The study analysed the risk of getting Delta compared to the risk of those most likely to get it, in other words, people who had neither been vaccinated nor infected in the past by the beginning of October.
Those that had been vaccinated but never infected with COVID-19 were six times less likely to get it in California, and about five times less likely in New York.
But the risk was even lower for previously infected but not vaccinated individuals: by 29 in California, and by 15 in New York.
When analysing the risk of hospitalisation, this time in California only, the researchers found a similar reversal between the two periods.