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Reinfection is not rare, Singapore has detected 26 cases of reinfection so far: https://www.straitstimes.com/singapore/politics/parliament-2... Also note worthy: recent infections in Singapore includes "56 cases involving people who were infected despite being fully vaccinated"

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Reinfection is very rare. The Israeli study is the most reliable, but going by your data point of 26 cases of reinfection and the ~61,000 cases[0] in Singapore, we're talking 1 in 2,500.

0 https://ourworldindata.org/explorers/coronavirus-data-explor...

But that statistic is useless on its own. The more salient statistic is "how much lower was the infection rate among people who have recovered, compared to people who had never had COVID, for the same time frame?".

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