Committee Chair

Wang, Jin

Committee Member

Kong, Lingju; Nichols, Roger; Bao, Feng

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

We propose two differential equation-based models to investigate the impact of awareness programs on cholera dynamics. The first model represents the disease transmission rates as decreasing functions of the number of awareness programs, whereas the second model divides the susceptible individuals into two distinct classes depending on their awareness/unawareness of the risk of infection. We study the essential dynamical properties of each model, using both analytical and numerical approaches. We find that the two models, though closely related, exhibit significantly different dynamical behaviors. Namely, the first model follows regular threshold dynamics while rich dynamical behaviors such as backward bifurcation may arise from the second one. Our results highlight the importance of validating key modeling assumptions in the development and selection of mathematical models toward practical application.

Acknowledgments

I would like to express my gratitude to my supervisor Jin Wang for the useful comments, remarks, and engagement through the learning process of this master thesis. Furthermore, I would like to thank my loved ones, who have supported me throughout the entire process, both by keeping me harmonious and helping me putting pieces together. I will be grateful forever for your love.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

8-2017

Subject

Cholera -- Mathematical models

Keyword

Cholera; Awareness program; Behavior change; Basic reproduction number; Threshold dynamics; Backward bifurcation

Document Type

Masters theses

Extent

vii, 28 leaves

Language

English

Rights

Under copyright.

License

http://creativecommons.org/licenses/by/3.0/

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