"A recent *preprint study published in bioRxiv, suggests that many people who contract SARS-CoV-2 but have mild or no clinical signs still develop so-called T-cell-mediated immunity to the virus, even in the absence of a positive antibody test. The researchers conclude that this is likely to mean that public immunity is probably higher than antibody testing has so far suggested.
The link says:
Our results indicate that roughly twice as many people have developed T-cell immunity compared with those who we can detect antibodies in.”
Sweden has about 8600 confirmed cases per million. If you multiply that by ten, to get roughly the number of people with Abs, then by another two, for T-cell immunity, they're still under 20% of the population. Stockholm will be higher, but not that much higher. In June, an Ab study reported that about 10% of the city's population was positive. Confirmed cases have risen by about 60% since the middle of June, so maybe 16% of the population now has Abs. Double that for T-cell immunity, and maybe one-third of the city's population has some form of immunity. There was another Ab study about a month ago that found 17.3% of the subjects were positive, though that was not a random sample. With T-cell immunity, maybe you can push Stockholm--not Sweden, but just the capital city--to 40%. That helps slow the spread a lot, but it is not herd immunity.
You also have to remember that T-cell immunity does not mean there is no spread, as Koronin notes. T cells reduce severity of symptoms, they don't necessarily prevent infections. We don't actually know whether individuals with only T-cell immunity to COVID harbor the virus and can spread it to others. The whole point of herd immunity is that such a large proportion of people are immune that the virus has nowhere to spread. But if it can still spread to people with T-cell immunity, then this may not contribute that much to herd immunity.
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