In　this　paper,　we　consider　a　stochastic　SIRS　model　with　parameter　perturbation,　which　is　a　standard　technique　in　modeling　population　dynamics.　In　our　model,　the　disease　transmission　coefficient　and　the　removal　rates　are　all　affected　by　noise.　We　show　that　the　stochastic　model　has　a　unique　positive　solution　as　is　essential　in　any　population　model.　Then　we　establish　conditions　for　extinction　or　persistence　of　the　infectious　disease.　When　the　infective　part　is　forced　to　expire,　the　susceptible　part　converges　weakly　to　an　inverse-gamma　distribution　with　explicit　shape　and　scale　parameters.　In　case　of　persistence,　by　new　stochastic　Lyapunov　functions,　we　show　the　ergodic　property　and　positive　recurrence　of　the　stochastic　model.　We　also　derive　the　an　estimate　for　the　mean　of　the　stationary　distribution.　The　analytical　results　are　all　verified　by　computer　simulations,　including　examples　based　on　experiments　in　laboratory　populations　of　mice.