As of Thursday, new school closings fell to three.

While the dramatic downturn is welcome, considering the havoc that swine flu, or H1N1, can wreak, health officials warn that circumstances could change and that the drop doesn't mean families should let down their guard.

"We should not assume this epidemic is over," says Amy Garcia, executive director of the National Association of School Nurses. "It is my sense that epidemics come in waves, and this is probably a temporary downturn."

By any measure, the drop has been dramatic: On Oct. 23, 351 schools reported closing in 19 states, according to U.S. Department of Education figures.

By Thursday, only three schools closed in Maine and Michigan.

Garcia says she's "delighted" by the downturn, saying the change may reflect closer attention to hand-washing and other common-sense approaches to stopping infection. But, she adds, "I do not think we should in anyway be less vigilant or slow down on our efforts to protect those vulnerable to H1N1 or seasonal flu."

Tom Skinner, a spokesman for the Centers for Disease Control and Prevention (CDC), notes that schools nationwide this fall changed their H1N1 policies, shutting down "only as a last resort."

While CDC guidelines aren't explicit, many schools close when absence rates exceed 40%.

The downturn, he says, reflects both the fact that fewer kids are getting sick — and that schools "really are doing everything they can to keep their schools open."

Skinner says it's too early to tell whether infection rates dropped because of the new H1N1 vaccine. CDC expects to release data on H1N1 vaccination rates today.

Skinner warns that flu activity "is very unpredictable," and that while CDC has recorded overall drops in infection rates in a few geographical areas, the USA as a whole is still seeing "unprecedented" numbers of flu cases for this time of year.

In its latest report, CDC says swine flu is still widespread in 46 states, with death rates remaining above the "epidemic threshold": It recorded 35 flu-related pediatric deaths in the week ending Nov. 1.