# Mathematical modelling of HIV/AIDS transmission under treatment structured by age of infection

Ejigu, Amsalework Ayele (2011-03)

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011.

Includes bibliography.

Thesis

ENGLISH ABSTRACT: This thesis takes into account the different levels of infectiousness of the human immunodeficiency virus (HIV) infected individuals throughout their period of infection. Infectiousness depends on the time since infection. It is high shortly after the infection occurs and then much lower for several years, and thereafter a higher plateau is reached before the acquired immunodeficiency syndrome (AIDS) phase sets in. In line with this, we formulated a mathematical model which is structured according to the age of infection. To understand the dynamics of the disease, we first discuss and analyse a simple model in which the age of infection is not considered, but progression of the HIV-AIDS transmission is taken into consideration by introducing three stages of infection. Analysis of these models tells us that the disease can be eradicated from the population only if on average one infected individual infects less than one person in his or her infectious period, otherwise the disease persists. To investigate the reduction of the number of infections caused by a single infectious individual to less than one, we introduce different treatment strategies for a model which depends on the age of infection, and we analyse it numerically. Current strategies amount to introducing treatment only at a late stage of infection when the infected individual has already lived through most of the infectious period. From our numerical results, this strategy does not result in eradication of the disease, even though it does reduce the burden for the individual. To eradicate the disease from the population, everyone would need to be HIV tested regularly and undergo immediate treatment if found positive.

AFRIKAANSE OPSOMMING: Hierdie tesis hou rekening met die verskillende aansteeklikheidsvlakke van die menslike immuniteitsgebreksvirus (MIV) deur besmette individue gedurende hulle aansteeklikheidstydperk. Die graad van aansteeklikheid hang af van die tydperk sedert infeksie. Dit is hoog kort nadat die infeksie plaasvind en daarna heelwat laer vir etlike jare, en dan volg n hoer plato voordat uiteindelik die Verworwe-Immuniteitsgebreksindroom (VIGS) fase intree. In ooreenstemming hiermee, formuleer ons n wiskundige model van MIV-VIGSoordrag met n struktureer waarin die tydperk sedert infeksie bevat is. Om die dinamika van die siekte te verstaan, bespreek en analiseer ons eers n eenvoudige model sonder inagneming van die tydperk sedert infeksie, terwyl die progressie van MIV-VIGS-oordrag egter wel in ag geneem word deur die beskouing van drie stadiums van infeksie. Analise van die modelle wys dat die siekte in die bevolking slegs uitgeroei kan word as elke besmette mens gemiddeld minder as een ander individu aansteek gedurende die tydperk waarin hy of sy self besmet is, anders sal die siekte voortduur. Vir die ondersoek oor hoe om die aantal infeksies per besmette individu tot onder die waarde van een te verlaag, beskou ons verskeie behandelingsstrategiee binne die model, wat afhang van die tydperk sedert infeksie, en ondersoek hulle numeries. Die huidige behandelingstrategiee kom neer op behandeling slegs gedurende die laat sta- dium van infeksie, wanneer die besmette individu reeds die grootste deel van die aansteeklikheidsperiode deurleef het. Ons numeriese resultate toon dat hierdie strategie nie lei tot uitroeiing van die siekte nie, alhoewel dit wel die las van die siekte vir die individu verminder. Om die siekte binne die bevolking uit te roei, sou elkeen gereeld vir MIV getoets moes word en indien positief gevind, dadelik met behandeling moes begin.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/6628

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