Three doctors -- Adriano Ossicini (1920-2019), Pietro Borromeo (1898-1961), and Vittorio Sacerdoti (1915-1999) -- are credited with inventing this horrific and highly contagious disease that wasn't even real - called "Syndrome K." Dr. Borromeo's son, Giacomo Borromeo, was a lawyer by trade and had extensive knowledge of Syndrome K. He is featured in the film though he passed away in 2019.
Syndrome K was named after 2 occupying Nazi officers in Rome - SS Commander Herbert Kappler (1907-1978) and Field Marshall Albert Kesselring (1885-1960) to poke fun at the oppressors, per Dr. Ossicini and Dr. Borromeo. They picked the letter "K" as the name of this fake disease - even though it didn't exist in any medical journals or textbooks. Both Kappler and Kesselring were tried after the war for atrocities but never sentenced to death.
Fatebenefratelli Hospital is still thriving in Rome and even has a memorial plaque describing the heroics of the doctors. During the war, the hospital operated a clandestine radio, approved by Dr. Ossicini, that sent critical information on Nazi troop movements to the Allies in Brindisi.