Pinning control of disease networks

Abstract

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.