The UTC Graduate School is pleased to announce that Jacob Derrick will present Doctoral research titled, Unified Mathematical Modeling, Analysis, and Simulation of COVID-19 and Ecological Processes on 06/18/2025 at 1:00 p.m. in https://tennessee.zoom.us/j/85779721297 (no passcode). Everyone is invited to attend. 

Mathematics

Chair: Dr. Jin Wang

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 COVID-19 transmission and the factors driving long COVID prevalence. 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.