WORCESTER — COVID-19 case counts in the city continued to fall over the past week, amid increasing vaccination availability, more reopenings and rule relaxations. The city confirmed 107 more cases of the pandemic virus over the past week for a total of 23,579 since March 2020. That number is down 63 cases from last week, when the city reported 170 new cases. Hospitalizations saw sharp decreases between St. Vincent Hospital and UMass Memorial Health Care; the two hospital systems reported a total of 35 COVID-19-positive inpatients, down 17 from last week. There were 15 COVID-19-positive intensive care unit patients, a decrease of one over last week. The hospital system confirmed another five deaths over last week for a total of 728 since the start of the pandemic. Two more city residents died from the virus, bringing the total in the city to 424.