The study, appearing in the Lancet medical journal, found that people over the age of 65 had only 47 percent protection against repeat infection, compared to 80 percent protection for younger people.
The majority of people who have had Covid-19 are protected from getting it again for at least six months, a study published on shows, but older people are more prone to reinfection than younger people.
The study, appearing in the Lancet medical journal, found that just 0.65 percent of patients tested positive a second time for Covid-19 after previously being infected during Denmark's first and second waves. That was much lower than the 3.27 percent who were positive for the virus using highly accurate PCR tests after initially being negative.
However, the study found that people over the age of 65 had only 47 percent protection against repeat infection, compared to 80 percent protection for younger people.
"Our study confirms what a number of others appeared to suggest: reinfection with Covid-19 is rare in younger, healthy people, but the elderly are at greater risk of catching it again," said Steen Ethelberg of Denmark's Statens Serum Institut.
"Since older people are also more likely to experience severe disease symptoms, and sadly die, our findings make clear how important it is to implement policies to protect the elderly during the pandemic."
The authors of the study found no evidence that protection against reinfection declined over a six month follow-up period, but said further studies were needed to assess protection against reinfection from variants of the coronavirus.
The data analysed was collected through Denmark's national testing strategy, under which 69% of the population, or 4 million people, were tested over the course of 2020.
Commenting on the results, Imperial College London professors Rosemary Boyton and Danny Altmann, said the results showed lower protection and were "more concerning" than previous studies.
"These data are all confirmation, if it were needed, that for SARS-CoV-2 the hope of protective immunity through natural infections might not be within our reach and a global vaccination programme with high efficacy vaccines is the enduring solution," they said in a linked comment piece also published in the Lancet.
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