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Native Americans and (European) Diseases
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Many diseases of the Old World were originally contracted from livestock. Think of the Swine Flu and Bird Flu in recent years. The Native Americans did not practice animal husbandry and didn't have diseases to transfer over. However, there is strong evidence that syphilis existed in the New World prior to Columbian first contact, but the evidence of it existing in Europe is inconclusive. It is, in my view, likely that it spread from the New to the Old world. The first major outbreak of the disease was reported in 1495 in Italy.
http://www.livescience.com/40885-syphilis-origin-mystery.html