Lucille  was tested positive for Feline Immunodeficiency Virus.  So  her babies were tested positive also.  
But upon much research our vet tech found very useful information from Cornell University.
"Because few, if any, cats ever eliminate infection, the presence of anitbodies indicates that a cat is infected with FIV.  This test can be performed by most veterinary diagnostic laboratories and also is availabale in kit form for use in veterinary clinics.  Since FALSE-POSITIVE results may occur, veterinarians recommend that positive results be confirmed using a test with a different format.  Infected mother cats transfer FIV antibodies to nursing kittens, so kittens born to infected mothers may receive a positive test results for several months after birth.    HOWEVER, FEW OF THESE KITTENS ACTUALLY ARE OR WILL BECOME INFECTED.  To clarify their infection status, kittens younger than 6 months of age that test positive for FIV should be RETESTED at 60-day intervals until they are at least 6 months of age.  As for Lucille, The primary mode of transmission for FIV is through bite worunds.  Casual, non-aggressive contact does not appear to be an efficient route of spreading the virus.  As a result, cats in households with stable social structures where housemates do not fight are at little risk of acquiring FIV infections.  So if you are interested in Lucille and have another friendly cat you should be fine.   Of course we do advise you to check with your vet.   Lucille is very calm and sweet, up to date on all shots.  If you want one baby she is the one for you who loves to cuddle.   Do your research also.  Lucille is available for fostering also.