Even the cheapest HEPA filter should filter COVID out of air that it filters. But a classroom etc isn't going to do full FAE through that filter often.
So, a HEPA filter running all night will probably clear out all of the COVID from that day, but then a bunch of kids come in with all their germs and if the filter isn't changing that air out several times per hour, it's not going to mean shit really.
Even a cheap HEPA filter is good enough to filter COVID.
But, all contaminated air has to actually go through the filter.
This means you need to do several full air exchanges in the required space per hour really if you want to keep people from getting sick. Like a laboratory clean room would do.
And setting up that level of HEPA filtration, is fucking expensive.
I built a very small flowhood for mycology. The filter was $200. The fan another $80. And I'm only keeping a one x two space clean. I imagine it's just not economical to really apply this technology to schools etc at this point in time.
This paper points out the filtration of SARS-CoV-2 isn't clear cut whatsoever. Papers stating it could be filtered from the air all demonstrated to have publication bias. The thing about viruses is they are super tiny. On average, a virus is 10x smaller than a bacterial cell. This makes filtration much more difficult to accomplish.
The study found the most effective methods for air purification were germicidal lights, ionisers, and electrostatic cleaners. With HEPA specifically, the filters can snag objects as small as 0.3μm. However, the largest viruses are 500nm or 0.5μm in diameter. Based on the numbers, HEPA filtration is capable of removing the largest viruses from the air, but that's a small minority of all viruses. SARS-CoV-2 comes in somewhere between 60nm/0.06μm to 140nm/0.14μm in diameter, meaning HEPA filtration can not remove it from the air.
I was taught μm stands for micrometers, which are 1,000 times smaller than millimeters. Nanometers(nm) are 1,000 times smaller than micrometers(μm), which means nanometers are CRAZY small!
Even clean rooms don't stay clean because great apes are not clean, and they have to work in the space. So even the best spaces aren't fool proof which is why lab teks wear masks and other equipment.
But yeah, work well enough to keep kids etc from being sick, would require lab level air filtration to make a difference. And we'd probably still have to dress the kids up like lab nerds even with lab level filters and fans.