I don't think there would be many following interactions for hundreds of years. Europe would not be looking to explore, conquer, or trade with anyone as they would have just lost a third of their population (concentrated in the cities that would have provided the demand for goods from the New World and the mercantile/lesser noble class necessary to exploit these goods).
In the wake of the plague, you might get some crazy religious groups that decide to sail across the sea and make a go at survival in the Americas, but these colonies will probably not last long without the support of their home nations. If potatoes have been brought back, you might see these adopted during the plague out of desperation. Potatoes could allow Europe to bounce back in population much faster.
In the Americas, the destruction of trade routes and large population centers by smallpox and measles will probably stop the spread of the black death. How/if the Natives recover depends on what interaction happened before the introduction of the diseases.
To rehash the Vinland threads, if barley and oats are introduced to the northeast of North America and adopted by the people there, you could see a population boom as these staple crops allow for a higher population. Bonus points if sheep have been introduced, as their wool will make clothes that will allow more people to survive the cold winters.
If horses are introduced, you might see a 'collapse into barbarism' by some of the centralized American states as warriors on horseback create the military coup de grace on their already shaken societies. As per OTL the most successful horseback-based societies would be hunters on the Great Plains and Pampas, but you could see the creation of feudalist states in the southeast of North America and in Mesoamerica.
In the most densely populated places, European diseases would become endemic. Mesoamerica definitely, maybe the North American southeast, possibly the Andes though an earlier contact might mean no Inca road system, so a more fragmented population.
Whatever equilibrium these societies would eventually reach (by the 16th century they would be vastly different due to the societal trauma), they will be able to better resist European encroachment as they would have already gone through the shock of epidemic disease. When Europeans arrive in the future, they may bring some minor diseases but no major killers that don't already exist on the American shores. These societies will thus be able to better resist any future attempts at European colonialism.