Committee Chair

Wang, Jin

Committee Member

Kong, Lingju; Nichols, Roger; Belinskiy, Boris

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

Cholera is an acute intestinal illness caused by infection with the Vibrio cholerae bacteria. The dynamics of the disease transmission are governed by human-human, environment-human, and within-human sub-dynamics. In this paper, a model is presented to incorporate all three of these dynamical components. The model is divided into three subgroups where the dynamics are analyzed according to their respective time scales. Specifically, the within host system incorporates the interaction of virus and immune cell interaction with the vibrios. For each subgroup, we discuss the existence and uniqueness of a DFE (Disease Free Equilibrium) by calculation of the Basic Reproduction number R_0, when applicable, and the existence and uniqueness of a positive EE (Endemic Equilibrium) solution. We also discuss the conditions needed to achieve local and global stability in each system. Finally, we combine the three smaller models together and discuss the existence and uniqueness of a DFE and EE for the full system.

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

8-2018

Subject

Cholera -- Mathematical models

Keyword

Epidemiology; Cholera; Dynamical systems; Differential equations; Mathematical modeling; Disease dynamics

Document Type

Masters theses

Extent

viii, 48 leaves

Language

English

Rights

Under copyright.

License

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

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