The number of people hospitalized with the coronavirus and the rate of new cases remains high in Nebraska. The state said Tuesday that 299 people were hospitalized with COVID-19. That’s just under the record of 305 people set last weekend but well above the spring peak of 232 set on May 27. An Associated Press analysis of data from Johns Hopkins University shows the state continues to have the seventh-highest rate of new cases. The seven-day rolling average of the positivity rate in Nebraska declined slightly over the past two weeks, going from 13.22% on Sept. 28 to 13.08% on Monday.