Landspeed? Then you rule out the aid of African swallows. With that speed, one would suspect Acme roller skates. :)
Speaking of the effects of newly introduced diseases, here's an interesting read: Spanish Conquest. Excerpt: Unknown to the Aztecs the Spanish had an invisible advantage. Apparently, one Spaniard soldiers was infected with the smallpox virus. Within two weeks the disease infected the Aztec Empire and one forth of the population died.