One of the health experts I follow is Dr. Sean Mullen. He is an Associate Professor within the Kinesiology & Community Health Department at the University of Illinois-Urbana-Champaign. He has a frightening but thoughtful #COVID19 message worth reading today on Twitter:
@augieray Portable air purification is compromised if the room it is used in is a part of the building HVAC system.
With this system air is circulated throughout the building with minimal filtrations. This negates the effect of portable purification devices. Hospitals use large, effective HEPA filters in their HVAC systems.
This is the only way to effectively clean the air used throughout a facility.
@trainman I do not believe you are totally correct. While circulating air throughout the building would decrease the effectiveness of portable air purification, anything that helps to filter air in a small area like a classroom will improve safety. I am not sure how much that declines, but I would very much hesitate to discourage people from using or promoting the use of air filters.
@augieray Hospitals use portable HEPA filters in private rooms. These filters are very large and 99.5% efficient.
I doubt that the small tabletop filters sold for home use are very effective, but something is better than nothing, I suppose.
@trainman @augieray According to an old NHS study, even putting a few of the cheapest portable filters in every classroom in a school makes a huge difference to infection rates.

@trainman @augieray
Yeah, the small table-top filters are about the right size for a passenger car, at best

On the other hand, if each room has an appropriately-sized HEPA filter for the room running, HVAC circulating the air isn't a problem