Leptospirosis or Weil's Disease is spread by contact with the urine from infected rats and not the bites.
The characters in the movie pronounce "Weil" (as in Weil's Disease) to rhyme with "wheel". The doctor after whom the disease was named, Adolph Weil (1848 -1916), was German; his name should be pronounced to rhyme with "while" (and if you're a stickler for accuracy, the "w" should be pronounced like an English "v").