Unified Mathematical Modeling, Analysis and Simulation of COVID-19 and Ecological Processes

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.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Derrick, Jacob

Contributors dc:contributor

• Wang, Jin
• Nichols, Roger; Le, Thien; Liang, Yu
• College of Engineering and Computer Science

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

Licence

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

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/1018

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-2202