I base it on what Greg mentions in his reply about the swine flu and also the reasoning that the reproduction number has to go below 1 for it to stop spreading. If its normal reproduction number before people have become immune (after being sick) is X (like 2 say), then to get the reproduction number below 1, (susceptible population proportion) * (normal reproduction number) < 1. So with a reproduction number of 2 the proportion who get infected will be 1⁄2.
This assumes that people have time to become immune so for a fast spreading virus more than that proportion would fall ill (note thought that pointing in the opposite direction is the effect that not everyone is uniformly likely to get ill though because some people are in relative isolation or have very good hygiene).
Just a note that the reproduction number can decrease for other reasons; in particular if and as the disease spreads you might expect greater public awareness, CDC guidance, travel bans, etc leading to greater precaution and less opportunity for infected individuals to infect others.
I base it on what Greg mentions in his reply about the swine flu and also the reasoning that the reproduction number has to go below 1 for it to stop spreading. If its normal reproduction number before people have become immune (after being sick) is X (like 2 say), then to get the reproduction number below 1, (susceptible population proportion) * (normal reproduction number) < 1. So with a reproduction number of 2 the proportion who get infected will be 1⁄2.
This assumes that people have time to become immune so for a fast spreading virus more than that proportion would fall ill (note thought that pointing in the opposite direction is the effect that not everyone is uniformly likely to get ill though because some people are in relative isolation or have very good hygiene).
Just a note that the reproduction number can decrease for other reasons; in particular if and as the disease spreads you might expect greater public awareness, CDC guidance, travel bans, etc leading to greater precaution and less opportunity for infected individuals to infect others.