When thinking about using a HEPA filter for dealing with air-borne virus and bacteria, there are two important things one need to know:
1- While a sieve traps objects larger than a certain diameter and let the smaller ones pass through, this is not what happens in a HEPA air filter. In this case, due to the principles of fluid mechanics, and also because of brownian movement, there is a critical size (around 0.3 Micron, 300nm) for which, the filtration efficiency is minimum. This means that for both particles larger and smaller than this critical size, a HEPA shows very good filtration efficiencies. As you can see in the graph below, for a True HEPA, even for this "most penetrating" size, the efficiency could be still very impressive (higher than 99.7%).
This means that a good quality microfiberglass HEPA filter can be very good in eliminating nano particles the size of a virus.
2- The second point is that very small airborne microorganisms, are in many instances attached to bigger particulate substances in the air, whether liquid micro droplets or solid particles. I do not know so much about the nature of the bonds and whether this happens for the coronavirus or not, but this may be reason for higher risk of respiratory infectious diseases when PM2.5 air pollution gets high.
For these two reasons, I believe that HEPA air filtration could help a lot in indoor spaces, reducing the risk of infection, by reducing the number of particles of any size from the air.
In contrast, when comparing to the application of UV-lamps, there are to negative points:
1- UV lamps have lifetime and the radiation wavelength is so much affected by working hours of the lamp.
2- If air speed and exposure to radiation is not enough, complete degeneration may not happen and we can not be sure if we are not producing a new genetically improved virus!
All Together, I think we should generally be more careful with the active control methods. With passive control methods such as HEPA filtration, we are sure we are not adding anything new to the air!!!
As a reliable reference on the efficacy of HEPA filters on bacteria and nanoparticles you can see the Technical Memorandum of NASA Marshal space flight Center of May 2016:
Perry, J. L., Agui, J. H., & Vijayakimar, R. (2016). Submicron and Nanoparticulate Matter Removal by HEPA-Rated Media Filters and Packed Beds of Granular Materials.