Massachusetts public health officials reported 4,378 new COVID-19 breakthrough cases in fully vaccinated individuals in the past week, data from the state’s Department of Public Health shows.A breakthrough case is when an individual tests positive for COVID-19 after they’ve been fully vaccinated against the disease.The 4,378 new breakthrough cases were reported to the DPH between Sept. 18 and Sept. 25.During the same seven-day period, the state reported 11,137 new COVID-19 cases among the state’s whole population.The data from the DPH shows there have been 36,723 total cases of COVID-19 in fully vaccinated individuals as of Sept. 25. Last week, the DPH reported 32,345 total breakthrough cases through Sept. 18.The 36,723 total breakthrough COVID-19 cases are among the 4.61 million residents considered fully vaccinated in Massachusetts, or about 0.8% of those individuals. The state health department said 1,155 total breakthrough cases have resulted in hospitalization, an increase of 154 over the previous week.The state said 254 breakthrough cases have resulted in death based on information reported to date, an increase of 37 in the past week.Massachusetts hospitals have begun to see a decline in hospitalizations since a summertime surge that started just after the Fourth of July. The number of COVID-19 patients currently stands at 606. It dipped to as low as 80 on July 4 and as high as 707 on Sept. 13. The seven-day average of hospitalizations has increased from a low of 85 on July 9 to the latest mark of 615.