In　this　paper,　we　consider　an　SIRS　epidemic　model　with　vaccination　on　heterogeneous　networks.　By　constructing　suitable　Lyapunov　functions,　global　stability　of　the　disease-free　equilibrium　and　the　endemic　equilibrium　of　the　model　is　investigated.　Also　we　firstly　study　an　optimally　controlled　SIRS　epidemic　model　on　complex　networks.　We　show　that　an　optimal　control　exists　for　the　control　problem.　Finally　some　examples　are　presented　to　show　the　global　stability　and　the　efficiency　of　this　optimal　control.　These　results　can　help　in　adopting　pragmatic　treatment　upon　diseases　in　structured　populations.　(C)　2014　Elsevier　B.V.　All　rights　reserved.