Committee Chair

Wang, Jin

Committee Member

Nichols, Roger; Le, Thien; Liang, Yu

Department

Dept. of Computational Science

College

College of Engineering and Computer Science

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

This dissertation is concerned with the modeling, simulation, and analysis of complex population dynamics using compartmental modeling frameworks based on ordinary differential equations (ODEs). First, we propose a mechanistic model to investigate the transmission dynamics of COVID-19, particularly focusing on the emergence and population-level impact of a post-acute sequela referred to as long COVID and vaccination effects. We then move forward with a model that incorporates multiple strains and reinfection dynamics. By fitting these models to epidemiological data from the United States and the United Kingdom, we conduct both mathematical analyses and numerical simulations to better understand the factors driving long COVID prevalence and the inter-strain dynamics of COVID-19 that affect transmission. In addition to epidemiological applications, we extend our compartmental modeling approach to ecological studies, specifically examining the group dynamics of degus, small rodents with complex social behaviors. We analyze how environmental factors such as temperature variations, seasonal rainfall patterns, and vegetation indices (NDVI) influence group sizes and social interactions over time. This ecological modeling employs similar mechanistic ODE-based frameworks, highlighting methodological consistency across biological systems.

Acknowledgments

I would like to thank the Department of Mathematics and the Graduate School of UTC for affording me the opportunity to obtain my Ph.D. I would also like to express my great gratitude to my advisor Dr. Jin Wang, whose support and knowledge were invaluable during my research. Thank you as well to the members of my committee, Dr. Roger Nichols, Dr. Thien Le, and Dr. Yu Liang. I appreciate the work and time that were put in to help finalize my research and dissertation. Thank you to Dr. Christopher Cox for leading such a strong, welcoming department as well as the kind words and advice you offered me. Lastly, I would like to thank all of my past professors and teachers who have supported me and helped to cultivate my passion for mathematics such as Mr. Seth Sutton, Dr. Martha Pratt, Dr. Rizwanur Khan, Dr. Micah Milinovich, and so many more.

Degree

Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.

Date

8-2025

Subject

COVID-19 (Disease)--Epidemiology--Mathematical models; Degus--Behavior--Ecology--Mathematical models

Keyword

Epidemiology; Ecology; Mathematical modeling; Applied mathematics

Document Type

Doctoral dissertations

DCMI Type

Text

Extent

vii, 74 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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