Grandsons With Asthma

I have three grandchildren, two of them boys and both with asthma. I find that strange since no one else in our family has asthma, that I know of. And we have cats, several cats who live in the house. Both grandsons and their dad are allergic to our cats, and therein lies our dilemma. We love our cats and enjoy living with them but don't like the fact that our home is toxic to those we love. So we are looking into air purifiers, taking up the carpet in the only room in the house with carpet, and replacing a couch that has become our cats' favorite roosting place. And I must be more dilligent with my vacuuming and dusting. Housekeeping has never been very important to me and to say I'm a casual house cleaner is putting it nicely but I really must try harder to keep my house as free of dust and cat dander as possible.