Despite　extensive　work　on　traffic　dynamics　and　epidemic　spreading　on　complex　networks,　the　interplay　between　these　two　types　of　dynamical　processes　has　not　received　adequate　attention.　We　study　the　effect　of　local-routing-based　traffic　dynamics　on　epidemic　spreading.　For　the　case　of　unbounded　node-delivery　capacity,　where　the　traffic　is　free　of　congestion,　we　obtain　analytic　and　numerical　results　indicating　that　the　epidemic　threshold　can　be　maximized　by　an　optimal　routing　protocol.　This　means　that　epidemic　spreading　can　be　effectively　controlled　by　local　traffic　dynamics.　For　the　case　of　bounded　delivery　capacity,　numerical　results　and　qualitative　arguments　suggest　that　traffic　congestion　can　suppress　epidemic　spreading.　Our　results　provide　quantitative　insight　into　the　nontrivial　role　of　traffic　dynamics　associated　with　a　local-routing　scheme　in　the　epidemic　spreading.