An　epidemic　model　with　the　saturated　incidence　rate　and　the　environmental　fluctuations　is　investigated　in　this　paper.　We　study　the　extinction　and　the　persistence　in　the　mean,　and　stationary　distribution　of　the　solution　as　well.　By　contradiction,　we　firstly　show　that　stochastic　epidemic　model　admits　a　unique　global　positive　solution　for　any　given　positive　initial　value.　Further,　when　R˜0>1　is　valid,　we　derive　the　persistence　in　the　mean,　and　also　prove　the　existence　of　an　ergodic　stationary　distribution　by　constructing　moderate　functions.　By　comparison　theorem　of　stochastic　differential　equations　and　properties　of　inequalities,　the　extinction　of　the　solution　is　finally　derived　when　R0<1　and　ν<0　hold,　where　ν　indicates　the　exponential　rate　for　decline.　Meanwhile,　the　distribution　for　the　density　of　the　susceptible　is　estimated.　As　a　consequence,　numerical　simulations　and　illustrative　examples　are　separately　carried　out　to　support　the　main　results　of　this　paper.　©　2022　Elsevier　B.V.