The modelling of contagion spread on contact networks provide valuable insights to epidemiologists
and policymakers trying to control and eradicate diseases. This thesis proposes,
implements and analyses a methodology for inserting disease contact networks of HIV into
feedback control loops and applying open-loop pinning control to their nodes. Pinning control
aims to medicate only a portion of an entire network in order to achieve the same outcomes
that would be seen when all nodes are controlled. The control loops are simulated using
networks ranging from size N = 100 nodes to N = 10000 nodes. Simulations aim to control
the average maximum incidence in the networks by first estimating the reference average
transmissibility from the statistical physics technique known as bond percolation. Once the
average transmissibility is known, node-, network- and population mass-action models can
be measured for incidence. Two selective pinning control strategies, namely proportional
feedback and nonlinear model predictive control (NMPC), are compared with one another
and also with a random pinning strategy. The budget, measured in quality-adjusted life
years (QALYs), is added to the cost-function for NMPC control. It is shown that budget
can indeed be controlled while incidence varies, while incidence may be controlled as budget
varies. Pinning control of disease networks is a feasible methodology to analyse the future
and steady-state outcomes of interventions in fast-spreading (high-risk) disease contact networks.
Modellering van die verspreiding van siektes oor kontak-netwerke verskaf waardevolle inligting
aan beleidmakers en epidemioloë wat besluit op maatreëls vir voorkoming teen die siekte.
Hierdie proefskrif hou n metode voor wat gebruik word om siekteverspreidings-netwerke te
simuleer en te analiseer. Dit word gedoen op netwerke met nodusse wat varieer tussen N =
100 en N = 10000. Netwerke waarin HIV versprei word gebruik. Penbeheer word in n oopluskonfigurasie
op elke nodus toegepas binne n geslote terugvoerlus op netwerkvlak. Penbeheer
se doel is om slegs sekere nodusse te beheer om dieselfde uitkomste vir die voorkoms van
HIV tydens n epidemie te meet. Die doel is om die gemiddelde waarskynlikheid vir oordrag
van die siekte tussen nodusse te beheer en sodoende, deur middel van die tegniek genaamd
bond percolation , te bepaal hoe groot die finale epidemie gaan wees. Sodra die gemiddelde
waarskynlikheid bekend is, kan nodus-, netwerk- en populasiemodelle saamgestel word. Twee
selektiewe penbeheer-strategieë (proporsioneel, en NMPC) word met mekaar en met n derde
willekeurige tegniek vergelyk. Die beheer van begrotings, gemeet in quality-adjusted life
years (QALYs), word deur die NMPC strategie hanteer. Siektes binne kontaknetwerke
kan dus beheer word met selektiewe penbeheer. Penbeheer-strategieë word ook vergelyk op
grond van die dosisse wat hulle benodig, asook die akkuraatheid van die bestendigde-toestand
resultate. Penbeheer van siekteverspreidings-netwerke is n werkbare metode om toekomstige
en bestendigde-toestand uitkomste van mediese ingrepe op netwerke mee te analiseer.
