Been there too. I have found that if you store your models so that they have an air space around them to allow for air circulation you lessen the chance for mold to form. When the boxes are in close proximity to an exterior wall they will absorb moisture and the mold spores will take root on the box and eventually creep into the contents.
If your basement is humid you need to address that issue by using a dehumidifier to lower the humidity. I have seen and recommend that if your basement is unfinished, you can make a "room" using sheet plastic to enclose an area of the basement that you use for storage or workshop area. Hanging plastic from floor to ceiling, you can make an area for the dehumidifier to do what it does best...dry the air.
In many cases, and I do this even in my current workshop stash area I routinely run a fan to circulate air in the room. My shelves that are on the exterior unfinished walls are several inches away from the wall. This allows the breeze to flow between the wall and the stash stacks.
Also keep your kits well off the floor...two to three feet above. Moist cool air tends to settle and form on objects in that zone...just like the dew forms on the lawn and stuff in the yard.
Kits that have been...infected with mold...I have taken those and washed the plastic sprues, then placed them into an appropriate sized Ziploc bag. The decals, well those were either left as is and placed into a separate bag or trashed. Instruction sheets were scanned or copied and also trashed. Reintroducing them into the stash only reseeds the mold spores to the stash.
For built kits...clean them the best way you can with a mild detergent. Once mold grabs on it is tough to kill. Some professionals use a gas bag to kill the mold...not sure what they use but it appears to work. I have seen the results of their efforts on fine collectibles.