Parameter values are usually assumed to be precisely known in many epidemic models but they could be imprecise due to various uncertainties. In this paper, we develop a stochastic SIRS model that includes imprecise parameters and white noise, formulate and analyze the near-optimal control problem for the stochastic model. We obtain priori estimates of the susceptible, infected and recovered populations. Sufficient and necessary conditions for the near optimality of the model are established using Ekeland's principle and a nearly maximum condition on the Hamiltonian function. Numerical simulations are also performed to demonstrate the analytical results and evaluate the influence of imprecise parameters, white noise and treatment control on the dynamics of epidemics.