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Estimating The Undiagnosed HIV-Positive Population A Mathematical Modeling Study Open Access


Other title
HIV incidence
Model Validation
Parameter Fitting
Undiagnosed HIV
drug resistance
Mathematical Model
bifurcation analysis
Type of item
Degree grantor
University of Alberta
Author or creator
deBoer,Rebecca A
Supervisor and department
Li, Michael (Mathematical and Statistical Sciences)
Examining committee member and department
Wong, Hao (Mathematical and Statistical Sciences)
Han, Bin (Mathematical and Statistical Sciences)
Muldowney, Jim (Mathematical and Statistical Sciences)
Zhu, Huaiping (York University)
Plitt, Sabrina (Public Health)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
Doctor of Philosophy
Degree level
In this thesis a mathematical model of HIV transmission and diagnosis is used to estimate the total size of the HIV-positive population and the HIV incidence from HIV case report data for the Province of Alberta. Worldwide, estimates of the size of the HIV-positive population are used to allocate medical resources and target disease prevention efforts, while estimates of HIV incidence are used to evaluate the effectiveness of intervention programs and track changes in risk behaviours. Many HIV surveillance programs are based on reports of newly diagnosed cases. Estimating the total size of the HIV-positive population from this data is challenging as those who are HIV-positive but have not been diagnosed are not included. Furthermore, trends in HIV diagnosis do not reflect trends in incidence as the length of time newly diagnosed HIV patients have been infected is usually unknown. Fitting the model used in this thesis is complicated by the presence of non-identifiable parameters. Non-identifiable parameters occur when all parameter values on a surface in the parameter space have identical model outcomes for the quantities represented in the data. Methods for systematic detection of this behaviour and resolution of nonidentifiabilities are discussed in a general modelling framework and applied to the HIV model for the assessment of the Province of Alberta data. Interval estimates for all parameters are obtained using an iterated Markov chain Monte Carlo (MCMC) method and the resulting fitted model is validated. The validated model is used to produce estimates of the total size of the HIV-positive population including those who have not been diagnosed for the years 2001 to 2020. Estimates of HIV incidence, time from infection to diagnosis, and the size of the undiagnosed population are also computed using the model. Uncertainty and sensitivity analysis are used to determine how much uncertainty remains in these estimates and which parameters are most important to the model outcomes. Finally, the model is used to simulate several potential intervention strategies to reduce HIV incidence in the province. The potential impact of antiretroviral drug resistant strains of HIV on a hypothetical “treatment as prevention” program in the context of a generalized HIV epidemic is studied using another model. This model includes the development and transmission of drug resistant viral strains. Sensitivity and uncertainty analyses are used to explore the potential outcomes. Finally, the asymptotic behaviour of a simple disease model similar to the Alberta HIV model, but using more general forms of population dependent transmission, is analyzed mathematically. It is shown that for some types of population dependence this model can display complicated dynamical behaviours including backward bifurcations and Hopf bifurcations.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
R. de Boer and M. Li, Density dependence in disease incidence and its impacts on transmission dynamics, Canadian Applied Mathematics Quarterly, 19 (2011), pp. 195–218.

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File title: Estimating The Undiagnosed HIV-Positive Population A Mathematical Modeling Study
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