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Georgia State University

1. Akossi, Aurelie. COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY.

Degree: PhD, Mathematics and Statistics, 2019, Georgia State University

URL: https://scholarworks.gsu.edu/math_diss/62

Stable estimation of system parameters for infectious disease outbreaks is of paramount importance to the design of adequate forecasting algorithms. Oftentimes parameter estimation procedures are cast as ODE-constrained nonlinear least squares problems, where infinite dimensional time dependent disease parameters need to be recovered from finite dimensional data sets. As the result, the Jacobian of the corresponding parameter-to-data operator is generally illconditioned and may be numerically singular. When such an operator is fitted to noise-contaminated epidemiological data, the estimated parameters tend to be entirely unreliable due to severe error propagation into the approximate solution. The sources of noise in the reported incidence data vary for different types of diseases and can be attributed to possible under or over reporting owing to, for instance, a large proportion of asymptomatic cases or false diagnostics. In our study we use the Levenberg-Marquardt algorithm to reconstruct a variable transmission rate. The regularization provided by this optimization scheme, which is a penalized version of the Gauss-Newton procedure, is enforced by the appropriate problem-oriented discretization tools. Specifically, we compare what we call parametric and non-parametric discretization routines. By parametric discretization we mean that the transmission rate is modeled by a pre-defined expression that involves only few parameters such as, for example, a declining transmission rate defined by a hyperbolic, harmonic, or exponential function. In a nonparametric discretization scheme the transmission rate is projected onto a subspace spanned by a finite set of orthogonal polynomials, or spline functions. Depending on the nature of the transmission, one may use Legendre or Chebyshev polynomials, B-splines, wavelets, or other base elements. The main goal of our project is to see how parametric and non-parametric discretization schemes compare in terms of accuracy of parameter estimation and in terms of their ability to provide a reliable forecasting tool. Numerical experiments with both synthetic and real data will be presented.
*Advisors/Committee Members: Alexandra Smirnova, Gerardo Chowell.*

Subjects/Keywords: Inverse Problems; Epidemiology; Regularization; Parameter Estimation; Forecasting

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APA (6^{th} Edition):

Akossi, A. (2019). COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY. (Doctoral Dissertation). Georgia State University. Retrieved from https://scholarworks.gsu.edu/math_diss/62

Chicago Manual of Style (16^{th} Edition):

Akossi, Aurelie. “COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY.” 2019. Doctoral Dissertation, Georgia State University. Accessed August 24, 2019. https://scholarworks.gsu.edu/math_diss/62.

MLA Handbook (7^{th} Edition):

Akossi, Aurelie. “COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY.” 2019. Web. 24 Aug 2019.

Vancouver:

Akossi A. COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY. [Internet] [Doctoral dissertation]. Georgia State University; 2019. [cited 2019 Aug 24]. Available from: https://scholarworks.gsu.edu/math_diss/62.

Council of Science Editors:

Akossi A. COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY. [Doctoral Dissertation]. Georgia State University; 2019. Available from: https://scholarworks.gsu.edu/math_diss/62