THE HAGUE, Netherlands—The Dutch health council advised the government Tuesday to begin giving COVID-19 vaccine booster shots to everybody 60 and older and residents of nursing homes, saying it was seeing indications that COVID-19 protection was waning among older people. “To get ahead of an increase in serious illness, the council advises the health minister to start offering boosters now,” the council said. The government, which was set to reimpose some COVID-19 preventive measures later Tuesday, usually follows the health council’s advice. Other European countries already have begun giving booster shots. France started giving boosters to people over 65 two months ago. Just under 80 percent of adults in the Netherlands are fully vaccinated. The government already has begun giving booster shots to people with severely compromised immune systems. COVID-19 cases have been rising sharply for weeks in the Netherlands. The country’s public health institute reported Tuesday that infections rose …