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

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Title: Unified Mathematical Modeling, Analysis and Simulation of COVID-19 and Ecological Processes
Authors: Derrick, Jacob
Committee Members: Wang, Jin; Nichols, Roger; Le, Thien; Liang, Yu; College of Engineering and Computer Science
Summary: 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.
URL: https://scholar.utc.edu/theses/1018
Database: OpenDissertations
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  Availability: 0
Header DbId: ddu
DbLabel: OpenDissertations
An: ddu.oai.scholar.utc.edu.theses.2202
AccessLevel: 6
PubType: Dissertation/ Thesis
PubTypeId: dissertation
PreciseRelevancyScore: 0
IllustrationInfo
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  Label: Title
  Group: Ti
  Data: Unified Mathematical Modeling, Analysis and Simulation of COVID-19 and Ecological Processes
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Derrick%2C+Jacob%22">Derrick, Jacob</searchLink>
– Name: Author
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  Data: <searchLink fieldCode="CO" term="%22Wang%2C+Jin%22">Wang, Jin</searchLink>; <searchLink fieldCode="CO" term="%22Nichols%2C+Roger%22">Nichols, Roger</searchLink>; <searchLink fieldCode="CO" term="%22Le%2C+Thien%22">Le, Thien</searchLink>; <searchLink fieldCode="CO" term="%22Liang%2C+Yu%22">Liang, Yu</searchLink>; <searchLink fieldCode="CO" term="%22College+of+Engineering+and+Computer+Science%22">College of Engineering and Computer Science</searchLink>
– Name: Abstract
  Label: Summary
  Group: Ab
  Data: 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.
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PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ddu&AN=ddu.oai.scholar.utc.edu.theses.2202
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: COVID-19 (Disease)--Epidemiology--Mathematical models
        Type: general
      – SubjectFull: Degus--Behavior--Ecology--Mathematical models
        Type: general
    Titles:
      – TitleFull: Unified Mathematical Modeling, Analysis and Simulation of COVID-19 and Ecological Processes
        Type: main
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          Name:
            NameFull: Derrick, Jacob
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          Dates:
            – D: 01
              M: 08
              Type: published
              Y: 2025
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