Date of Award

Winter 2010

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics & Statistics

Program/Concentration

Computational and Applied Mathematics

Committee Director

Jin Wang

Committee Member

John Adam

Committee Member

Yan Peng

Committee Member

Holly D. Gaff

Abstract

In this dissertation, we present a careful mathematical study of several epidemic cholera models, including the model of Codeco [11] in 2001, that of Hartley, Morris and Smith [22] in 2006, and that of Mukandavire, Liao, Wang and Gaff et al. [60] in 2010. We formally derive the basic reproduction number R0 for each model by computing the spectral radius of the next generation matrix. We focus our attention on the stability analysis at the disease-free equilibrium which determines the short-term epidemic behavior, and the endemic equilibrium which determines the long-term disease dynamics. Particularly, we incorporate the Volterra-Lyapunov matrix theory into Lyapunov functions to facilitate the analysis of the global endemic stability. Based on the previous cholera models, we propose a new and unified deterministic model which incorporates a general incidence rate and a general formulation of the pathogen concentration, to improve our understanding of cholera dynamics. In addition, we briefly discuss the changes of the dynamics for the cholera models when several control measures are incorporated.

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DOI

10.25777/bawd-5d35

ISBN

9781124458663

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