It would be rather difficult to picture a world Aldous Huxley portrays in Brave New World in 2013. In his dystopian world, mankind has taken everything to extremes. No one works. People spend time "wallowing" in materialistic wealth and personal pleasures. One man, John the Savage, decides to question everything. In his questioning, Savage must decide if his challenges are worth his life.
Despite the extremes depicted in the novel, one could connect it to 2013. We, as a race, do question the things around us. We scrutinize and analyze how things are, why things are, and how they could be changed to make life better. In this sense, Savage represents the only realistic thing one could bring forth from the text to the world today. While some people live in excess, the vast majority do not (in the real world). We, as a global culture, tend to be beings which are concerned with the betterment of our lives and (although most would vehemently deny this) are not happy "vegging out" all of the time (at least not on a whole).
Essentially, the novel connects to 2013 because we are not content with our world as it is. We wish to fight disease, oppression, lack of empowerment, and idleness.