | Nyabadza, Farai Gatyeni, Siphokazi Princess |
| author_sort | Gatyeni, Siphokazi Princess |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2015 |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/97781 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:46:55.034Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/97781 Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments Gatyeni, Siphokazi Princess Nyabadza, Farai Stellenbosch University. Faculty of Science. Department Mathematical Sciences (Mathematics) Substance abuse -- Patients -- Rehabilitation Patients -- Rehabilitation --Mathematical models Substance abuse -- Treatment -- Mathematical models Substance abuse -- Patients -- South Africa -- Mathematical models UCTD Thesis (MSc)--Stellenbosch University, 2015 Stellenbosch : Stellenbosch University 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. AFRIKAANSE OPSOMMING : Dwelm misbruik is wêreldwyd ‘n ernstige problem met onmeetbare gevolge vir die gesondheid van gebruikers. Rehabilitasie is een van die strategieë wat dwelm misbruik kan help beveg. Dit word in twee vorms verdeel: binnepasiënt- en buitepasiëntrehabilitasie. In hierdie studie ondersoek ons ‘n kompartementele model van dwelmgebruikers in rehabilitasie, waar ‘n periodieke funksie ingesluit word om seisoenale skommelings aan te toon met betrekking tot dwelmgebruikers wat rehabilitasie aanpak. In hierdie tesis lei ons twee basiese reproduksienommers af, R0 en [R0], waar R0 die model met periodisiteit en [R0] die model sonder periodisiteit is. Ons toon aan dat die model ‘n dwelmvrye ekwilibrium het wanneer die basiese reproduksienommer R0 minder as een is en ‘n dwelm-voortsettingsekwilibrium het wanneer R0 meer as een is. Ons pas die model op die data toe en verkry ‘n vooruitskouende blik op die toekoms van hierdie vorms van rehabilitasie. Ons resultate dui aan dat wanneer R0 minder as een is, die binne- en buitepasiënt-bevolkings vinnig verminder en wanneer R0 meer as een is, die gebruik van dwelms voortduur en dat nà ‘n lang tydperk individue in rehabilitasie nader aan w-periodieke oplossing beweeg. Sensitiwiteitsontleding word uitgevoer en die resultate toon aan dat daar ‘n bewustheid moet bestaan dat die graad van effektiewe kontak tussen vatbare individue en dwelmgebruikers beperk moet word ten einde die epidemie onder beheer te bring. Hierdie resultate het betekenisvolle implikasies vir die bestuur en beplanning van rehabilitasieprogramme in Suid-Afrika. rs201601 2015-12-14T07:42:25Z 2015-12-14T07:42:25Z 2015-12 Thesis http://hdl.handle.net/10019.1/97781 en_ZA Stellenbosch University xv, 20 : illustrations (some colour) application/pdf |
| spellingShingle | Substance abuse -- Patients -- Rehabilitation Patients -- Rehabilitation --Mathematical models Substance abuse -- Treatment -- Mathematical models Substance abuse -- Patients -- South Africa -- Mathematical models UCTD Gatyeni, Siphokazi Princess Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments |
| title | Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments |
| title_full | Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments |
| title_fullStr | Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments |
| title_full_unstemmed | Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments |
| title_short | Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments |
| title_sort | modelling in and out patient rehabilitation for substance abuse in dynamic environments |
| topic | Substance abuse -- Patients -- Rehabilitation Patients -- Rehabilitation --Mathematical models Substance abuse -- Treatment -- Mathematical models Substance abuse -- Patients -- South Africa -- Mathematical models UCTD |
| url | http://hdl.handle.net/10019.1/97781 |
| work_keys_str_mv | AT gatyenisiphokaziprincess modellinginandoutpatientrehabilitationforsubstanceabuseindynamicenvironments |