This paper provides a rigorous mathematical and sensitivity analysis on the cholera epidemic model with vaccination. The model consists of six system of nonlinearly differential equation. The basic properties of the model for positivity of solutions were investigated which the solution S t  , E t  , I t  , V t  , R t  and P t  are found to be nonnegative for t  0 . Existence and uniqueness of the model reveals that there exist a unique solution which is bounded and continuous in region D . The theoretical analysis of the model reveals that cholera will dies out whenever the threshold quantity R0 is less than unity and it will persists in the community if otherwise The sensitivity analysis was performed around the baseline parameter value. The result shows that the contact rate in human 1 with the value 0.6868, and the shedding rate  with the value 0.5901 are the most sensitive parameter that influenced the threshold quantity R0 . Furthermore it was observed that any increase in the following parameter 2   results in the increase of R0 . Similarly, increase in the following parameter  1  2   1  decrease the threshold quantity R0 . The numerical simulation using an arbitrary set of parameter values were carried out and plotted in which the results for sensitivity analysis and threshold criterion were found to be in agreement with analytical results shown in Table 3 and Theorem 2.

Keywords : Cholera epidemic Model; differential equation; sensitivity analysis; threshold quantity; Vaccination.