Abstract

Since the work of John Snow, scientists and medical professionals have understood that individuals develop cholera by means of consuming contaminated water. Despite the knowledge of cholera's route of infection, many countries have experienced and still experience endemic cholera. Cholera is caused by the Vibrio cholerae (V. cholerae) bacterium and presents with acute diarrhea and vomiting. If untreated, infected individuals may die due to dehydration. Cholera is a disease that most commonly affects countries with poor infrastructure and water sanitation. Despite efforts to control cholera in such countries, the disease persists. One such example is Haiti which has been experiencing a cholera outbreak since 2010. While there has been much research in the field of microbiology to understand V. cholerae, there has been comparably less research in the field of mathematical biology to understand the dynamics of V. cholerae in the environment. A mathematical model of V. cholerae incorporating a phage population is coupled with a SIRS disease model to examine the impact of vibrio and phage interaction. It is shown that there might exist two endemic equilibria, besides the disease free equilibrium: one in which phage persist in the environment and one in which the phage fail to persist. Existence and stability of these equilibria are established. Disease control strategies based on vibrio and phage interactions are discussed.

Notes

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Graduation Date

2019

Semester

Summer

Advisor

Shuai, Zhisheng

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematical Science

Format

application/pdf

Identifier

CFE0007604

URL

http://purl.fcla.edu/fcla/etd/CFE0007604

Language

English

Release Date

8-15-2019

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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