Here is an interesting approach to estimate the number of international visitors going to Brazil during World Cup: Check-Ins on Facebook! I couldn't find who is the author of this video.
But when it comes to using the Internet to identify human mobility patterns though, I think Emilio Zagheni is a great academic reference. In this blog, we have already mentioned one of Zagheni's work, where he uses e-mail data to estimate global migration rates. He has also developed similar studies using Twitter Data and IP Geolocation.
There is also a whole different group of studies using Internet services to identify mobility patterns at the city scale. If you're more interested in this scale of analysis, this post might work as a starting point `A day in the life of a city`, but you should not forget the research of Cesar Hidalgo and colleagues using mobile phone data to study human mobility (and this one).