Cholera is a waterborne intestinal infection which causes profuse, watery diarrhea, vomiting, and dehydration. It can be transmitted via contaminated water as well as person to person, with 3-5 million cases/ year and over 100,000 deaths/year. A major public health question involves understanding the modes of cholera transmission in order to improve control and prevention strategies. One issue of interest is: given data for an outbreak, can we determine the role and relative importance of waterborne vs. person-to-person routes of transmission? To examine this issue, we explored the identifiability and parameter estimation of a differential equation model of cholera transmission dynamics. We used a computational algebra approach to establish whether it is possible to determine the transmission rates from outbreak case data (i.e. whether the transmission rates are identifiable), and then applied the model to a recent cholera outbreak in Angola which resulted in over 80,000 cases and over 3000 deaths. Our results show that both water and person-to-person transmission routes are identifiable, although they become practically unidentifiable with fast water dynamics. Using these results, parameter estimation for the Angola outbreak suggests that both water and person-to-person transmission are needed to explain the observed cholera dynamics. I will also discuss some ongoing work using this model, including modeling the spatial spread of outbreaks, public health interventions and control strategies, and applications to the ongoing cholera outbreak in Haiti.