In　this　paper,　an　SIR　epidemic　model　considering　hospital　resources　and　vaccination　is　established　and　the　rich　dynamics　and　complex　bifurcations　are　investigated.　Firstly,　the　existence　of　disease-free　equilibrium　and　endemic　equilibria　is　explored.　It　is　founded　that　when　the　vaccination　rate　is　not　high,　the　number　of　endemic　equilibrium　points　changed　easily　with　the　number　of　hospital　resources　and　vaccination,　resulting　in　transcritical　bifurcation　and　saddle–node　bifurcations.　Secondly,　different　types　singularities　such　as　degenerate　saddle–node　of　codimension　1　at　the　disease-free　equilibrium,　and　cusp　or　focus　type　Bogdanov–Takens　singularities　of　codimension　3　at　endemic　equilibria　are　presented.　Thirdly,　bifurcation　analysis　at　these　equilibria　is　investigated,　and　it　is　found　that　the　system　undergoes　a　sequence　of　bifurcations,　including　Hopf,　degenerate　Hopf　bifurcation,　homoclinic　bifurcation,　the　cusp　type　Bogdanov–Takens　bifurcation　of　codimension　2,　and　the　focus　type　Bogdanov–Takens　bifurcation　of　codimension　3　which　are　the　organizing　centers　for　a　series　of　bifurcations　with　lower　codimension.　And　the　system　shows　very　rich　dynamics　such　as　the　existence　of　multiple　coexistent　periodic　orbits,　homoclinic　loops.　Finally,　numerical　simulations　are　presented　to　verify　the　theoretical　results.　©　2023　The　Author(s)