I think it's a metaphor for the sheer numbers, and the decay of what was once the vitality (the leaves/the young men) of the trees (society).

The leaves falling off the trees depends on the species of tree and where you are. Generally, it's a rather short occurrence: The leaves change color in about a week, they're gone a week to two weeks later, depending on the prevailing winds. Oddly, continuing the analogy, trees with dramatic color shifts (such as sugar maples or birch trees) lose their leaves rather quickly. Trees with bland, even ugly colors, such as oaks, shed their leaves more slowly, stretching over several weeks, even up to a month or two.