A　stochastic　susceptible–infected–vaccinated　model　with　a　general　incidence　rate　and　varying　population　size　is　considered　in　this　paper.　By　means　of　constructing　a　suitable　Lyapunov　function,　the　sufficient　conditions　for　the　extinction　are　derived.　Further,　some　conditions　that　guarantee　the　existence　of　a　unique　stationary　distribution　is　obtained.　The　main　results　are　illustrated　by　computer　simulations.　©　2019　Elsevier　B.V.