Award Date

5-1-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Committee Member

Rachidi Salako

Second Committee Member

Hossein Tehrani

Third Committee Member

Monika Neda

Fourth Committee Member

Paul Schulte

Number of Pages

100

Abstract

Infectious diseases are a great challenge to the health and successful function of society. Therefore, it becomes crucial to develop methods and tools that would allow us to be able to control an infectious disease once it starts spreading within an environment. In this regard, mathematical research on epidemic models has provided important tools in the qualitative and quantitative analysis of the spread and control of infectious diseases. Each mathematical epidemic model incorporates important factors that could affect the spread of a disease, such as population movement and temporal or environmental heterogeneity.

This dissertation focuses on a susceptible-infected-susceptible (SIS) model in the form of a system of diffusive partial differential equations that takes into account a moving population within a spatially heterogeneous environment. Our goal is to assess the effectiveness of disease control strategies aimed at restricting population movement. To this end, we first consider basic fundamental questions such as existence, uniqueness, and global stability of solutions to the model. Next, we discuss how population movement may affect the disease dynamics by looking at the asymptotic profiles of endemic equilibrium (EE) solutions of the model. Consequently, we determine conditions leading to a multiplicity of EE solutions, which demonstrate that the disease can become difficult to control when movement is included in the model. In doing so, we discover various bifurcation curves describing multiple EE solutions for the diffusive SIS epidemic model.

Keywords

Asymptotic Profiles; Diffusive Epidemic Model; Large-Time Behavior; Reaction-Diffusion System

Disciplines

Applied Mathematics | Mathematics

File Format

pdf

File Size

15300 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

Available for download on Saturday, May 15, 2027


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