As of Wednesday, 87 percent of hospital staff were fully vaccinated, up from 84 percent the previous week, the state reported. Between 89 and 92 percent of staff working in hospitals, nursing homes and adult care facilities had received at least one dose of a coronavirus vaccine, it added.

The state’s mandate has not been without protest — some doctors, nurses and other providers filed lawsuits, arguing that the state didn’t provide sufficient exemptions. However, the rise in vaccination rates suggests that New York has so far succeeded in rolling out the requirement without causing severe staffing shortages.

New York was the state with the earliest vaccination deadline for health-care workers, and its experience will be watched closely by other states that have instituted vaccine mandates for the sector.