The figure, which Sweden's Public Health Authority confirmed to CNN, is roughly similar to other countries that have data and well below the 70-90% needed to create "herd immunity" in a population.
It comes after the country adopted a very different strategy to stop the spread of coronavirus to other countries by only imposing very light restrictions on daily life.
Sweden's chief epidemiologist Anders Tegnell said the number was a "little lower" than expected "but not remarkably lower, maybe one or a couple of percent."
"It squares pretty well with the models we have," he added, while speaking at a news conference in Stockholm.
The study carried out by Sweden's Public Health Agency aims to determine the potential herd immunity in the population, based on 1,118 tests carried out in one week. It aims to carry out the same number of tests every seven days over an eight-week period. Results from other regions would be released later, a Public Health Authority spokesperson said.
Sweden has adopted a different strategy to other Nordic nations during the pandemic, choosing to avoid a lockdown and keep most schools, restaurants, salons and bars open. It did, however, ask people to refrain from making long journeys, placing an emphasis on personal responsibility.
The strategy was criticized by Swedish researchers early on, who said that attempting to create herd immunity had low support. But the authorities denied that achieving herd immunity was their goal.
Herd immunity is reached when the majority of a given population -- 70 to 90% -- becomes immune to an infectious disease, either because they have become infected and recovered, or through vaccination. When that happens, the disease is less likely to spread to people who aren't immune, because there just aren't enough infectious carriers to reach them.
No community has yet achieved this and a vaccine "will get us to herd immunity quicker" than infection, Michael Mina, Assistant Professor of Epidemiology at Harvard T. H. Chan School of Public Health, said in a recent
interview with Public Radio International's The World.
Sweden's percentage of people with antibodies is not far off that of other countries that did enforce lockdowns. In Spain, 5% of people had developed coronavirus antibodies by May 14, according to preliminary results of an epidemiological study by the government.
According to Martin Kuba, an official Jihocesky region in the Czech Republic who spearheaded a randomly selected mass testing for coronavirus among the general public and frontline workers, the initial results showed that the proportion of people who have had the disease stood at "single digit percent" rather than "fraction of a percent".
Michael Osterholm, the director of the Center for Infectious Disease Research and Policy at the University of Minnesota, estimated earlier this month on CNN Tonight with Don Lemon that between 5% and 15% of people in the US have been infected.
He said the coronavirus was going to circulate and infect at least 60% to 70% of the population before it slows down, but warned that the country had "a long ways to go" to get to a level of herd immunity. A report he wrote along with other epidemiologists and a historian estimated this would likely take 18 to 24 months.
Dr. Mike Ryan, executive director of the World Health Organization (WHO) Health Emergencies Program, said the concept of herd immunity was a "dangerous calculation."
When asked if he would be comfortable with immunity passports based on his company's tests, CEO of Swiss drugmaker Roche Severin Schwan told CNN's Julia Chatterley: "I do believe that we are in a world with a lot of ambiguity, and we also have to make decisions on incomplete information. So, I do think it is valuable information, but we should not fully rely on it."
On April 24, chief epidemiologist Tegnell told BBC radio that the authorities believed Stockholm had "an immunity level... somewhere between 15 and 20% of the population."
He said the strategy had "worked in some aspects ... because our health system has been able to cope. There has always been at least 20% of the intensive care beds empty and able to take care of Covid-19 patients."
Asked whether Sweden's approach will help it withstand a possible second wave, Tegnell said he believed it would.
"It will definitely affect the reproduction rate and slow down the spread," he said, but added that it wouldn't be enough to achieve "herd immunity."
But Sweden's foreign minister Ann Linde and Peter Lindgren, managing director at the Swedish Institute for Health Economics (IHE), said last month that it had failed to prevent a high number of deaths in care homes.
Sweden has now had 32,172 cases and 3,871 deaths, according to figures from Johns Hopkins University.
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