Researchers actually did models on this, and it was actually determined, the black death spread too fast to be by rats! It was more likely human-to-human that spread the fleas!

Source: K.R. Dean, F. Krauer, L. Walløe, O.C. Lingjærde, B. Bramanti, N.C. Stenseth, & B.V. Schmid,

Human ectoparasites and the spread of plague in Europe during the Second Pandemic, Proc. Natl. Acad. Sci. U.S.A. 115 (6) 1304-1309, https://doi.org/10.1073/pnas.1715640115 (2018).

Gone… reduced to boils