For models on display, I use custom built cases made from 1/8" or 3/16" acrylic sheet. The cases are sized to fit my book shelves and seal tightly.
For models in storage, I use plastic storage tubs with dust proof, weather seal gaskets. They are light weight, sturdy, and stack nicely.
To keep dust out of a traditional display case like the ones in the first picture above, an aquarium fish pump, supplying filtered air into the case, will create enough positive air pressure inside the case to keep dust out. It works just like the over pressure system in a modern armored vehicle. Such a system requires a display case with relatively good seals in the first place. Even quiet pumps are noisy, at least for me, and generate heat.
It should be possible to add foam weather seal tape to just about any container or piece of furniture, improving the seal. The down side is that the tape will break down over time and may leave residue. It becomes a maintenance item.
I have a lot of card models out in the open and use anti-static cloths to dust them. While not a panacea, such cloths are better than rags. It is way better to prevent dust from landing on a model in the first place, which is why I made so many display cases and purchased so many storage bins with weather seal gaskets.
I noticed that living spaces in my own house with high air flow attract significantly more dust. If you can keep air flow through a room low, the rate of dust accumulation will diminish. Note that fans in a computer generate air flow and thus move dust around. This strategy worked with my old office, which currently serves as a display room and library. The biggest improvement occurred when I moved a big computer (and myself) out of that space.
Make sure your air conditioner and furnace filters are clean. If you want to go extreme, have all your ducts cleaned.
Pets generate a ton of dust and detritus. Keep them out of display rooms. My sincere apologies to Callie Cat.
Dust and vacuum frequently. If you keep dust accumulation low in the first place, it will not settle on your models.