We're talking about a quantity of air (equivalent to a portion of the cabin air contimuoussly being drawn from the cabin at a given time) that would be miniscule in comparison to the tremendous volumes of air taken into the aforementioned combustion chambers in a single second.
The system essentially would be closed and would be controlled by valves, one-way and otherwise; sensors; etc. The efficiency of the aircraft's engines would be virtually unaffected while the microbial content of cabin air at any given point in time would be minimal.
For even the most virulent of infections, multiplicity of infection -- i.e., the number of bugs that enter the body of a potential host during exposure to an etiologic agent-- is critical re: whether one becomes "exposed" to the extent that the pathogens in question can multiply at all or beyond the capacity of an individual's specific and non-specific immune respionses to successfully address.
Indeed, the small volume of air expelled during one or many sneezes and coughs by an individual infected with smallpox, ebola, etc. would be drawn immediately and ++without fanfare under negative pressure into vents above and below each seat and other areas of a fully-laden aircraft and subsequently submitted to incineration as described in the foregoing.
Granted, I'm only a fifty-year-old-plus. doctoral-level microbiologist, but at present have a few of my Gyro Gearloose-type engineering friends working up a small working prototype for the purposes of submitting a patent in the very near future.
Hopefully you can "read all about it" and benefit therefrom someday soon. Sleep well, and happy trails to us all...