Modelling the co-infection dynamics of HIV-1 and M. tuberculosis

This dissertation focuses on the modelling, identification and the parameter estimation for the co-infection of HIV-1 and M. tuberculosis. Many research papers in this field focus primarily on HIV, but multiple infections are explored here, as it is common in many individuals infected by HIV. Tuberculosis is also responsible for the highest number of casualties per year in the group of HIV-infected individuals. A model is proposed to indicate the populations of both pathogen as well as key information factors, such as the overall infected cell population and antigen-presenting cells. Simulations are made to indicate the growth and decline in cell-type numbers for a specific individual. Such simulations would provide a means for further, well-founded investigation into appropriate treatment strategies. One previous such model developed by Kirschner is used to obtain a nominal parameter set. Furthermore, the nominal set is then used in conjunction with real-world samples provided by the National Institute for Communicable Diseases in South Africa, to solidify the credibility of the model in the practical case. This is achieved via simulations and employs parameter estimation techniques, namely the Nelder-Mead cost-function method. An identifiability study of the model is also done. Conclusions drawn from this study include the result that the treatment of M. tuberculosis does not affect the course of HIV-1 progression in a notable way, and that the model can indeed be used in the process of better understanding the disease profile over time of infected individuals.Dissertation (MEng)--University of Pretoria, 2008.Electrical, Electronic and Computer EngineeringMEngunrestricte

Selective pinning control of the average disease transmissibility in an HIV contact network

Medication is applied to the HIV-infected nodes of high-risk contact networks with the aim of controlling the spread of disease to a predetermined maximum level. This intervention, known as pinning control, is performed both selectively and randomly in the network. These strategies are applied to 300 independent realizations per reference level of incidence on connected undirectional networks without isolated components and varying in size from 100 to 10 000 nodes per network. It is shown that a selective on-off pinning control strategy can control the networks studied with limited steady-state error and, comparing the medians of the doses from both strategies, uses 51.3% less medication than random pinning of all infected nodes. Selective pinning could possibly be used by public health specialists to identify the maximum level of HIV incidence in a population that can be achieved in a constrained funding environment.South African Centre for Epidemiological Modelling and Analysis (SACEMA).In part by the National Research Foundation of South Africa (Grant Number 90533).http://journals.aps.orghb201

Pinning control of disease networks

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.Thesis (PhD)--University of Pretoria, 2015.tm2016Electrical, Electronic and Computer EngineeringPhDUnrestricte