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It has been reported in relation to the recent US travel ban on the EU's 26-country Schengen area that

The President justified the ban by saying the EU had failed to take the same precautions as the U.S. in banning travel from China in order to stop the spread of the virus. “As a result, a large number of new clusters in the United States were seeded by travellers from Europe,” he said Wednesday.

How much data backs up this assessment?

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    Questions about unresolved current events and issues currently under investigation by a court of law, government, or other similar investigative body are off-topic because there is insufficient data for a meaningful answer. – Daniel R Hicks Mar 12 at 13:14
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    31 were people who traveled from Italy according to the New York Times. nytimes.com/interactive/2020/us/coronavirus-us-cases.html – DavePhD Mar 12 at 14:29
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    @DavePhD: that seems to be talking about US citizens traveling to Italy (and contracting it there), which would not be really affected as the ban doesn't affect US citizens... But I see now the shift in frame of reference in Trump's statement, i.e. "travellers from Europe" might not be those groups he actually banned. – Fizz Mar 12 at 14:36
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    @Fizz Robert Redfield, director of CDC, said "a lot of people coming back and forth from Europe that are now starting to seed these communities" apnews.com/96e87b81f05f7ec54fc3e0ad152bd25c – DavePhD Mar 12 at 14:41
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    @Fizz "Those who are exempt from these restrictions, such as American citizens, will be directed to a limited number of airports where screening can take place" whitehouse.gov/briefings-statements/… – DavePhD Mar 12 at 14:44
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There's minimal (ie, no) data to back that up that assertion.

Here's the timeline of first detection after China:

  • January 13 Thailand
  • January 16 Japan
  • January 20 South Korea
  • January 21 United States
  • January 25 Australia, France, Canada, Malaysia
  • January 27 Cambodia, Germany, Sri Lanka

and after that it really started breaking out.

It was first detected in the US days before it was detected in Europe.

Further, the lack of testing in the US makes it impossible at the moment to determine how far it might have spread and be spreading internally. Based on evidence from Canada where new cases have been traced back the United States, it's just as possible that the US introduced the virus to European countries as is the reverse.

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  • Even if most cases in the US are of other origin, it could still be that "a large number" are travelers from Europe. – GEdgar Mar 14 at 11:19
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    Keith, in the president's statement, it is clear that "new clusters" are not referring to the oldest clusters. whitehouse.gov/briefings-statements/… He is saying that the US prohibited travel from China, while Europe did not, and therefore "new clusters" formed in the US due to travel from Europe. Why does your answer say "No travel restrictions from China or other Southeast Asian nations were ever put in place"? That is clearly false. – DavePhD Mar 14 at 13:33
  • I made an error regarding the China one. However the other part was accurate. Also, what part of his statement are you indicating? What he said or what his staff had to correct because he was full of shit? – Keith Morrison Mar 15 at 8:06
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No. The tracking of virus mutations shows that this is not true. The replication of the virus is not perfect and causes minor mutations. These mutations can be observed and give evidence about the origin of the virus. This is shown in the a graphical representation in the attached link.

Genomic epidemiology of novel coronavirus (hCoV-19)

enter image description here

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    Can you elaborate a bit more on that? "link-only" answers are discouraged. This article might also help sciencemag.org/news/2020/03/… – Fizz Mar 13 at 23:21
  • 41 cases are directly from travel to Egypt, 35 from travel to Italy, 15 China, 2 Korea and 2 Iran. nytimes.com/interactive/2020/us/coronavirus-us-cases.html Another 56 are from unspecified oversea travel. I know of 1 case (in Montgomery county, MD) from travel to Spain and 1 (in Harford county, MD) from travel to Albania and Turkey. – DavePhD Mar 14 at 1:00
  • @DavePhD How should I interpret your post, since it seems to be about travelling to other countries from the US, while the question is about travelers from Europe to the US? As I understand it, the ban is for inbound travelers from a number of European countries, and not for US citizens traveling outbound. – fatdoor Mar 14 at 8:14
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    Even if most cases in the US are acquired by community spread, or travelers from China, it could still be that "a large number" are travelers from Europe. – GEdgar Mar 14 at 11:18
  • There's an article/interview that discusses that map (albeit an older iteration from Feb 25). – Fizz Mar 14 at 12:32
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Interestingly, a recent paper draft from the Icahn School of Medicine at Mount Sinai supports Trump's claim as far NYC is concerned. It could have been a matter of luck as to which strain actually spread (the most) in NYC, but there were apparently a more introduction events from Europe, so basically more "coin flips" in that basket until one turned lucky.

The first isolate had documented exposure through travel to the Middle East (clade A3) and the second through travel to Europe (clade B). Neither of these showed evidence of onward transmission, so we therefore excluded these two cases from any inference made from the phylogenetic analyses. For the remaining isolates, the great majority (87%) cluster with clade A2a. This clade is largely composed of isolates obtained from patients with COVID19 in Europe (72%; Figure 2B), suggesting that introductions from Europe account for the majority of cases found in NYC in the first weeks of March 2020.

[...] The earliest sequences at the base of clade A2a include isolates from Italy, Finland, Spain, France, the UK, and other European countries from late February, in addition to a few North American isolates (Canada and US) from the first week of March 2020. [...]

For the rest of the clades (B, B1, and B4), we identified four putative SARS-CoV-2 virus introductions to NYC as early as February 20 (90%CI: January 29 to February 26) (Table 1). Notably, two of these introductions were inferred to be of domestic origin based on their close relationship with US isolates, including those from the main community transmission in Washington state (Clade B1) (Bedford et al. 2020). The introduction of this clade to the East Coast was recently reported (Fauver et al. 2020). Although more than half of the sequences in clade B were of Asian origin (Figure 2B) the closest relatives to the NY isolates were of European and North American origin. The isolate that belongs to clade B4 is positioned in a cluster with two US sequences from WA state, with an inferred date of introduction to NY in early March (Table 1) and a prior period of untracked transmission in unknown location(s) since January 21 2020 (90% CI: January 18 to January 23). Prior to this period, the closest viral isolates basal to this cluster are from Australia and China (Figure S1). [...]

enter image description here

Taken together, our results show that the NYC SARS-CoV-2 epidemic has been mainly sourced from untracked transmission between the US and Europe, with limited evidence of direct introductions from China where the virus originated.

So yeah, the strain that spread the most in NYC apparently came mostly directly from Europe, but it was preceded e.g. by one from the Middle East. Why that other one didn't spread is of course hard to peg to a concrete event like luck or something else (e.g. effective quarantine) since the paper doesn't detail such matters.

Also, a smaller fraction of the NYC cases was traced (domestically) to Washington state and from there to China/Australia.

They also note some limitations of their study, mainly in terms of sampling

A limitation of our analysis is the relatively small number of isolates from cases identified in the first week of March 2020 which means that our model relies on inferences based on sequences deposited in the GISAID database. Since sequencing efforts vary by country, the fraction of sequences available by region/country is not necessarily representative of the number of cases reported for each of these regions. Thus, some of these inferences may change as more complete and representative SARS-CoV-2 sequences become available.

Also, one can quibble that NYC is a "single cluster", but I think the ISMMS paper is still interesting enough in its findings in terms of (which) strain(s) spread in NYC.

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    Excellent update, though of course it may be worth noting that this answer is not in conflict with the previous answers; if nothing else, the relative size of the WA and NYC outbreaks on the genomic epidemiology map shows how early in the process its conclusions were. That the president's statement is true now (mid-April) doesn't mean that it was true when stated because the data themselves have changed over time, not just our knowledge. – Steven Stadnicki Apr 14 at 23:09
  • Also theintercept.com/2020/04/12/… "The Intercept reviewed hundreds of media reports detailing the first recorded coronavirus cases — known as the “index cases” — in U.S. states and territories. European travel preceded the index cases in at least 13 states and territories, compared to only six from China. There were as many imported index cases from cruise ships (six) as from China, while Italy accounted for at least 10 of the first Covid-19 cases." This is from fairly political publication though... – Fizz Apr 16 at 23:30

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