Surviving a previous infection provided better protection than vaccination against Covid-19 during the Delta wave, federal health authorities said, citing research showing that both the shots and recovery from the virus provided significant defense.

The Centers for Disease Control and Prevention said Wednesday that data from 1.1 million Covid-19 cases in California and New York last year showed people who were unvaccinated and hadn’t previously contracted Covid-19 faced a far greater risk than both people who had gotten the shots and people who had been infected.