We formulate a stochastic differential equation(SDE) model from a deterministic model of imperfect vaccination building on a recent analytical approach of Allen et al [5] 81(2):487-515, 2020. https://doi.org/10.1007/s00285-020-01516-8), which derivation procedure is based on the elementary events occurring during the epidemiological dynamics and their corresponding probabilities. We prove the global existence of a unique weak non-negative solution starting from the non-negative initial value of the formulated model. We compute the conditions under which extinction and persistence in mean hold, and illustrate our theoretical results using numerical simulations. Determining the stochastic outcome of epidemiological dynamics under imperfect vaccination is important to optimize vaccination campaigns.
