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Immunity is not skill levels that you add up on your character sheet.
Alleles for particular antigens will disappear, due to random drift, or being replaced with new more relevant alleles.
To become a pandemic, a pathogen must match a very fine-tuned set of epidemiological characteristics, which normal strains lack under their usual living circumstances.
The American Exchange was so lethally extensive for two main reasons:
1) All the old world domesticated species that had served to generate all these new diseases through cross-species contamination
2) Constant exposure to new disease vectors, year after year, decade after decade, as new settlers arrived, preventing the native immunity from building up, if they survived one variant the next one that came got them.
An isot is a one-off shot. You have the shock at the moment of contact, but afterwards it not more any likely.
The results are a very wide spectrum of more or less virulent epidemics, more or less noticeable, catastrophic ones are just a subset of the possibilities.
Also, keep in mind that contamination is bidirectional. Here, in this exchange, it's Byzantium that has a small population exposed to a vast reservoir of potential pathogens, so the shoe could be on the other foot.
It's best to handwave the impact of disease away entirely.
Yes. It's just too random and unpredictable what will happen, when it will happen, what will be the effects if and when it happens. It's just playing roulette. It could be nothing much, it could be a doomsday combo of the Justinian and Black plagues, it could be anything in between, it could happen at once, it could happen centuries later in the future.