New York Gov. Kathy Hochul said Tuesday that unvaccinated public and charter school employees must undergo weekly testing.

"I think that's a compromise,” she said.

Hochul is also working to establish vaccine requirements for all staff at state-regulated facilities and congregate settings. New York officials announced last week that all health care facility staff must be vaccinated.

-ABC News' Aaron Katersky

Fully vaccinated immunocompromised individuals still produce immunity, but at reduced levels compared to healthy individuals, according to a study released Monday by the American College of Physicians.

Researchers at the Washington University School of Medicine compared antibody responses between 133 immunosuppressed and 53 healthy participants between Dec. 10, 2020, and March 20. The study looked at mRNA COVID-19 vaccines produced by Pfizer and Moderna.

The study's main findings found reduced antibody levels in the immunosuppressed group, particularly those taking steroids and specific drugs depleting white blood cells.

Researchers said the study emphasizes the need for booster shots among immunocompromised patients.

-ABC News' Alexis E. Carrington

Doctors from Lee Health Facilities, a health care system in Florida that consists of four acute care hospitals and two specialty hospitals, are begging residents to get vaccinated as hospital beds remain unavailable.

Patients are currently waiting for beds in hallways and closets, doctors announced at a news conference Monday.

Lee Memorial Hospital in Fort Myers, Florida, admitted 92 COVID-19 patients on Sunday alone, and eight to 12 patients in the health system are dying every day, Dr. Larry Antonucci, CEO of Lee Health, told reporters, saying the deaths are “not necessary.”

"Our COVID rate in this county is three times what we’re seeing throughout the rest of the United States," Antonucci said.

Nearly 50% of people coming into the hospital system’s emergency department are seeking treatment for issues related to COVID-19, said Dr. Timothy Dougherty, medical director for emergency management.

"That number is insane," Dougherty said, adding that people in their 20s and 30s are dying as well. "No other disease demands these amounts of resources, including BiPAP and ventilators, and all that could be prevented with the vaccine."

The neonatal intensive units within the hospital system are "overflowing" as well, Dr. Stephanie Stoval, a pediatric infectious disease specialist said, adding that pregnant women who contract COVID-19 are more likely to go into labor early or have pregnancy complications.

"It’s never been this full before," Stoval said.

The hospital system is looking for additional spaces to expand treatment, Antonucci said.

-ABC News’ Cherise Rudy

As COVID-19 infections steadily increase across the country, the U.S. continues to see a concerning surge in pediatric cases just as children head back to the classroom for a new school year.

Just under 204,000 new child COVID-19 cases were reported last week, marking the second-highest week on record, according to a newly released weekly report that compiles state-by-state data on COVID-19 cases among children from the American Academy of Pediatrics (AAP) and the Children’s Hospital Association (CHA).

After declining throughout the early summer, new child cases have increased "exponentially," the organizations said, with an over five-fold increase the past month, rising from about 38,000 cases the week ending July 22 -- a 427% increase in the weekly rate.

Since the onset of the pandemic, nearly 4.8 million children have tested positive for COVID-19. Last week, children represented 22.4% of all reported COVID-19 cases.

At this time, severe illness due to COVID-19 remains “uncommon” among children, the two organizations wrote in the report. According to the nearly two dozen states, which reported pediatric hospitalizations, 0.1% to 1.9% of all child COVID-19 cases resulted in hospitalization. ​Similarly, in states which reported virus-related deaths by age, 0.00%-0.03% of all child COVID-19 cases resulted in death.

However, the AAP and CHA warned that there is an urgent need to collect more data on the long-term consequences of the pandemic on children, "including ways the virus may harm the long-term physical health of infected children, as well as its emotional and mental health effects."

-ABC News' Arielle Mitropoulos