The pandemic begins twenty years previously in the early 21st century, with the infection of a boy in a village in Dachang, China; the release of the virus, referred to as "Solanum" in The Zombie Survival Guide, is implied to have been caused by the construction of the Three Gorges Dam.
Simple, he's already been infected with a deadly disease and the zombies ignore him. He had no chance of fighting his way out of that apartment with so many zombies pouring the one door unless he was already sick. If this is the case, the answer was right under Brad Pitt's nose the entire time.
