Even as vaccinations against COVID-19 are being administered at a brisk pace, Maine health officials reported 588 new cases of the infectious disease on Saturday and four additional deaths.

The seven-day daily case average has fluctuated somewhat but has remained stubbornly high – at or above 450 cases – for all but a few days over the last month. It was at 470.6 on Saturday. Across the country, meanwhile, cases have been steadily declining, from an average of 113,003 a month ago to 68,792 cases now. Some of that is attributable to testing volume, which has dropped off dramatically in many states, especially in the South.

Saturday’s case count comes during a time of increased vaccinations in Maine. The per-day pace of vaccines administered to protect against COVID-19 in Maine is at its highest rate since May, according to the Maine Center for Disease Control and Prevention, and on Friday the U.S. Food and Drug Administration cleared the way for children ages 5 to 11 to get Pfizer’s vaccine, a move that Maine CDC Director Nirav Shah hailed as “a solid step forward in our response to the pandemic” in a tweet.

1/The @US_FDA has just authorized the use of @pfizer's #COVID19 #vaccine for children 5-11.

This is a solid step forward in our response to the pandemic. The @FDACommissioner found the vaccine safe and effective. https://t.co/CgJEq0tUvi

— Nirav D. Shah (@nirav_uscdc) October 29, 2021

There are roughly 80,000 children in that age range in Maine.

On Tuesday, nearly 8,000 doses were administered across the state, the highest daily total since May. Maine already is in the top five among states with the highest vaccination rates – all of which are in New England. Overall, Maine has given 933,815 final doses of a COVID-19 vaccine, which accounts for 69.47 percent of all residents and 78.85 percent of those 12 and older who are currently eligible.

In addition to final doses, Maine has administered 85,641 booster shots, which are now recommended for anyone 65 and older, individuals who are immunocompromised, and anyone who received the Johnson & Johnson vaccine at least two months ago.

Also Friday, the U.S. Supreme Court rejected an appeal from health care workers in Maine to block the vaccine mandate that went into effect Friday, though a dissent by three conservative judges on the court gave hope to the plaintiffs that their case was not over.

Since the pandemic began, there have been 104,259 confirmed or probable cases of COVID-19 in Maine and 1,167 peopled have died with the virus, according to data from the Maine CDC.

Among those who have tested positive is Maine House Speaker Ryan Fecteau, who announced a “breakthrough” infection on Friday and said he would be working remotely.

On Saturday, 195 individuals were hospitalized with COVID-19 in Maine, down three from the day before; 71 were in critical care, and 39 were breathing with the assistance of ventilators. The number of people hospitalized in Maine remains at a sustained high level even as hospitalizations have come down nationally. According to the U.S. Centers for Disease Control and Prevention, the average number of people in hospitals nationwide is about 45,500, which is down 11 percent from the previous week and down 50 percent since early September during the height of the delta variant surge.

Health care systems in Maine have been forced to delay certain surgical procedures due to bed shortages, and some hospitals are holding patients who are medically cleared but don’t have a long-term care facility to move into because of staffing shortages.

According to the Maine CDC, 41 critical care beds were available in Maine on Saturday, along with 205 ventilators.