There is evidence that syphillis came from the Americas. There is evidence it was introduced to the Americas by Europeans. One problem is that it's hard to distinguish teritiary syphillis from tuberculosis or leprosy on bones.
As for Borreliosis, there are many variants of it endemic to Europe and spread by ticks. No evidence that it came from the Americas.
My understanding is that if the tick was only a vector between two humans (for instance, malaria isn't a zoonosis, because the mosquito is just transmitting the disease between humans), then it would not be a zoonosis. But in most cases with Lyme disease, the tick is actually transmitting the disease from another animal to a human, therefore it is indeed a zoonosis.[1]
There's quite a lot of debate over the precise origins of syphilis. I'm only peripherally familiar with the literature, but my understanding is that recent work suggests (but not concludes) that it might have been endemic to afroeurasia rather than or as well as the Americas. Lyme disease is indeed wholly American, but it's not epidemic or even particularly mortal.
I'm surprised that paper got published, considering the basic spelling errors ("jaws" for "yaws") and errors of fact ("Española Island…a part of the Galápagos Islands").
There are several islands in the world that have had the name Española. The one that is relevant to the discussion about syphilis is now more commonly known as Hispanola, home to Haiti and the Dominican Republic. Columbus visited in 1492/3 and supposedly brought back Syphilis in 1493. The Galapagos islands are in the Pacific, and were never visited by Columbus.
Ah, yeah that make sense. I just looked at the immediate sentence, rather than question which island it referred to. I'm assuming that's the cause for the error too - just someone wanting to reference location and popping the name into Google -, though it's certainly a much more serious error than the spelling mistake.
Aren't syphilis and Lyme disease of New World origin?