The annual flu season isn't in high gear yet, but several states are already starting to see an uptick in cases.

Louisiana is the top state in the U.S. for flu activity so far this fall, according to the latest weekly influenza report from the Centers for Disease Control. Puerto Rico was also reported to have a high rate of flu cases.

The CDC also cited flu outbreaks in 10 other states: Arizona, Georgia, Hawaii, Idaho, Indiana, Kentucky, Mississippi, Nevada, Tennessee and Texas.

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Only one state, Rhode Island, reported no flu activity.

(MORE: Flu Virus Clinical Trial Will Pay Volunteers $3,000 To Be Infected)

The flu season in the U.S. generally starts in October or November and peaks between December and February. The CDC says it's still too early to tell how bad this year's flu season will be, but early numbers are consistent with the same time last year.

At least four people in the U.S. have died of the flu in recent weeks.

The youngest was a 4-year-old California child with other health problems who died in September, according to a press release from the Riverside County University Health System.

The death prompted a cautionary statement from Riverside County Public Health Officer Dr. Cameron Kaiser.

"We should never forget that the flu still kills," Kaiser said. "I always recommend people get their flu shots every year, but a death so early in the flu season suggests this year may be worse than usual."

A second fatal case of the flu was reported last month in California, as well deaths in Indiana and Minnesota.

As many as 61,000 people died from the flu in the U.S. last year, according to the CDC.

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