Estimating The Undiagnosed HIV-Positive Population A Mathematical Modeling Study

• Author / Creator

  deBoer,Rebecca A

• 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.

• Subjects / Keywords

  • Parameter Fitting
  • Identifiability
  • Mathematical models
  • Bifurcation analysis
  • HIV incidence
  • HIV
  • Drug resistance
  • Undiagnosed HIV
  • Model Validation

• Graduation date

  Fall 2014

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R37D2QF1X

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.