We　introduce　the　stochasticity　into　a　deterministic　model　which　has　state　variables　susceptible–exposed–infected　with　varying　population　size　in　this　paper.　The　infected　individuals　could　return　into　susceptible　compartment　after　recovering.　We　show　that　the　stochastic　model　possesses　a　unique　global　solution　under　building　up　a　suitable　Lyapunov　function　and　using　generalized　Itô’s　formula.　The　densities　of　the　exposed　and　infected　tend　to　extinction　when　some　conditions　are　being　valid.　Moreover,　the　conditions　of　persistence　to　a　global　solution　are　derived　when　the　parameters　are　subject　to　some　simple　criteria.　The　stochastic　model　admits　a　stationary　distribution　around　the　endemic　equilibrium,　which　means　that　the　disease　will　prevail.　To　check　the　validity　of　the　main　results,　numerical　simulations　are　demonstrated　as　end　of　this　contribution.　©　2016　Elsevier　B.V.