Committee Chair

Wang, Jin

Committee Member

Kong, Lingju; Ledoan, Andrew; Yu, Liang

Department

Dept. of Mathematics

College

College of Engineering and Computer Science

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

We propose multiple models to investigate the transmission dynamics of cholera. At first, we consider the intrinsic growth of cholera bacteria in cholera transmission and find that the regular threshold dynamics take place if the intrinsic growth is logistic; there are multiple endemic equilibria if the growth exhibits Allee effects, which may lead to backward bifurcation and forward hysteresis. In addition, we introduce a multi-scale modeling framework. At the population level, a Susceptible-Infected-Recovered (SIR) model for the between-host transmission of cholera is employed. At the individual host level, the evolution of the pathogen within the human body is incorporated. The between-host and within-host dynamics are connected through an environmental equation that characterizes the growth of the pathogen and its interaction with the hosts outside the human body. We put a special emphasis on the within-host dynamics by making a distinction for each individual host. We conduct both mathematical analysis and numerical simulation for the model in order to explore various scenarios associated with cholera transmission and to better understand the complex, multi-scale disease dynamics. Finally, we analyze the impact of available medical resources on cholera transmission by taking a realistic case: Yemen cholera outbreak during 2017-2018. By fitting our simulation results to the epidemic data published by the World Health Organization (WHO), we find that different levels of disease prevalence and severity are linked to different geographical regions in this country and that cholera prevention and intervention efforts should be implemented strategically with respect to these regions in Yemen.

Acknowledgments

I am grateful to the Department of Mathematics and the College of Engineering and Computer Science of the University of Tennessee at Chattanooga for the support they always provide to me. I would like to express my great appreciation to my supervisor, professor Jin Wang, for his continued concern and advice throughout the research process and I also offer my sincere thanks to each of my graduate committee members for their valuable suggestions and help.

Degree

Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.

Date

8-2020

Subject

Cholera--Transmission; Mathematical models

Keyword

cholera transmission dynamics; Mathematical modeling

Document Type

Doctoral dissertations

DCMI Type

Text

Extent

xi, 96 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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