Graduation Semester and Year
Summer 2024
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Hristo Kojouharov
Second Advisor
Jianzhong Su
Third Advisor
Souvik Roy
Fourth Advisor
Gaik Ambartsoumian
Abstract
The proposed mathematical biology research utilizes mathematical models to gain insight into biological systems. These systems of ordinary differential equations model diverse topics, ranging from gut microbiomes to harmful algal blooms. A complete stability analysis, supporting phase plane portraits, bifurcation diagrams, and numerical simulations will accompany the models presented. In Chapter 2, the murine gut microbiome is modeled to match laboratory experiments in the literature. In these experiments, mice eat plasmid-carrying “donor” bacteria and naturally carry plasmid-free “resident” bacteria in their gut. The models aim to capture the behavior of plasmids, donor bacteria, and resident bacteria. Chapter 3 explores dormancy and its impact on the population dynamics of microorganisms across different environments. Dormancy is a state of reduced metabolic activity that enables dormancy-capable organisms to survive unfavorable or harsh conditions. Each of the three dormancy models presented concerns a select combination of these topics: the murine gut microbiome, golden algae, nutrient recycling, batch cultures, and chemostats. Lastly, Chapter 4 provides a biological interpretation of the theoretical results and situates each model in context with others found here and in recent mathematical and scientific literature.
Keywords
ODE, model, plasmid, gut microbiome, dormancy, nutrient recycling, stability, simulation
Disciplines
Applied Mathematics | Ecology and Evolutionary Biology | Microbiology
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Mendez, Ana C., "Batch Culture Models of the Murine Gut Microbiome & The Impact of Simple Dormancy on Dormancy-Capable Microorganisms Models" (2024). Mathematics Dissertations. 161.
https://mavmatrix.uta.edu/math_dissertations/161
Included in
Applied Mathematics Commons, Ecology and Evolutionary Biology Commons, Microbiology Commons