Parameter Estimation of Mathematical Models: Estimation of the Burden of HIV Epidemics as a Case Study

• Author / Creator

  Su, Zhimin

• Mathematical models are widely used to describe dynamics in various fields. In practice, it is necessary and important to determine model parameters based on existing data. A major challenge for parameter estimation under modeling framework lies in non-identifiability issue: parameter values on a curve or a multidimensional surface in the parameter space produce almost the same observable model outputs. A variety of techniques and methodologies for resolving non-identifiability have been proposed from different disciplines, such as mathematics, statistics and engineering. The existing methods can inform us whether there is non-identifiability issue or not, if there is, we are suggested to fix some least identifiable parameters such that all remaining parameters can be uniquely estimated. However, it is not always possible to fix some least identifiable parameters such as transmission coefficients in disease models. In this case it is desirable to investigate dependencies among model parameters. Dependencies among model parameters are related to linear dependencies among the columns of the Jacobian matrix of observable model outputs with respect to model parameters. Due to the existence of numerical error, it is not possible to observe exact linear dependencies among the columns of the Jacobian matrix. Instead, some nearly linear dependencies can be observed. These nearly linear dependencies are the potential exact linear dependencies when numerical error is not present. In this thesis, a matrix decomposition method was proposed to detect and resolve non-identifiability issue by checking nearly linear dependencies among the columns of the Jacobian matrix. Our method can inform us how many nearly linear dependencies exist and which columns are involved in each nearly linear dependency. Our method for diagnosing non-identifiability was applied to several HIV datasets from Chinese Center for Disease Control and Prevention (China CDC) to produce HIV assessment for China. We also demonstrated the applicability of our new method for diagnosing non-identifiability for a simple one-group model and a complex multi-group model.

• Subjects / Keywords

  • Mathematical models
  • Parameter estimation
  • Identifiability

• Graduation date

  Fall 2016

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3GM81T51

• 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.