A question I get asked often is :
"Is the air in an airplane safe? Am I at increased risk of infection in a plane?"
Let's separate fact from fiction. The air in a plane is constantly circulating and it is passed through a HEPA filter. The highly filtered air is also mixed with clean outside air which further improves air quality.
Every research paper I have read clearly shows that air contaminant levels during flight are well within acceptable levels.
Why do people get "more" sick on flights
This is an interesting question but the premise is wrong. People get more sick not because they are on a planes but because they are sitting in very close proximity. It is the proximity which increases the risk of infection and not the plane, its air or anything else related to the flight.
If someone next to you is caughing, sneezing or otherwise exhibiting sick behaviour. Try to have your seat changed. Typically plan for a "2 seat" buffer from Mr Sick in every direction and you should be fine.
What about ozone?
Passengers are now aware about the "dangers of ozone exposure" and tend to worry about how much ozone they might be exposed to during a flight. Some flights (depending on location and altitude) may subjected to more ozone exposure but typically those planes are equipped with ozone converters for external air being pushed into the cabin.
Conclusion
Planes are an extremely reliable and safe method of transportation. When you get on a plane, plan to enjoy the experience and leave your worries at the gate.