Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

My research develops and analyzes ODE-based within-host models at multiple scales. Using dynamical systems theory and numerical methods, I study host–pathogen interactions and immune responses, providing insights into disease dynamics and control. The first model describes the complex dynamics of Hepatitis B virus (HBV) infection and addresses the question: what mechanisms determine whether the infection is cleared during the acute phase or progresses to a chronic state? A key feature of this model is the assumption that all classes of liver cells (uninfected, infected, and protected from reinfection) proliferate at different rates. The findings provide insight into two important aspects of HBV infection dynamics. First, they reveal that viral clearance within the bistable region depends on the infection process, specifically the initial viral inoculum (initial viral load). Second, they help explain why HBV infection during infancy and childhood, when the immune system is still developing, often leads to chronic disease. The second model examines the dynamics of sequential infection. For many diseases, there is considerable viral diversity, with multiple lineages circulating in the target population. At various times after primary infection, sequential infection can occur. Here, a simple model is introduced that presents a balance between two distinct adaptive immune responses: cross-reactive antibodies derived from preexisting immunity and specific antibodies generated during secondary infection. The results suggest that cross-reactive ($C$) antibodies dominate the adaptive ($A$) immune response when viral strains are similar, even if the initial cross-reactive response is small; thus, the waning period does not significantly affect the ratio $A:C$. However, the waning period and antigenic similarity both influence viral production and host damage (with the greatest effects when the initial cross-reactive response is large and viruses are dissimilar). Moreover, adaptive immunity lowers disease severity, while a higher pathogen growth rate increases it, showing that disease outcomes depend on both immune responses and pathogen traits. Sequential infections with antigenically similar strains may also limit the diversity of the immune response, highlighting the importance of immune imprinting for effective protection during an epidemic.

Date

2-6-2026

DOI

https://proquest.com/docview/3347820550

First Committee Chair

Hayriye Gulbudak

First Committee Member

Anna Jolles

Second Committee Member

Cameron Browne

Third Committee Member

Stanca Ciupe

Fourth Committee Member

Xiang-Sheng Wang

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