Wouldn’t we all like to know! Seriously, there seems to be two schools
of thought. One group (from Cornell-based publications and seminars)
states that the spread is not known with certainty, but is believed to
be by ingestion or inhalation of the virus. The other school of thought
(from Dr. Pedersen and the UC, Davis based publications) believes that
transmission is most prevalent when cats have close contact with other
infected cats or their feces/urine. Both schools seem to feel that feces
may play a large role in the method of transmission.

Some studies suggest that viruses that can cause FIP can survive
on dry surfaces (food/water bowls, litter boxes, human clothing, etc.) and
can survive at room temperature probably up to 2 or 3 weeks. If this is
the case, then the two schools of thought on methods of transmission may
not be so far apart, especially given that litter can contain dust to
which small particles of feces can adhere. Thus the virus can possibly be
spread via litter dust on shoes or clothing or etc. making it behave as if
it were an airborne virus!