ORCID Identifier(s)

0000-0001-5186-3015

Graduation Semester and Year

2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Benito Chen-Charpentier

Abstract

Wound healing encompasses a group of processes categorized into overlapping stages known as the inflammation, proliferation, and maturation/remodeling stage. The dynamics of these processes are important in studying outcomes of wound care and determining factors that contribute to certain wound outcomes. A system of ordinary differential equations is constructed for the inflammation, proliferation, and remodeling stage. Parameter sets for this model are investigated based on output dynamics according to the literature and based on experimental data. A bifurcation analysis is conducted to determine sudden changes that can occur in the inflammation system. Fourier Amplitude Sensitivity Test (FAST) is implemented to investigate sensitivity in regard to each mechanism considered. Next, the system is turned into a stochastic differential equation to analyze possible realizations that result from biological random fluctuations.

Keywords

Immune system, Ordinary differential equations, Global sensitivity analysis, Inflammation, Proliferation, Stochastic differential equations, Collagen, Macrophages

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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