Keywords

Mathematical Epidemic Models, Total Infectious Contacts, Final Size Relation, Optimal Control Strategies, Multi-patch Models, Turing Instability

Abstract

Heterogeneity, influenced by diverse factors such as age, gender, immunity, behavior, and spatial distribution, plays a critical role in the dynamics of infectious disease transmission. Discrete mathematical structures, including matrices and graphs, can offer effective tools for modeling the interactions among these diverse factors, resulting heterogeneous epidemiological models. This dissertation explores analytical approaches, specifically utilizing eigenvalues and eigenvectors of discrete structures, to characterize heterogeneity within mathematical models of infectious diseases. Theoretical results, along with numerical simulations, enhance our understanding of heterogeneous epidemiological processes and their significant implications for disease control strategies.

In this dissertation, we introduce a unified approach to establish the final size formula in heterogeneous epidemic models, based on a new concept of “total infectious contacts” as an eigenvector-based aggregation of disease compartments. This approach allows us to identify the peak of total infectious contacts, offering a novel method to pinpoint the turning point of a disease outbreak. Furthermore, we examine spatial heterogeneity through two distinct mathematical frameworks: the Lagrangian and Eulerian models. The Lagrangian model assesses the epidemiological consequences of spatio-temporal residence time matrices, while the Eulerian model investigates “Turing instability” as a new underlying mechanism for spatial heterogeneity observed in disease prevalence data.

Completion Date

2024

Semester

Summer

Committee Chair

Shuai, Zhisheng

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Format

application/pdf

Release Date

8-15-2024

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Campus Location

Orlando (Main) Campus

Accessibility Status

Meets minimum standards for ETDs/HUTs

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