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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Liao, Shu"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Jin Wang","John Adam","Yan Peng","Holly D. Gaff"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T03:34:53Z","subjects":["Cholera","Disease-free","Endemic equilibrium","Epidemic","Reproduction number","Stability","Applied Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ 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).
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"]},{"key":"dc:title","label":"Title","values":["Mathematical Models and Stability Analysis of Cholera Dynamics"]}]}],"canonical_facts":{"dc:contributor":["Jin Wang","John Adam","Yan Peng","Holly D. Gaff"],"dc:creator":["Liao, Shu"],"dc:date.available":["2019-06-06T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["9781124458663","https://digitalcommons.odu.edu/mathstat_etds/39"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ 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).
"],"dc:subject":["Cholera","Disease-free","Endemic equilibrium","Epidemic","Reproduction number","Stability","Applied Mathematics"],"dc:title":["Mathematical Models and Stability Analysis of Cholera Dynamics"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:34:53Z"}