We spend a lot of time inside buildings.  Besides dilution (ie ventilation, like opening a window),how else can we reduce the number of virus particle which may be present?

Did someone say filter?...Great Idea!  There are classifications to rate the degree of filtration acheived  known as MERV rating*  (ie - MERV 13 is nice) . HEPA is a well understood technology which does a spendid job of removing reliably very small particles ... much better than the routinely used paper filters in most homes and small buildings.

[*An air filter 's minimum efficiency reporting value (MERV) rating measures how effectively the filter stops dust and other contaminants from passing through the filter and into the air stream. Filters with higher MERV ratings trap small particles more effectively than filters with lower MERV ratings.]

What else can we do to make our breathing air cleaner?   There is a long list - but if you can dilute and filter like above- you have done well!

Additional Ways to Improve Indoor Air Quality:
#1 Air Distribution   (ie it is best not to blow air from an infected person onto an uninfected person)
Let's look at another engineering approach which has been utilized in recent years to improve the outcome of some very delicate surgical procedures which are performed.  The concept which is used to avoid contamination is called "laminar flow". Using such principles we are able to have air flow moving in such a way makes it less likely that all the air mixes.  
Think of it more like a nozzle of air.  Somewhat like how water flows out of a water fountain nozzle.
Now compare that to the airflow resulting from a ceiling fan evenly distributing and mixing the air.
In fluid dynamics, laminar flow is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards.
 In the operating room special ventilation piping creates laminar flow so the air uniformly moves where the surgeons wish it to.
The air falls down on the center of the operating table and then flows off the operating table rolling down the floor where it is captured and flushed out of the room.
This prevents any airborne particles which might be in the air from getting near the surgical site which must remain absolutely clean.

We have many years ago discovered how to manage contaminated air to reduce the concentration of chemicals and infective agents and render it harmless.

This was determined in detail by mechanical engineers to create containment laboratories so that scientists could examine and learn about very ineffective and dangerous bacteria and viruses. 

Containment laboratories and laminar flow operating rooms however cost millions and are gross overkill for general use.

It could however be possible to look at these engineering marvels and learn how we may be able to improve the health of our population.


#2 Air Cleaning: some useful opportunities exist here

1- Activated Charcoal - fabulous - however it must be changed as it becomes saturated.
2 - Germicidal Ultraviolet Light -  probably the most promising among various new offerings being promoted early days however . 
3-Possible new discoveries among many currently unproven claims 
Please remember that industrial safety generally depends upon good engineering and design so that hazards are managed and humans are not exposed to the hazards.

After all engineering options have been exhausted - PPE is the remaining option to ensure safety

Learn More about PPE