The　question　as　to　how　traffic　or　transportation　processes　on　complex　networks　can　shape　the　dynamics　of　epidemic　spreading　is　of　great　interest　for　a　number　of　areas.　We　study　traffic-driven　epidemic　spreading　on　networks　of　mobile　agents　by　incorporating　two　routing　strategies:　random　and　greedy.　We　find　that　for　the　case　of　infinite　agent　delivery　capacity,　increasing　the　moving　velocity　has　opposite　effects　on　the　outbreak　of　epidemic　spreading　for　the　two　routing　strategies.　However,　expanding　the　communication　range　among　agents　can　increase　the　transportation　efficiency　but　counterintuitively　suppress　epidemic　spreading.　For　finite　delivery　capacity,　the　emergence　of　traffic　congestion　can　effectively　inhibit　epidemic　spreading　for　both　routing　strategies.　We　provide　a　mean-field　theory　to　explain　the　numerical　findings.　Our　results　can　provide　insights　into　devising　effective　strategies　to　suppress　the　spreading　of　harmful　epidemics　on　time-varying　networks.　©　2012　Europhysics　Letters　Association.