Date of Award
8-8-2017
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Statistics
First Advisor
Alexandra Smirnova
Second Advisor
Vladimir Bondarenko
Third Advisor
Gerardo Chowell-Puente
Fourth Advisor
Michael Stewart
Abstract
When an emerging outbreak occurs, stable parameter estimation and reliable projections of future incidence cases using limited (early) data can play an important role in optimal allocation of resources and in the development of effective public health intervention programs. However, the inverse parameter identification problem is ill-posed and cannot be solved with classical tools of computational mathematics. In this dissertation, various regularization methods are employed to incorporate stability in parameter estimation algorithms. The recovered parameters are then used to generate future incident curves as well as the carrying capacity of the epidemic and the turning point of the outbreak.
For the nonlinear generalized Richards model of disease progression, we develop a novel iteratively regularized Gauss-Newton-type algorithm to reconstruct major characteristics of an emerging infection. This problem-oriented numerical scheme takes full advantage of a priori information available for our specific application in order to stabilize the iterative process. Another important aspect of our research is a reliable estimation of time-dependent transmission rate in a compartmental SEIR disease model. To that end, the ODE-constrained minimization problem is reduced to a linear Volterra integral equation of the first kind, and a combination of regularizing filters is employed to approximate the unknown transmission parameter in a stable manner. To justify our theoretical findings, extensive numerical experiments have been conducted with both synthetic and real data for various infectious diseases.
DOI
https://doi.org/10.57709/10459145
Recommended Citation
DeCamp, Linda, "Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting." Dissertation, Georgia State University, 2017.
doi: https://doi.org/10.57709/10459145