| Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. Mathematical models play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. This dissertation is concerned with mathematical modeling and analysis of cholera dynamics. First, we study an autonomous model in a homogeneous environment with added controls that involves both direct and indirect transmission pathways. We conduct a careful equilibrium analysis and, in particular, investigate the threshold dynamics of this model. Next, we propose a general multi-group model for cholera dynamics that incorporates spatial heterogeneity and dispersal. Under biologically feasible conditions, we show that the basic reproduction number R 0 remains a sharp threshold for cholera dynamics in multi-group settings. We verify the analysis by numerical simulation results. Then, we propose a deterministic compartmental model for cholera dynamics in time-periodic environments. The model incorporates seasonal variation into a general formulation for the incidence (or, force of infection) and the pathogen concentration. The basic reproduction number of the periodic model is derived, based on which a careful analysis is conducted on the epidemic and endemic dynamics of cholera. Several specific examples are presented to demonstrate this general model, and numerical simulation results are used to validate the analytical prediction. Finally, we extend the general multi-group cholera model to a periodic environment. |
