There are a lot of ideas out there about transoceanic contact between the Old and New Worlds before Columbus. The Viking expedition in the 1000s seems to be pretty well established, but there are other theories generally considered fringe (Roman legions, Phoenecian trade routes, lost tribes of Israel - versions of the Solutrean hypothesis might fall into this category too depending on who you ask). An aspect of this that I don't often see discussed is that of epidemiology. We know that a main reason European colonization was so devastating was because indigenous groups didn't have immunity to Old World diseases like smallpox that are associated with herd animals. If a sizable population from the Old World had settled in or had extensive contact with the Americas before Columbus, one would expect them to have carried these highly infectious diseases with them, potentially causing an earlier epidemic and creating immunity in indigenous American groups. This to me seems like good prima facie evidence against prior sustained contact.
I have recently been wondering, though, about how far back this line of reasoning can go. Smallpox hasn't been around forever, and it didn't reach all of the Old World at once. My question is, for any given place of origin in the Old World, how far back would you have to go before that area did not have any of the diseases associated with post-Columbian epidemics (e.g. smallpox or any disease similar enough to confer immunity)? In other words, how recently could sustained contact have happened and there be no chance of it conferring immunity to indigenous populations of the Americas? For example, 12,000 BC would probably be too early since it's before many herd animals were domesticated.
I'm looking for either of two types of literature:
(1) Any literature that has directly addressed the question I've posed. The closest I have found is independent blog posts like this one discussing possible reasons for why Vikings didn't bring epidemic diseases (possible reasons given include low population density, lack of sustained contact, and that those diseases simply hadn't reached Iceland by the 1000s). I suspect that there isn't published literature on this because it's more of a long shot than just using archaeological evidence (or lack thereof), but since there are posts like the one I linked, I know I'm not the first person to think of it.
(2) Secondarily, any good overviews of the epidemiology of smallpox and its close relatives in the Old World (or the other diseases that Europeans brought and caused mass devastation). If someone were trying to write an article of type (1), this is the kind of data they would need.
We know that a main reason European colonization was so devastating was because indigenous groups didn't have immunity to Old World diseases like smallpox that are associated with herd animals.
You'll be interested in our FAQ on diseases in the Americas, as well as the answers on /u/anthropology_nerd's profile. While this idea has had substantial attention in the popular press, and is often picked up by authors in unrelated fields, it's never been well-received by people actually studying Contact period indigenous groups. To summarize, smallpox and other European diseases killed millions because policies of colonialism and genocide created environments in which they could thrive. Furthermore, numbers for deaths by disease are often distorted by the extrapolation of high death rates in urban area to entire regions, and by over-assigning disease. If one's lungs have been ruined by years of slaving away in the mines of Potosi, was it really pnuemonia that killed you?
The short answer, then, is that epidemiology cannot be used as such a tool because contact itself, even sustained, would not have necessarily resulted in the same sort of depopulation that occurred the 16th and 17th centuries. While, as noted in one of the FAQ answers, smallpox didn't reach Iceland until the 13th-century, there's no reason to think that, had it crossed to Canada, it would have caused any sort of epidemic meaningfully distinguishable from a local pathogen.