Mathematical Models and Stability Analysis of Cholera Dynamics

<p>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 <em>et al.</em> [60] in 2010. We formally derive the basic reproduction number <em>R</em>0 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.</p>

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics & Statistics

Year dc:date.available

2010

Author dc:creator

• Liao, Shu

Contributors dc:contributor

• Jin Wang
• John Adam
• Yan Peng
• Holly D. Gaff

• Cholera
• Disease-free
• Endemic equilibrium
• Epidemic
• Reproduction number
• Stability
• Applied Mathematics

Statement dc:rights

• <p>In Copyright. URI: <a href="http://rightsstatements.org/vocab/InC/1.0/">http://rightsstatements.org/vocab/InC/1.0/</a> This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).</p>

Identifier

9781124458663

OAI identifier oai:identifier

oai:digitalcommons.odu.edu:mathstat_etds-1032