Among Europeans, when it first arrived from the American, syphilis outbreaks was far more virulent than it is today, with a mortality rate of 80% to 90%. But it didn't kill that many people in the Old World, because the Europeans, and the rest of the inhabitants of the Old World, managed to be incredibly lucky IOTL- the disease was carried back to Europe from Guyana solely by the survivors among the original 30 crew members on a single vessel in Columbus' fleet, Martín Alonso Pinzón's Pinta, who'd travelled there during his 3rd Voyage. And even then, the disease is known to have caused as many as five million deaths across Europe during the original epidemics- wiping out 1/12th of the European population at the time.
Now, imagine what would have happened if the Native Americans had carried the disease to Europe with them. In particular, what if Columbus and his crew had brought Taino captives carrying the disease back to Europe with them on the return leg of his 3rd Voyage? Columbus enslaved five hundred and sixty people on the the island of Dominica during his 2nd voyage IOTL, and shipped all the slaves were shipped to Spain, with 360 slaves surviving the trip. Columbus also allowed settlers to return to their homeland with any Indian women with whom they had started families, or who they'd kidnapped and claimed slave ownership of. But IOTL, Columbus only explored the coastline of Guyana in passing; only one or two crew members made landfall in this region.
So what if, in an alternate timeline (ATL), Columbus had instead elected to establish a fortified settlement here on the mainland of the newly discovered continent of South America, in either the Orinoco or Essequibo Delta, raided the region for slaves, and subsequently taken them back to Spain and Italy on his return to Europe, in similar numbers to the slaves he'd brought back on his 2nd voyage? In this scenario, you'd easily be looking at ten to twenty times as many infected individuals carrying the disease back to Medieval Europe to create the original epidemics. And IOTL, all of the original carriers of the disease to Europe were European natives who lacked any immunity to the disease whatsoever, the vast majority of whom undoubtedly swiftly died before they were able to pass it on to too many people. With the imported Taino slaves, who'd been natives of the disease's region of origin, forming the majority of the source carriers in Europe ITTL, and in numbers comparable to Cortes' expeditionary force IOTL, then they'd be able to carry the disease as far into Europe as they could go.
Europe's superior transport infrastructure would also have facilitated a far swifter, more devastating transmission of the Syphilis epidemics far and wide. IMHO, in this ATL, we could well be looking at a total population collapse in Europe- and indeed, across the Old World in general- which would make that caused by the Black Death which preceded it (and indeed is still rampant in many regions even at this late stage, which would further exacerbate the Syphilis outbreaks) pale in comparison. In this timeline, the Old World Syphilis epidemics could be just as devastating for the natives of the Old World as the Smallpox epidemics were for the natives of the New World IOTL, with as much as 80% (representing roughly a sixfold increase on the death rates in Europe IOTL's first epidemics) of the European population (who'd be by far the worst hit) dying as a result- with a mere 12 million Europeans surviving the syphilis epidemics. For comparison, this would be roughly equivalent to the population of every single European kingdom in existence besides those of Italy being wiped out by 1600.
As such, the native Europeans may well be devastated beyond all hopes of recovery- and without support and reinforcements from Spain and Portugal, the short-lived settlements in the Caribbean would almost certainly soon be overrun by the Taino chiefdoms. After all, Columbus had already introduced the most important European innovations, such as writing, education, metallurgy, mining, shipbuilding and gunpowder weaponry; ITTL, the disruption would mean that the arrival of smallpox in the Americas may be delayed for centuries, and prior to its arrival, the total Western, Classic and Eastern Taino populations across the Caribbeam still numbered roughly 8 million. The cruel practices by in place by Columbus on his 2nd voyage, prior to the point of divergence (POD) had stated that each adult over 14 years of age was expected to deliver a hawks' bell full of gold every three months, or when this was lacking, twenty-five pounds of spun cotton. If this tribute was not brought, the Spanish cut off the hands of the Taíno and left them to bleed to death.
This soon inspired many revolts by the Taíno and campaigns against the Spanish IOTL, many of which were successful. In this timeline, the Taino would overthrow the crippled, helpless Spaniards, reassert their control over the region and integrate the surviving Spaniards along with their mixed-race hidalgo children swiftly enough. 1514 census records reveal that 40% of Spanish men on the island of Hispaniola had Taíno wives IOTL, and evidence also suggests that some Taíno women and imported African slaves inter-married and lived in relatively isolated Maroon communities in the interior regions of the Greater Antilles, evolving into a hybrid rural population with little or no interference from the Spanish authorities.
In this timeline, these hybrid creole Taino populations should have by far the easiest time recovering from the devastation of both the Old World and New World disease epidemics, since they'd have inherited the native populations' levels of genetic immunity to both; and IMHO, this Taino civilisation, uplifted and toughened markedly by their brief interchange with the European Spaniards, as the only civilisation in the Americas to have acquired knowledge of both the requisite navigational technology and of the passage across the Atlantic to Europe (and hence to Africa), would be by far the best candidate to send an expedition to Europe. What state would Europe and the rest of the Old World be in by the time they're ready to do so- one of recovery, or still reeling in disarray from the societal collapse? And who would end up colonising who ITTL?