I think the exponential growth in Western Europe and the US isn't surprising. But any country, like China, Italy and South Korea that faces a significant outbreak will simply ratch up the measures to more drastic levels to contain to the point that the outbreak peaks and then drops, as it has done in China and South Korea and will soon in Italy.
The thing is, as experts have warned, you can't deploy these measures too soon because public will simply not respect them and get bored and frustrated by the time they are required. So you have to wait for the eye of the storm, to the point where there is a localised sense of actual danger and people almost don't need to be told to socially isolate anymore.
Of course, it also helps - and perhaps is required - to have politicians who care about incisively facing the issue as soon as possible (like in South Korea, where the MERS outbreak is still remembered) instead of downplaying the threat as a hoax or whatever.
Essay Pro