A　stochastic　susceptible–exposed–infected–recovered　(SEIR)　model　with　nonlinear　incidence　rate　is　investigated.　Under　suitable　conditions,　existence　and　uniqueness　of　a　global　solution,　stationary　distribution　with　ergodicity,　persistence　in　the　mean,　and　extinction　of　the　disease　are　obtained.　Numerical　simulations　and　conclusions　are　separately　carried　out　at　the　end　of　this　paper.　©　2020,　The　Author(s).