A cholera transmission model incorporating water-borne and horizontal transmissions as well as infectivity of deceased individuals is formulated and studied. The model also describes an imperfect and waning vaccination. Global stability of the disease-free equilibrium is proved when the basic reproduction number is less than one. It is also proved that there are bistable situations, where when the vaccination reproduction number is less than one, there are two endemic equilibria, although it is shown numerically that the region where this occurs is small. The computational analysis also considers the local asymptotic stability of endemic equilibria and the interplay between vaccination strategy, vaccine efficacy and waning.