The consensus among virologists is that while air purifiers probably don't offer much protection in most circumstances, they may be 'worth trying' in a few specific ones. If someone in your household is sick with COVID-19, running an air purifier in their quarantine room may give additional protection to  other family members or caregivers, if they also follow other directions. The same goes for healthcare workers who are self-quarantining when they come home. 

But even if you live with  someone sick with COVID-19, experts say,  simply opening up the windows in your home to let in fresh air will help dilute indoor contaminants—including virus particles. If airing out the room isn’t an option, you could try using a high-efficiency particulate air (HEPA) purifier. We don’t yet have direct evidence that filtration works to reduce transmission of the novel coronavirus.

In theory, if , and that is a big if, an air purifier removes viruses from the air, it reduces concentrations in the room and thus reduces the potential for exposure. 

Even, if HEPA filters are good at catching coronavirus-size particles,  the particles must first physically travel to the filter.  That means an air purifier has to be capable of consistently drawing in enough air to reduce the amount of virus particles in the air. The faster an air purifier can cycle air through the filter, the better its chances of catching virus particles. You can see how fast an air purifier cleans the surrounding air by looking for its CADR (clean air delivery rate) number on the packaging.

CADR reflects, in cubic feet per minute, the volume of clean air that an air purifier produces at its highest speed setting. At lower speeds, the rate a machine is able to clean air decreases. The packaging should have three CADR ratings, one for smoke, dust, and pollen, which represent small, medium, or large particles, respectively. For example, a purifier with a CADR of 250 for smoke reduces smoke particle levels to the same concentration that would be achieved by adding 250 cubic feet of clean air each minute. (Smoke particles are similar in size to the smallest virus droplets while larger droplets are closer to the pollen size range.) 

Based on lab tests of air purifiers,  a model with a CADR over 240, which can perform roughly five air exchanges per hour in its suggested room size are good. In tests, these air purifiers perform well for quickly removing particles of all sizes from the air. 

Placing the unit three feet from the person who is sick with COVID-19 is also recommended. One should also take extra precautions when handling the air purifier and changing the HEPA filter.

Some air purifiers claim to kill viruses using UV light or some kind of photocatalysis technology. Take these claims with a grain of salt because there isn't enough concrete evidence yet that proves they work in these settings.

So after considering all the above things, scientists say air purifiers are not the best preventive measure against the coronavirus.

Your typical HEPA filter is not going to be able to remove individual particles of coronavirus from the air. The filter itself is .3 microns and the virus itself is roughly .1 microns. [ The average diameter of the virus particles is around 120 nm (.12 μm) (2)]. Viral particles are too small to be blocked by HEPA and MERV air filters, but ventilation strategies can still play a role in reducing disease transmission (3).

Even if the viral particles are trapped in big droplets of aerosols, these won't stay in the air for long and travel to the filters to get filtered.

Cleaning the filters put people to grave danger too.

Research suggests  that viral aerosol levels can be reduced through effective ventilation (5,6).

Air purifiers may do more harm than good in confined spaces with airborne viruses

The positions of air inlets and outlets in confined spaces, such as elevators, greatly affect airborne virus transmission. In Physics of Fluids, researchers from University of Nicosia in Cyprus show while air purifiers would be expected to help, they may actually increase the spread.

Air quality in small spaces can quickly degrade without ventilation. However, adding ventilation will increase the rate at which air, possibly laden with viruses, can circulate in the small space. Elevator manufacturers have added air purifiers to take care of this problem, but the systems have not been designed to account for their effect on overall air circulation. 

Air purifiers use UV radiation to kill viruses and other microbes, but they also circulate air, sucking it in and exhausting cleaned air. This adds to overall circulation, an aspect that has not been considered in previous research.

Previous work from the scientists indicated droplets of saliva can travel 18 feet in five seconds when an unmasked person coughs. The authors extended the same model to examine the effects of face masks and weather conditions.

Investigators carried out calculations for a 3-D space equivalent to an elevator capable of holding five people. A mild cough was simulated at one position in the space, and air inlets and outlets were added in various locations to study their influence on circulation. An air purifier was also included in the simulation.

Researchers quantified the effect of air circulation on airborne virus transmission and showed that installing an air purifier inside an elevator alters the air circulation significantly but does not eliminate airborne transmission.

The investigators found the risk of airborne virus transmission is lowest for low ventilation rates.

This is due to reduced flow mixing inside the elevator. Regulatory authorities should thus define the minimum ventilation required depending on the type of building.

The study looked at the role of an air purifier, considering only the air intake and exhaust associated with the purifier, but not the mechanism inside the purifier that kills the virus. Even with an air purifier in place, airborne virus transmission is still significant.

The results show that installing an air purifier may increase the droplet spread. The air intake integrated inside the purifier equipment induces flow circulation that can add to the transport of contaminated saliva droplets in the cabin.

The observed effect increases with the number of infected persons in the elevator. Restricting the number of people allowed in an elevator would minimize the spread of the virus as would better design of air purifier and ventilation systems.