(CNN) Heavy rain and intense flooding have ravaged parts of central and southern states for the past week, leaving at least three people dead, and the risk of flooding continues into this week.

Flash flood warnings were issued for Arkansas, Louisiana, Oklahoma and Texas through Thursday, according to the National Weather Service, and the governors of Indiana, Missouri and Ohio issued states of emergency due to the possibility of further flooding.

Flooding from the Ohio River is seen near the Paul Brown Stadium in Cincinnati, Ohio, on Monday.

A long-term forecast for the Ohio River Valley shows possible heavy rain Wednesday night into Thursday. Much of the heavy rain will stay south of Kentucky, across Tennessee and northern regions of Gulf Coast states, according to the National Weather Service, which also predicts around one-half to three-quarters of an inch of rain falling across southern Indiana and northern Kentucky. South-central Kentucky could see 1 to 1.5 inches of rain.

Floodwaters surround homes in Plainfield Township, Michigan, on Monday.

Last week's heavy rains have kept much of the central, southern and Great Lakes region river systems in flood stage, the weather service said. More rain is expected across the lower and mid-Mississippi and Tennessee River valleys Tuesday and Wednesday, which will worsen the ongoing flood threat.

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