I had cause to spend time some years ago studying logistical impact of rattus rattus and rattus norvegicus. You would be unwise to hitch your wagon to your bizarre imagined gotcha of a handful of years.
The Yuan Dynasty was called that by Kublai Khan circa 1290ish. He then died and his son took over. Plague arrived in the 1330s. Your superficial wiki look did not lead you to what happened to the dynasty over a fifty year sequence of acute absence of farming personnel.
Plague killed society via starvation. The mechanism of starvation death is rarely a calorie deficit that creates too few such to power lungs or heart. It is much more a failed immune system that permits opportunistic infection.
Plague persisted for decades because of the synergies of food. Rattus Rattus appeared when there was food for it to eat. Killed the farmers that created it, often before any children could be taught farming.
Decades upon decades this went on in the dynasty. Its roots were the Mongol Empire. Sieges of expansion were ended as often by food lack as by the disease in the surrounding army.
The Hundred Years War persisted because of plague.
About 10 yrs ago some uncomfortable analysis unfolded concerning transportation speed of that time in both China and Europe. It led to suspicion Y. Pestis was not the agent. This ended with DNA analysis of bodies in graves, but there was never a rebuttal to the speed issue.
You have a few years of reading to do. I’ll wait.
Various other comments you've composed across other threads speaks volumes about the volumes of volumes you say you have read, in order to be wiser than a mere worldtraveler.
If there is any “bizarre imagined gotcha of a handful of years,” it not mine. It is ours, including you, a Doktor Allwissend.
These last two years of the pandemic — “event,” scamdemic, case-demic, and so on — is less than a handful of years. And you have so much about which to opine because you've read about black rats, which are part of our world today. Gee whiz, rats carry plague. Even today, so let's just bring your little equation across to today. Six hundred plus years of plague! Arithmeric based on assumptions and statistics and all.
Few if any will look back at this thread, so neither of us doing more than a silly back-and-forth. But to adopt a superior academic stance seems a pretense to me, as if you want “appeal to authority” to anoint you as an authority. Rattus rattus, indeed.
I'll just cite "official" statstics, deaths and populations and such.