The　bumpless　transfer　(BT)　control　issue　for　switched　positive　systems　(SPSs)　with　dissipativity　is　investigated　in　this　brief.　The　aim　is　to　achieve　dissipativity　of　the　SPSs　while　cutting　down　the　unwanted　big　jumps　of　control　input　at　switching　points.　The　alleviation　level　of　the　control　input　jumps　is　described　by　the　BT　performance.　By　the　multi-linear　copositive　storage　functions　methods,　the　switching　laws　and　controllers　are　designed　to　solve　the　dissipativity-based　BT　control　issue　of　SPSs　in　continuous-time　and　discrete-time.　Under　the　established　controllers　and　switching　logics,　subsystems　are　permitted　not　to　ensure　the　dissipativity　as　well　as　the　BT　performance.　Finally,　a　simulation　case　study　of　muscle　relaxants　in　surgery　reveals　the　superiority　of　the　provided　control　method.