In this paper we investigate the positivity and boundednessof the solu-tion of a stochastic seasonal epidemic model for the respiratory syncytialvirus(RSV). The stochasticity in the model is due to fluctuating physicaland social environments and is introduced by perturbing thetransmissionparameter of the seasonal disease. We show the existence anduniquenessof the positive solution of the stochastic seasonal epidemic model whichis required in the modeling of populations since all populations must bepositive from a biological point of view. In addition, the positivity andboundedness of solutions is important to other nonlinear models that arisein sciences and engineering. Numerical simulations of the stochastic modelare performed using the Milstein numerical scheme and are included tosupport our analytic results.