If we consider cats a medical technology, during the dark ages approximately how many human lives did cats save by reducing rat populations in dirty european villages?

Obviously, can't really answer it accurately but I wonder what a good ballpark is. The black death killed 75-200 million people in a 7 year starting in 1347. One of the main vectors for disease were rats, so... how many more people would have died without cats keeping rat populations down in some places?