The poverty rate is based on the bell curve of income, which, of course, means that you cannot eliminate poverty. Everyone below that magic floating dollar amount on the curve is in "poverty", even if the same income in Sweden would place them solidly in the middle class.
Why are so many children "in poverty"? Because young people have children while still low on that bell curve. Of course, as they mature and gain job skills, their income rises until their children strike out on their own - and become instant "poverty" stats.
If poverty is a houshold income below $15000 I think for sure that would be not enough to get into the middle class in sweden. Even if I admit the Swedes have had some bad years latelly.
I for example earned the equallent of $11000 in 9 weeks at my Summer job in 1999. Wage is lower in Sweden, but not that low.