Date of Award
Doctor of Philosophy (PhD)
Mathematics and Statistics
Computational and Applied Mathematics
Holly D. Gaff
In this dissertation, we present a careful mathematical study of several epidemic cholera models, including the model of Codeco  in 2001, that of Hartley, Morris and Smith  in 2006, and that of Mukandavire, Liao, Wang and Gaff et al.  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.
"Mathematical Models and Stability Analysis of Cholera Dynamics"
(2010). Doctor of Philosophy (PhD), dissertation, Mathematics and Statistics, Old Dominion University, DOI: 10.25777/bawd-5d35