# A comparative analysis of mathematical models for HIV epidemiology

De la Harpe, Alana (2015-04)

Thesis (MSc)--Stellenbosch University, 2015.

Thesis

ENGLISH ABSTRACT: HIV infection is one of the world’s biggest health problems, with millions of people infected worldwide. HIV infects cells in the immune system, where it primarily targets CD4+ T helper cells and without treatment, the disease leads to the collapse of the host immune system and ultimately death. Mathematical models have been used extensively to study the epidemiology of HIV/AIDS. They have proven to be effective tools in studying the transmission dynamics of HIV. These models provide predictions that can help better our understanding of the epidemiological patterns of HIV, especially the mechanism associated with the spread of the disease. In this thesis we made a functional comparison between existing epidemiological models for HIV, with the focus of the comparison on the force of infection (FOI). The spread of infection is a crucial part of any infectious disease, as the dynamics of the disease depends greatly on the rate of transmission from an infectious individual to a susceptible individual. First, a review was done to see what deterministic epidemiological models exist. We found that many manuscripts do not provide the necessary information to recreate the authors’ results and only a small amount of the models could be simulated. The reason for this is mainly due to a lack of information or due to mistakes in the article. The models were divided into four categories for the analysis. On the basis of the FOI, we distinguished between frequency- or density-dependent transmission, and as a second criterion we distinguished models on the sexual activity of the AIDS group. Subsequently, the models were compared in terms of their FOI, within and between these classes. We showed that for larger populations, frequency-dependent transmission should be used. This is the case for HIV, where the disease is mainly spread through sexual contact. Inclusion of AIDS patients in the group of infectious individuals is important for the accuracy of transmission dynamics. More than half of the studies that were selected in the review assumed that AIDS patients are too sick to engage in risky sexual behaviour. We see that including AIDS patients in the infectious individuals class has a significant effect on the FOI when the value for the probability of transmission for an individual with AIDS is bigger than that of the other classes. The analysis shows that the FOI can vary depending on the parameter values and the assumptions made. Many models compress various parameter values into one, most often the transmission probability. Not showing the parameter values separately makes it difficult to understand how the FOI works, since there are unknown factors that have an influence. Improving the accuracy of the FOI can help us to better understand what factors influence it, and also produce more realistic results. Writing the probability of transmission as a function of the viral load can help to make the FOI more accurate and also help in the understanding of the effects that viral dynamics have on the population transmission dynamics.

AFRIKAANSE OPSOMMING: MIV-infeksie is een van die wêreld se grootste gesondheidsprobleme, met miljoene mense wat wêreldwyd geïnfekteer is. MIV infekteer selle in die immuunstelsel, waar dit hoofsaaklik CD4+ T-helperselle teiken. Sonder behandeling lei die siekte tot die ineenstorting van die gasheer se immuunstelsel en uiteindelik sy dood. Wiskundige modelle word breedvoerig gebruik om die epidemiologie van MIV/vigs te bestudeer. Die modelle is doeltreffende instrumente in die studie van die oordrag-dinamika van MIV. Hulle lewer voorspellings wat kan help om ons begrip van epidemiologiese patrone van MIV, veral die meganisme wat verband hou met die verspreiding van die siekte, te verbeter. In hierdie tesis het ons ‘n funksionele vergelyking tussen bestaande epidemiologiese modelle vir MIV gedoen, met die fokus van die vergelyking op die tempo van infeksie (TVI). Die verspreiding van infeksie is ‘n belangrike deel van enige aansteeklike siekte, aangesien die dinamika van die siekte grootliks afhang van die tempo van oordrag van ‘n aansteeklike persoon na ‘n vatbare persoon. ‘n Oorsig is gedoen om te sien watter kompartementele epidemiologiese modelle alreeds bestaan. Ons het gevind dat baie van die manuskripte nie die nodige inligting voorsien wat nodig is om die resultate van die skrywers te repliseer nie, en slegs ‘n klein hoeveelheid van die modelle kon gesimuleer word. Die rede hiervoor is hoofsaaklik as gevolg van ‘n gebrek aan inligting of van foute in die artikel. Die modelle is in vier kategorieë vir die analise verdeel. Op grond van die TVI het ons tussen frekwensie- of digtheidsafhanklike oordrag onderskei, en as ‘n tweede kriterium het ons die modelle op die seksuele aktiwiteit van die vigs-groep onderskei. Daarna is die modelle binne en tussen die klasse vergelyk in terme van hul TVIs. Daar is gewys dat frekwensie-afhanklike oordrag gebruik moet word vir groter bevolkings. Dit is die geval van MIV, waar die siekte hoofsaaklik versprei word deur seksuele kontak. Die insluiting van die vigs-pasiënte in die groep van aansteeklike individue is belangrik vir die akkuraatheid van die oordrag-dinamika van MIV. Meer as helfte van die uitgesoekte studies aanvaar dat vigs-pasiënte te siek is om betrokke te raak by riskante seksuele gedrag. Ons sien dat die insluiting van vigs-pasiënte in die groep van aansteeklike individue ‘n beduidende uitwerking op die TVI het wanneer die waarde van die waarskynlikheid van oordrag van ‘n individu met vigs groter is as dié van die ander klasse. Die analise toon dat die TVI kan wissel afhangende van die parameter waardes en die aannames wat gemaak is. Baie modelle voeg verskeie parameter waardes bymekaar vir die waarskynlikheid van oordrag. Wanneer die parameter waardes nie apart gewys word nie, is dit moeilik om die werking van die TVI te verstaan, want daar is onbekende faktore wat ‘n invloed op die TVI het. Die verbetering van die akkuraatheid van die TVI kan ons help om die faktore wat dit beïnvloed beter te verstaan, en dit kan ook help om meer realistiese resultate te produseer. Om die waarskynlikheid van oordrag as ‘n funksie van die viruslading te skryf kan help om die TVI meer akkuraat te maak en dit kan ook help om die effek wat virale dinamika op die bevolkingsoordrag-dinamika het, beter te verstaan.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/96983

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