Question: In the show Jessica Jones, in the last two episodes Kilgrave takes steps to enhance his powers, which leads to him

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>  being able to control people through phones, loudspeakers, tvs, and other electronic communication devices. He uses a phone call in the hospital, which is Jessica's first realization he can use electronic equipment. He then uses the broadcasting system and the televisions in the hospital to turn all of the hospital staff against Jessica, uses phone calls to control Luke Cage, and uses a microphone and sound system to take over a concert.
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Given that we are told his powers work because he emits an air-borne virus that affects people near him, how does this make any sense at all? How does a (presumably) biological virus get transmitted electronically?

Answer: 
It doesn't get transmitted electronically, though it's not clear at all from the scene.

Kilgrave's power is

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>  a virus that his body continuously emits into the air around him. 
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Once you are exposed, you become very open to suggestions from Kilgrave's voice. His power is only limited by those people who are physically exposed to the environment where Kilgrave happens to be.

Initially, his limits are around the size of a medium-sized room, and about 10 hours. That is the distance his powers can travel in the air from Kilgrave, and the length of time it stays active in the victims after exposure. At any time during that 10 hours, he can order you to do something and you will do it, even if he's not physically there anymore.

At the end of the series, Kilgrave has

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>  his father work on expanding those limits.
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Once done, his power is able to spread out further away from him, including

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>  through the circulation system of the entire hospital.
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All of those people are *already exposed* to Kilgrave's ability; they are just waiting around open to his suggestion. Once he announces over the loudspeaker what he wants them to do, they're forced to obey his commands.
Those in Kilgrave's presence (e.g. those that are

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>  infected by the virus he exudes)
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are prone to following his verbal commands. This also extends to commands given to other people to pass on as well as commands heard via phone/microphone, etc. 

The key factor is that people must have been in his physical presence to have been 

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>  infected in the first place.
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In the final episodes, his *range* is extended to the point that he can control an entire theatre or an entire hospital almost at once, but the key factor is that he has to have been inside the building at the time.