DES MOINES — Iowa continued Monday to record a high number of new positive coronavirus cases as the state continues to struggle with spreading virus in several counties, including those with university campuses.

Data from the Iowa Department of Public Health showed 611 new positive cases, sending the total to 64,929. Four additional deaths were reported raising the total to 1,116 deaths.

With many K-12 schools back in class, some districts also are struggling with high levels of county virus activity. Twelve counties had a positivity rate of 15 percent or higher, the threshold Gov. Kim Reynolds has set for schools to request to go to online teaching. The rate is three times the 5 percent rate recommended by the World Health Organization and the U.S. Centers for Disease Control and Prevention.

Five counties have positive rates above 20 percent, the data shows.

On Saturday, the state’s 14-day rolling total of positive cases reached an all-time high of 11,091. The 14-day average positivity rate, which is the percentage of those tested getting positive tests, is 11 percent.