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Firstly note that asymptomatic carriers are very common. But are they contagious? Let's examine the scientific research...

On February 21st 2020 a case study was published in the Journal of the American Medical Association. The following day a peer summed it up in a Guardian report...

“You had this patient from Wuhan where the virus is, traveling to where the virus wasn’t. She remained asymptomatic and infected a bunch of family members and you had a group of physicians who immediately seized on the moment and tested everyone.”

Meanwhile in Europe...

The German Health Ministry debunked a case of a Shanghai business-woman in a peer-reviewed paper from Munich University in early February. However on the 13th March another Munich researcher was quoted, this time from a teaching hospital, saying that (though she may have had symptoms) the male German colleague she infected was asymptomatic and in turn infected others.

nature_yellow A single article in "nature" magazine
summarised most of the papers below...

June 6th
56% infected kids asymptomatic or just mild symptoms
nature_green Peer-reviewed Chinese paper by Dong et al
Looked at seven hundered infected kids in China

March 6th
59% of the infected in were undiagnosed
nature_green Preprint Chinese study by Wang et al
Looks at Hubei cases

March 8th
Some had high virus levels early on when symptoms were mild
nature_green Preprint German paper by Woelfel et al
Looked at nine hospital cases

March 12th
18% of the infected found to be permanently asymptomatic
nature_green Peer-reviewed study by Mizumoto et al
Looks at passengers on Diamond Princess cruise ship
CDC said 46.5% were asymptomatic at the time of testing.

March 13th
31% of the infected found to be permanently asymptomatic
nature_green Peer-reviewed study by Nishiura et al
Looks at Japanese evacuated from Wuhan

March 18th
Infectiousness starts 2.5 days before the onset of symptoms and peaks 15 hours before
Preprint Chinese paper by He et al
Also says about 44% of transmissions occur before symptoms.

March 19th
High virus levels early on and even in a patient who was permanently asymptomatic
nature_green Peer-reviewed Chinese (Guangzho, Zuhai, Hong Kong) paper by Zou et al
Looked at eighteen ex Wuhan and contacts

March 20th
10% of infections might be from asymptomatic transmission
Austin Texas Uni Preprint paper by Meyers et al
Looks at 450 case reports from 93 Chinese cities

April 2nd
WHO acknowledges presymptomatic transmission but not asymptomatic