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I think a reasonable summary is that the homemade versions are cheaper and actually more effective than most commercial versions, with the downside that they are usually larger and often noisier. The largest factor for effective air purification is airflow, and the homemade versions offer higher airflow but at the cost of greater noise and looking janky. There are somewhat reasonable fears that the homemade versions might be fire hazards, but in practice they are probably no more dangerous than the bare fans on which they are based. Really, both solutions work just fine. If looking commercial, be sure to consider the cost and availability of replacement filters. If considering DIY, realize that you don't need to get it perfect, almost anything is better than nothing.

> how these DIY compare to actual commercial products

That's actually what this article discusses:

"If you’re in a hurry, this post says that if you strap two HEPA filters to a box fan, it will clear the air of basically all the particles we can measure, and it will do it faster than a commercial filter that costs twice as much."

Thank you

Radial fans (also known as squirrel cage blower, or visualize a water wheel from an old fashioned water driven flour mill) will move air more quietly than an axial fan in a box fan. Levoit on Amazon are some great, relatively inexpensive units and when the HEPA filter it comes with needs replacing I use use furnace filters cut down to size. If you want it to last a bit longer, you can use quilt batting as a pre-filter before the furnace filter to catch the big stuff and extend the life of the furnace filter.