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Dissertation
Epidemiological modeling: A study of reproduction numbers, backward bifurcations, and vaccination strategies
Washington State University
Doctor of Philosophy (PhD), Washington State University
07/2025
DOI:
https://doi.org/10.7273/000007881
Abstract
Mathematical epidemiology is the discipline dedicated to the study of the transmission dynamics and management of communicable diseases within a population. Compartmental models governed by systems of ordinary differential equations (ODEs) are an efficient tool commonly used in epidemiological modeling. These models can be analyzed by means of analytical, numerical, and statistical approaches. In this dissertation study, we use ODE-based compartmental models in conjunction with diverse mathematical techniques to understand various dynamics of disease spread. The goals of the dissertation are three-fold: to examine the reproduction number of a relatively novel structure of vaccination models; to explore the phenomenon of backward bifurcations in epidemiological models; and to address some vital questions concerning the epidemiological dynamics of COVID-19 (and emerging infections) in terms of factors such as differential morbidity, waning immunity, vaccine hesitancy, imperfect vaccination, double-dose vaccination, and multi-factorial vaccine effectiveness. The research methodology employed in this dissertation study encompasses qualitative investigations of dynamical systems, explorations of reproduction numbers, local and global sensitivity analyses, and computational simulations. This doctoral study enriches the field of mathematical modeling in epidemiology through analyses of both theory and applications of ODE-based deterministic compartmental models. The theoretical contributions of this scholarly work include detailed examinations of reproduction numbers and backward bifurcations in epidemic models that comprise distinct structures. Moreover, this study contributes to enhance the current knowledge on waning immunity, vaccine hesitancy, and optimal vaccination strategies for respiratory infections. Overall, the findings of this dissertation not only deepen our understanding of the theory of reproduction numbers and backward bifurcations in mathematical epidemiology, but also have the potential to inform decision-making on vaccine development and epidemic control.
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Details
- Title
- Epidemiological modeling
- Creators
- Indunil Madhusankha Hewage
- Contributors
- Elissa J Schwartz (Chair)Haijun Li (Committee Member)Nikolaos Voulgarakis (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 416
- Identifiers
- 99901296776101842
- Language
- English
- Resource Type
- Dissertation