Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Clinical results have indicated that abuse of multiple drugs/substances has devastating
health and social consequences. The combined abuse of alcohol and the highly
addictive methamphetamine has worsened the drug epidemic in South Africa, especially
in the Western Cape Province. Using non-linear ordinary differential equations,
we formulate a deterministic mathematical model for alcohol-methamphetamine coabuse
epidemic. We prove that the growth of the co-abuse epidemic is dependent
on the threshold parameters of the individual substances of abuse. The substance
with the maximum reproduction number dominates the epidemic. We also prove
that the equilibria points of the co-abuse sub-models are locally and globally asymptotically
stable when the sub-model threshold parameters are less than unity. Using
parameters values derived from the sub-model fittings to data, a population estimate
of co-users of alcohol and methamphetamine under treatment is estimated with a
prevalence of about 1%. Although the results show of a small proportion of co-users
of alcohol and methamphetamine in the province, the prevalence curve is indicative
of a persistent problem. Numerical simulation results reveal that co-abuse epidemic
would persists when both reproduction numbers are greater than one. Results from
sensitivity analysis shows that the individual substance transmission rates between
users of methamphetamine and/or alcohol and the general susceptible population
are the most vital parameters in the co-abuse epidemic. This suggests the need to emphasise
on preventive measures through educational campaigns and social programs
that ensure minimal recruitment into alcohol or methamphetamine abuse. Model
analysis using the time-dependent controls (policies) emphasizes the need to allocate
even more resources on educational campaigns against substance abuse and on effective
treatment services that minimizes or eliminates rampant cases of relapse into
substance abuse. / AFRIKAANSE OPSOMMING: Kliniese resultate toon dat die misbruik van meer as een dwelmmiddel verwoestende
gesondheids-en sosiale gevolge het. Die gekombineerde misbruik van alkohol
en die hoogsverslawende methamphetamine het die dwelm-epidemie in Suid-Afrika
vererger, veral in die Wes-Kaapse provinsie. Deur van nie-lineere gewone diffensiaalvergelykings
gebruik te maak, formuleer ons ’n deterministiese wiskundige model
vir epidemie van die gesamentlike misbruik van alkohol en methamphetamine. Ons
toon aan dat die groei van die sogenaamde mede-misbruik epidemie afhanklik is van
die drumpelparameters van die individuele middels wat misbruik word. Die middels
met die grootste voortbringende syfer domineer die epidemie. Ons bewys ook dat
die ekwilibriumpunte van die mede-misbruik submodelle plaaslik en globaal asimptoties
stabiel is wanneer die sub-model drumpelparameters kleiner as een is. Deur die
submodelle op werklike data te pas word waardes vir die drumpelparameters afgelei
en word daar beraam dat daar ongeveer 1% van die populasie mede-misbruikers
van alkohol en methamphetamine onder behandeling is. Alhoewel die data ’n klein
persentasie van mede-misbruikers van alkohol en methamphetamine in die provinsie
toon, dui die voorkomskurwe op ’n groeiende endemie en voortdurende probleem.
Resultate uit numeriese simulasie toon dat die mede-misbruik epidemie sal
voortduur indien beide reproduserende syfers groter as een sal wees. Resultate van
sensitiwiteitsanalise toon dat die individuele middeloordragkoerse tussen gebruikers
van methamphetamine en/of alkohol en die gewone vatbare populasie die mees
noodsaaklike parameters in die mede-misbruik epidemie is. Dit stel voor dat daar
meer klem gelê moet word op voorkomingsmaatreëls deur opvoedkundige veldtogte
en sosiale programme om te verseker dat minder alkohol en/of methamphetamine
misbruik sal word. Model-analise wat gebruik maak van tyd-afhanklike kontroles
(beleide) lê verder klem op die feit dat selfs meer hulpbronne aan opvoedkundige
veldtogte teen dwelmmisbruik toegewy moet word, asook die effektiewe behandeling
wat gevalle van terugval in dwelmmisbruik sal minimeer of elimineer.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/95982 |
| Date | 12 1900 |
| Creators | Orwa, Titus Okello |
| Contributors | Nyabadza, Farai, Stellenbosch University. Faculty of Science. Department of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | xiii, 90 p. : ill. |
| Rights | Stellenbosch University |
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