Cholera, as an epidemic disease is usually transmitted through eating food or drinking water contaminated with a bacterium called Vibrio cholerae. Despite the advances made in understanding this disease and its treatment, cholera continues to be a major public health problem in many countries. In this paper, we propose a mathematical model susceptible-symptomatic infected-asymptomatic infected-removed-bacteria incorporating both water treatment and vaccination as the control strategies to study the dynamic of cholera epidemic. The basic reproduction number of the formulated model is derived, existence, uniqueness and stability conditions of the model are verified and checked. Numerical simulation is carried using least square method to estimate the model parameters. Different rates of vaccination on susceptible and infected individuals over time are used and discussed in details. The results indicate that the estimates of model parameters are indeed close to the true parameter values. Also, it is observed that both water treatment and vaccination are very effective strategies to the control of cholera epidemic as they lead to high reduction of cholera infected individuals.

cholera, mathematical modeling, stability condition, least square method, vaccination.