I had always thought that there was one Black Plague and that was it. In my genealogy research, I was lucky enough to discover a treasure trove of letters written by an ancestor between 1588-1595. By his letters, the plague broke out in London every summer. It was very ho-hum, “Oh do tell mum I’ll be coming out to the country, the plague is running thick here and bodies are stacked like cord wood in the streets...”
The Black Plague entered (well, re-entered) Europe in the 14th century; outbreaks continued from time to time right up into Tudor times (Shakespeare managed to survive his toddler years, perhaps by having been kept indoors, the Pestilence took a lot of people in Stratford).