Interesting article in Smithsonian's daily magazine, on recent testing for animal fecal matter on sidewalks, shoes and interior floors in New York City.
The supposition (quite reasonably) is that the poop plops (as it were) on sidewalks, spreads via water and traffic, and enters one's building. Rather evocatively, in testing for bacteria load, per the article:
"They detected the highest amounts of enterococci in the building’s entryway and smaller amounts on interior floors. And carpets had more bacteria than bare flooring: While a carpeted entryway had around 22,000 enterococci per square meter, uncarpeted floor in the same area had only 100 per square meter".
Thus, it appears that carpeting in the entry area (doesn't say how much, as in how far you must walk over the carpet for the observed effect) seems to do a marvelous job stopping bacteria. Stopping various varieties of "dirt" is the rational behind entry matting; a rented, regularly laundered and treated mat should perform even better than a hunk of carpet.
That's why we suggest them to our clients. The more dirt (and poop bacteria) stopped at the door, the cleaner the building stays. Better for our cleaners, and better for our client.