I don't believe they do, because the death rates just aren't that high. Population-limiting factors for Humans have historically been mostly food supply and childhood diseases. I've heard that Malaria wasn't so much of a problem until people where driven into malaria-infested areas due to population growth.
Today the population limiting factor for Humans seems to be women's education. No kidding, this seems to be the number one factor in birth-rates. The more education women are getting the less babies are born. And I am generally in favor of both, more education and less procreation.