Modelling Drug Abuse and Drug-related Crime

98 Pages·2015·4.45 MB·English

Modelling Drug Abuse and Drug-related
Crime: A Systems Approach
by
Lezanie Coetzee
Thesis presented in partial fulfilment of the
academic requirements for the degree of
Master of Science
at the University of Stellenbosch
Supervisor: Prof. Farai Nyabadza
(University of Stellenbosch)
December 2015
Stellenbosch University https://scholar.sun.ac.za
Declaration
By submitting this thesis/dissertation electronically, I declare that the entirety of the
workcontainedthereinismyown,originalwork,thatIamthesoleauthorthereof(save
to the extent explicitly otherwise stated), that reproduction and publication thereof by
Stellenbosch University will not infringe any third party rights and that I have not pre-
viouslyinitsentiretyorinpartsubmitteditforobtaininganyqualification.
December 2015
Copyright© 2011StellenboschUniversity
Allrightsreserved.
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i
Abstract
In this study we look at the syndemic of substance abuse and drug-related crime in
the Western Cape province of South Africa. The intent of this study is to provoke crit-
ical thinking about the possibilities systems thinking and system dynamics posses for
social and health challenges in a diverse and complex environment like that of South
Africa, especially the Western Cape. This study ventures into cross-discipline work
between Epidemiology, Biomathematics and System Dynamics, with the hope of en-
couragingresearchersfromdifferentfieldstocollaborateinordertocurbthescourgeof
substance abuse and drug-related crime in South Africa. Substance abuse and the as-
sociated health and social hazards such as drug-related crime is a major problem in the
Western Cape. Drug-related crime cases reported by the South African Police Services
(SAPS) for the Western Cape exhibited a 311.5% growth in the past decade. This high-
lightshowthereductionofsubstanceabuseanddrug-relatedcrimewithintheWestern
Capeprovince,willbeanelixirforthesafetyanddevelopmentofthecommunities. The
fight against substance abuse has been driven by a multi-sectorial approach involving
several government departments, non-governmental organisations and communities.
With systems thinking the assumption is that the world is systemic, which means that
phenomenaisunderstoodtobeanemergentpropertyoftheinterrelatedwhole. Firstly,
using non-linear ordinary differential equations, we formulate a deterministic mathe-
matical model for the substance abuse and drug-related crime syndemic, evaluate the
threshold number and use sensitivity analysis to analyze the model. Secondly, a dy-
namicsystem,calledtheSubstanceAbuseandDrug-relatedCrimeintheWesternCape
(SADC-WC)systemisconstructedusingtheSTELLAinordertoexploreandclassifythe
underlying relationships and structures within the substance abuse and drug-related
crime system. Both the sensitivity analysis, and the simulations of the SADC-WC sys-
tem indicate that an increase of successful convictions will have a significant influence
onthesyndemic,andpromisetoreducedrug-relatedcrimecases.
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ii
Opsomming
Inhierdiestudieondersoekondiesyndemie(‘syndemic’)vandwelmmisbruikendwelm-
verwante misdaad in die Wes-Kaap provinsie, in Suid-Afrika. Die moontlikhede wat
sistemiese denke en dinamiese sisteme inhou vir sosiale en gesondheid kwale in ’n di-
verseenkomplekseomgewingsoosSuid-Afrika,wordondersoek. Hierdiestudiewaag
interdisiplinêre werk tussen Epidemiologie, Biowiskunde en Dinamiese sisteme, met
die hoop om navorsers van verskillende velde aan te moedig om saam te werk om
die plaag van dwelmmisbruik en dwelm-verwante misdaad in Suid-Afrika te bekamp.
Dwelmmisbruikendiegepaardgaandegesondheidenmaatskaplikegevaresoosdwelm-
verwantemisdaadis’ngrootprobleemindieWes-Kaap. DieSAPDsevermeldedwelm-
verwantemidaadhet’ngroeivan311,5%ondergaanindieafgelopedekade,enisaan-
duidendvirhoediebeheerenbeperkingvandwelmmisbruikendwelm-verwantemis-
daad in die Wes-Kaap provinsie bevordering van beide die veiligheid en ontwikkeling
vandiegemeenskapsalverseker. Ditbeklemtoonhoedieverminderingvandwelmmis-
bruikendwelm-verwantemisdaadindieWes-Kaapland,sal’nelikservirdieveiligheid
en ontwikkeling van die gemeenskappe. Die stryd teen dwelmmisbruik is gedryf deur
’n multi-sektorale benadering waarby verskeie regeringsdepartemente, nie-regerings
organisasiesengemeenskappe. Stelselsdenkeendinamiesesistemeisgebasseuropdie
aanname, dat die wÃłreld is sistemiese en dat verskynsels verstaan word ten opsigte
vandieontluikendeeienskapvandieomvattendegeheel. Eerstensstelons’nkomparte-
mentele model op wat deur nie-liniêre gewone differensiële vergelykings beskryf kan
word vir die dwelmmisbruik en dwelm-verwante misdaad epidemies. Ons evalueer
die drumpel getal en gebruik sensitiwiteitsanalise om die parameters van die model te
analiseer. Tweedens, is ’n dinamiese sisteem genaamd die Middelmisbruik en dwelm-
verwantemisdaadindieWes-Kaap(SADC-WC)stelselgeboumetbehulpvandieSTELLA
platformomteverkenenklassifiseerdieonderliggendeverhoudingsenstrukturebinne
diedwelmmisbruikendwelm-verwantemisdaadstelsel. Beidediesensitiwiteitsanalise,
en die simulasies van die SADC-WC stelsel dui aan dat ’n toename in suksesvolle
vonisse ’n beduidende invloed op die epidemies sal hê; en beloof om sake van dwelm-
verwantemisdaadteverminder.
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Dedications
FormyLordandSaviour,thankyouforYourGrace. ForwhenIamweak,Iamstrong.
2Corinthians12:10
iii
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Acknowledgements
I would like to extend my sincere appreciation to my academic supervisor Prof. Farai
Nyabadza. I am honoured to know you, and to work with you. Thank you for always
keeping your office door open. Your wisdom will be cherished, and your kindness and
capacity to care will inspire me for many years to come. My colleague and dear friend
JohnBoscohHatsonNjagarah,thankyouforalltheinsightfuldiscussionsonworkand
life. Mayyoukeeponextendingyourhandtothoseinneed.
My loving family, especially my parents Diek and Zelia Coetzee, thank you for always
standingrock solidbehind me. I loveyou somuch. Tomy friendsthat isalways onthe
frontieroflifewithme,thankyouforalwaysstandingnexttome.
Finally, I want to acknowledge and honour Our Father in heaven. By Your grace we
shallnotceasefromexploration.
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Contents
Opsomming ii
1 Introduction 1
1.1 Problemandmotivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Aimsandobjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Projectoutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Literaturereview 10
2.1 Substanceabuseanddrug-relatedcrimeintheWesternCape . . . . . . . . 10
2.2 Fromasystemsperspective . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Systemsthinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Systemdynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.3 STELLA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Modelsofsubstanceabuseanddrug-relatedcrime . . . . . . . . . . . . . . 19
3 Deterministicmodelforthesubstanceabuseanddrug-relatedcrimesyndemic 24
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Modelformulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
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Contents vi
3.1.2 Basicpropertiesofthesyndemicmodel . . . . . . . . . . . . . . . . 27
3.2 Modelanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Thedrug-freeequilibriumandthebasicreproductionnumber . . . 30
3.2.2 Globalstabilityofthedrug-freesteadystate . . . . . . . . . . . . . 31
3.2.3 Thedrugpersistentequilibrium . . . . . . . . . . . . . . . . . . . . 33
3.3 Sensitivityanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 Parameterestimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 Resultsofouranalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Asystemdynamicsmodel 43
4.1 Modelbuilding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1.1 Modelboundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.2 Stocksandflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.3 Sourcesofinformationfortheflows . . . . . . . . . . . . . . . . . . 45
4.2 Modelanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Casualloopdiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.2 Mainfeedbackloops . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.3 Modeldiagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Simulationofthemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.1 Equationsthatdeterminetheflows . . . . . . . . . . . . . . . . . . 52
4.3.2 Initialconditionsandparameterestimation . . . . . . . . . . . . . . 53
4.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
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Contents vii
5 Discussionandconclusion 66
Appendix 70
A STELLAequations 70
A.1 EquationsfortheSADC-WCsystemmodelfor2004−2014 . . . . . . . . . 70
A.2 EquationsfortheSADC-WCsystemmodelfor2004−2024 . . . . . . . . . 72
A.3 Equations for the SADC-WC system model for 2004−2024 with inter-
vention1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
A.4 Equations for the SADC-WC system model for 2004−2024 with inter-
vention2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
A.5 Equations for the SADC-WC system model for 2004−2024 with inter-
vention3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
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List of Figures
1.1 Drug-relatedcrimesrecordednationallyin2014bytheSouthAfricanPoliceSer-
vices(SAPS),themoreintensethecolourthehigherthedrug-relatedcrimelevel
[3,32]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Drug-related crimes and total crimes of 2014 recorded in the Western Cape by
theSouthAfricanPoliceServices(SAPS)[3] . . . . . . . . . . . . . . . . . . . . 3
1.3 Thetoptenprecintsofdrug-relatedof2014recordedintheSouthAfricabythe
SouthAfricanPoliceServices(SAPS)[3] . . . . . . . . . . . . . . . . . . . . . . 3
1.4 TheapplicationofSystemDynamics[42]. . . . . . . . . . . . . . . . . . . . . . 5
1.5 An illustration of a simple conceptual model for drug abuse from a systems
perspective. Where DAP = Drug sssociated problems, PR = Perceived risks,
DSP=DrugsupplyandpriceandNB=Normsandbeliefs. . . . . . . . . . . . 7
2.1 Drug-relatedcrimeintheWesternCape[64]. . . . . . . . . . . . . . . . . . . . 12
2.2 Crime maps of South Africa showing police precincts with drug-related crime
levels, the more intense the colour the higher the crime level. The escalation
of drug-related crime in the past decade is evident from the images, with the
crime concentrated in the Western Cape province for the year 2005 and 2014
respectively[32] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 BasicmodellingiconsinSTELLAusedasbuildingblocksforasystem. . . . . . 19
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