Laszlo B. Tamas, Neurosurgeon with ties to the Bay area and Silicon Valley.
My only surprise is that many people are surprised by the growth curve the U.S. is on. But then most have little understanding of exponential curves.
Breathless media reports that cases doubled over the last 3 days? It’s been doing that since early March - just look at the raw data. Why a recent “explosion” of cases? Because that’s what exponential curves do.
Look at the graph below. There is a “deceptive zone” early on when exponential and linear growth do not appear that different. The average person could feel a (false) sense of security 3-4 weeks ago, if it weren’t for the scientists warnings of what was to come. Now we are seeing the “exponential explosion:”
There is also more testing now than before (though still woefully little). Want an example of how under-reported Covid-19 has been in the U.S.? Let me suggest a number experiment.
On March 26, 249 Americans died of Covid-19. Death usually represents disease contracted about 20 days before. Assume a mortality rate of 1% in the U.S. That means there must have been around 24,900 new cases on or near March 6. Yet officials reported only 74 new cases that day.
in other words, more than 99% of cases would seem to have remained undetected, and free to spread the disease around the country.
American leadership seems to have learned the “ostrich lesson” very well early on: “the less testing you do, the fewer cases you find.”
The “ostrich lesson”, in graphic form:
Hence the surprisingly low number of tests per capita in the U.S.: As for the future, where exactly is the U.S. on the curve? Let me suggest that death rates may be a better index than case rates, since they are less dependent on the degree of testing performed. Let me also present Covid-19 deaths per day, rather than cumulative deaths, and compare it with that of China, Italy and Germany: Now we all know the strict measurers taken to deal with Covid-19 in China. Italy’s criteria for a “Covid-19 death” is somewhat looser than in the U.S., and it has a much older population structure. Meanwhile, Germany has tested widely and from early on.
If we line up the above graphs such that their starting point (“Day 1”) was the first day with >10 deaths in either country, you get:
How far will the U.S. follow Italy’s curve (with a 10–12 day delay)? It’s hard to tell, but I’m pretty sure the worst is yet to come. Cheers!
Laszlo B. Tamas, 與舊金山灣區和硅谷有聯繫的神經外科醫生
我唯一感到驚訝的是，許多人對美國的增長曲線感到驚訝。但大多數人對指數曲線知之甚少。
令人窒息的媒體報道稱，病例在過去3天翻了一番?然而它從3月初開始就已經如此了——看看原始數據就知道了。為什麼最近病例“激增”?因為這就是指數曲線的作用。
請看下面的圖表。當指數增長和線性增長看起來並沒有那麼不同時，早期就有一個“欺騙區”。3-4周前，如果沒有科學家們對未來的警告，普通人可能會有一種(錯誤的)安全感。現在我們看到的是“指數爆炸”:
現在比以前有更多的檢測(儘管仍然少得可憐)。想知道新冠病毒在美國是如何被低估的嗎?這裡要提到一個數字實驗。
3月26日當天有249個美國人死於新冠。死亡通常代表在20天前感染的疾病。假設美國的死亡率為1%，這意味著在3月6日或3月6日前後一定有大約24900個新病例。然而，官員們當天只報告了74例新病例。
換句話說，超過99%的病例似乎仍未被發現，並可在全國範圍內自由傳播。
美國的領導層似乎很早就吸取了“鴕鳥的教訓”:“你做的檢測越少，發現的病例就越少。”
因此，美國的人均測試次數低得驚人。
至於未來，美國究竟處於什麼位置?我建議，死亡率可能是比病例更好的指標，因為它們較少依賴於執行的檢測程度。此外我建議用新冠每日死亡人數作為指標，而不是累積死亡人數，並將其與中國、意大利和德國的死亡人數進行比較:
《每日死亡人數》——藍線中國，橙線美國，灰線意大利，黃線德國
現在我們都知道中國處理新冠病毒所採取的嚴格措施。意大利對新冠致死的標準比美國要寬鬆一些，而且它的人口結構要老得多。與此同時，德國從一開始就進行了廣泛的檢測。
如果我們將上面的圖表排列起來，把它們的起始點——導致10人死亡看作疫情第一天，那麼你將得到這樣的圖表:
美國將在多大程度上跟隨意大利的步伐(10-12天的滯後)?很難說，但我很確定最壞的還在後面。
Jeff Little
It looks like cases per day in NY have slowed at the second derivative with the number of new cases only growing from 5k per day to 7k per day over about 4 days.
I am having trouble putting this into context, though. It could be that testing is catching up in that area and it will start declining after another 10 days or it could be that as hospitals get overrun, we will have a second surge and this can balloon out of control.
Any thoughts?
看起來紐約的每日新增病例在二階導數上有所放緩，從新增5000例到4天后的新增7000例。
不過，我很難把這個問題放到大背景中去考慮。可能是該地區的檢測正在迎頭趕上，10天后將開始下降，也可能是由於醫院人滿為患，我們將出現第二次激增，這可能會失控。
有什麼看法嗎？
Laszlo B. Tamas
Great observation, and thank you for your Comment Jeff! Perhaps consider looking at Covid-19 deaths. Less sensitive to testing. Can’t think of much else …
很棒的觀察，感謝你的留言！
也許我們可以考慮一下新冠死亡病例，畢竟檢測相對不敏感。除此之外想不出別的了……
Pat McCormack
Small world network spread. You start to run out of new connections. Prof Andrea Cristina mentioned that in Italy it could be 70 % asymptomatic. ( The Italians have eliminated the virus in the city of Võ with mass testing (twice) and quarantine - so it can be done) So far this is the best estimate if base rate infections that I can find.
We desperately need to know the base rate for other statistics to be useful.
A big test here in Spain has stalled as the test kits from China were rubbish. They only tested correctly 30% of the time. Going to set us back ten days of do which is an age in this situation.
Andrea Cristina教授提到意大利70%的感染者可能都沒有症狀。（意大利人通過大規模檢測和隔離清除了Vo市的病毒，所以病毒是可以解決的）
…………由於來自中國的檢測盒子是XX，西班牙的大型檢測已經停止。它們的檢測準確率只有30%。在這種情況下，我們要倒退十天的時間。
Roberto Cazzaro
One thing worth keeping in mind is that hypertension, obesity and diabetes are the 3 leading causes of co-morbidity for COVID-19. And the USA is the worldwide leader for all 3.
So it’s entirely possible that death rates in the USA will be higher than other countries. Which is what makes creating good estimates hard. What is clear is that between Thursday and Saturday this week, deaths doubled from 1000 to 2000, so the growth is really scary
值得注意的是，高血壓/肥胖和糖尿病是與新冠病毒共同發病的三大疾病。而美國在這三種疾病方面都處於世界領先地位。
因此，美國的死亡率完全有可能高於其他國家。這就是為什麼很難進行良好評估的原因。很明顯，從週四到週六，死亡人數從1000人增加到2000人，這樣的增長真的很可怕。
Sam Johnson
However, I think Italy will still hold that record. They have a very high elderly population, and most of the population smokes, which has a high correlative risk factor for death with Covid.
儘管如此，我覺得意大利依然在死亡人數上領先。它們的老年人口非常得多，並且大多數人都抽菸，這是與新冠死亡密切相關的風險因素。
Roberto Cazzaro
The biggest problem in Italy (beyond the two you mention which are absolutely true, even if smoking is not as much a problem as in the past) is that most of the outbreak happened in a relatively small area and hospitals were swamped. So they had to start triaging relatively early. Older people and people with co-morbidity need a respirator for 2-3 times as long as healthier people, are more likely to die anyway and their outcomes are much worse even if they survive, with reduced quality of life. So given the choice to save 3 people or possibly one with the same resources, the decision is obvious, even if terrible.
An older people in Italy didn''t die because they were old, but because they were more likely to have hypertension and other pre-existing conditions. The healthy older people did just fine, with recently a 101 and 102 years old recovering just fine.
Pre-existing conditions kill, not age. Which doesn''t bode well for the USA. Also, even if Italy has fewer ICU beds than the USA, it has more hospital beds and more doctors and nurses. More than 20% of Italian doctors got sick and unable to work. ICU rooms with no specialists are not very useful, and the skills needed to intubate and monitor COVID-19 patients is very high and hard to find.
And American doctors are having much more trouble getting enough PPE than Italian doctors had at a similar time in the outbreak (now they are struggling, too)
So, I still think that there is a good shot of being, in the best of Trump''s tradition “America first”
在意大利，最大的問題(除了你提到的兩個絕對正確的問題，即使吸菸導致的問題不像過去那麼嚴重)是，大部分的爆發發生在一個相對較小的地區——醫院人滿為患。所以他們不得不在相對較早的時候開始篩選（救誰）。老年人和有三大基礎疾病的患者比健康人對呼吸機的需求高2-3倍，且無論如何都更容易死亡，即使他們活下來，結果也更糟，生活質量下降。
所以在同等資源下，是選擇救3個人還是1個人，這個決定是顯而易見的，即使這個決定是可怕的。
意大利的老年人並不是因為年老而死亡，而是因為他們更有可能患有高血壓和其他疾病。健康的老年人過得很好，最近101歲和102歲的人恢復得很好。
是基礎疾病導致死亡，而不是年齡。這對美國來說不是好兆頭。而且，即使意大利的重症監護病房床位比美國少，它的醫院床位卻比美國多，醫生和護士也比美國多。即便如此，超過20%的意大利醫生因為生病而不能工作。
而美國醫生在獲得足夠的個人防護裝備方面比意大利醫生在疫情爆發時遇到的困難要多得多(現在他們也在掙扎)。
TJ Berens
As the US is over 100k cases now, the chart needs to be upxed…. after all, its now March 28, two days after the above chart ends… as the chart ends at only 12k cases
當前美國的確診病例已達10萬人，你的表格需要更新了。
畢竟現在是3月28號，距離你提供的圖表已過去了2天，你提供的圖表美國居然只有12000例病例。。。
Geoffrey Verity Schofield, Health Consultant at Fitttle.com
I think the answer is, quite obviously, yes.
In a few days, NYC alone will have more cases than all of China did, despite China…having a much larger and much more dense populationbeing the epicenter of the diseasehaving to be the first responder (sequence the genome, etc)it occurring during the time of the year where hundreds of millions of people are travelingMany places are still very much “icebergered” with a lot of cases undetected. China at least had an epicenter, meaning they could track people traveling from there. But this is now everywhere in America, there are dozens of new epicenters. Very little is being tracked.
Furthermore, many people are not, in technical terms, “staying the fuck at home”.
I got in an argument with someone on Instagram (like a moth to the flame, I am) who argued that everyone should go back to work immediately. President Trump wants to pack the churches for Easter.
The Mississippi governor said that he won’t issue a stay at home order, because “America is not China”.
Well, he’s right about that. It’s gonna be way worse.
In the past ten days, cases in Mississippi have gone from 50 to over 600 — and that rate of growth is the norm.
At the root of this problem is choosing economics over health.
Numbers on a screen or report over people.
Some more quotes:“155,934 people tested in New York State” (with 50,000 cases. Safe to say there are a LOT more cases that have been missed)“Need a total of 40,000 ICU beds. Currently have 3,000, with 3,000 ventilators. An additional 37,000 ICU beds are needed”“"We''ve procured about 7,000 ventilators. We need, as a minimum, other 30,000 ventilators. This is a critical and desperate need for ventilators [..] We need them in 14 days. Fema is sending 400 ventilators only. Federal action is needed to address this now through the Federal Defense Production Act"”“We need a faster testing process. Can''t wait 5 days as it is now. Other countries now also have home tests. We should do the same”So, the testing is slow, the incubation period is long, and the peak is 2–3 weeks away. Buckle up.
Follow me on Instagram for daily diet and training tips! Subscribe to my YouTube channel for longer form, informative content. Or both. Keep that immune system strong :)
Geoffrey Verity Schofield, Fitttle.com健康顧問
我認為答案是相當肯定的。
再過幾天，紐約的病例就會比全中國的病例都多，儘管中國：1.人口多得多，密度大得多；2.疾病的中心；3. 不得不成為第一反應者(對基因組進行排序等)；4. 它發生在一年中數以億計的人旅行的時候。
許多地方仍然有很多未被發現的“冰山”。中國至少有一個疫情中心，這意味著他們可以追蹤從那裡旅行的人。但是現在在美國到處都是這樣，有幾十個新的疫情中心。很少有人被跟蹤。
此外，很多人，用專業術語來說，並不是“呆在家裡”。我在Instagram上和一個人吵了一架(我就像一隻撲火的飛蛾)，他說每個人都應該馬上回去工作。特朗普總統想讓教堂擠滿復活節的人群。
密西西比州州長表示，他不會發布呆在家裡的命令，因為“美國不是中國”。
嗯……他是對的。因為美國的情況只會比中國更糟。
在過去的10天裡，密西西比州的病例從50例增加到600例以上，而這種增長速度是正常的。這個問題的根源是選擇經濟而不是健康。
死亡人數甚至更多——超過半數的死亡發生在過去3天內。紐約州州長 Andrew Cuomo表示，距離頂點還有14-21天。
更多相關信息：
“紐約州有155934人接受了檢測”(其中50000例陽性)。可以肯定的說，還有更多的病例被遺漏了)
“總共需要40000個重症監護病房床位。目前只有3000個，還有3000臺呼吸機。還需要37000張ICU床位。”
“我們買了大約七千臺呼吸機，我們至少還需要三萬臺，這都是急需的，我們14天內就需要它們，聯邦應急管理局只送來了400臺呼吸機。現在需要聯邦政府採取行動，通過《聯邦國防生產法》來解決這個問題。“
“我們需要一個更迅速的檢測過程。不能再像現在這樣等5天了。其他國家現在已經有居家檢測了，我們也應該這樣做。"
檢測太慢了而且潛伏期很長，而高峰是在2-3周後，繫好安全帶抓穩了。
Carl Jacobson
In terms of New York City - the mayor didn’t shut down schools and businesses until it was too late. His own staff were in revolt against his lack of action. Finally, he issued the closures, but it was too late. The infection rates are the highest in the nation. California is a little better - but not that much. There is so much population movement here, especially from Asia, that we’re going to be a major infection epicenter, regardless of any preventive actions.
就紐約市而言，市長沒有關閉學校和企業，直到為時已晚。他自己的職員都反對他不採取行動。最後，他發佈了關閉命令，但為時已晚。
這裡感染率是全國最高的。加州稍微好一點，但也好不到哪兒去。這裡有如此多的人口流動，尤其是來自亞洲的人口流動，無論採取什麼預防措施，我們都將成為一個主要的感染中心。
Geoffrey Verity Schofield
Yea…travel bans do not work. Only one person slipping through can infect thousands. They do delay the peak, but we didn’t use that time to prepare, so it didn’t matter.
是啊，而且旅遊禁令沒用，只要有一人溜出去就可以感染數千人。這可以延緩高峰期的到來但我們並沒有用這段多出來的時間做準備，所以，不重要了。
Krister Sundelin, UX Writer at HiQ Göteborg (2011-present)
Note how the total cases or the daily new cases haven’t even started to slow down. So the infection spread is accelerating, and will continue to do so for some time.
On top of that, there’s the incubation time. There are all these people infected who don’t know it yet. Whatever you do now to stop or alleviate the pandemic will not have any effect until at least seven days, so the new cases curve will not change for at least that time.
Now remember that the death curves lags about 14 days behind. People contracting covid-19 now will start dying in about 14 days. So, rough estimate, seven days before any isolation takes effect. Then at least another seven days until the inflection happens and new cases start to drop off. And then another 14 days until deaths start to drop off.
Sum it up, and you have at least a month of hell before you.
And that’s the best case scenario.
“How can it get worse than that?” I hear you ask. Hospitals are already screaming for resources and supplies, and states and counties have started a bidding war on the little supplies there is. Many counties have said that they have supplies for a few days, maybe a week. Then they’re out.
And when that happens, corona patients cannot be treated. And that means that many patients, who would survive if they had care, will not. That will increase the deaths even more. Cases who could have remained minor cases with hospital care will now become severe cases. Severe cases who would have remained severe cases with proper care will now be critical cases. And critical cases who could have been saved … may no longer be saved.
On top of that, corona patients compete with resources from all other cases, and they will not simply stop. People will still need trauma care, cancer treatments, dialysis and so on, but now hospitals will not have the resources to care for all of those either because of corona.
Michael Feely, Lived in the United States most of my life, know some of its history.
The US has only, barely, begun to bend the curve, and the US’s curve has been seeing a more rapid spread of SARS-CoV2 than Italy almost the whole time. And we know how many dead Italy’s infection curve left in its wake. It takes a large absolute number of people to overwhelm the greater capacity of hospital beds in our larger country with a larger population, but there is no reason to believe the US in aggregate won’t hit that point and NYC is beginning to hit it now. Add in the US’ relatively low number of tests administered, and the curve here is realistically even steeper than it looks from the plot of known positives. And it typically takes 5–9 days or so to develop symptoms, and another week or two to recover (or not) so there are a lot of illnesses and deaths baked in from before states started issuing lock downs.
So it’s going to get worse. Quite a lot worse. Especially as more of the frontline people who are fighting like hell for all of us in the hospitals, clinics, and ambulances get sick.
I keep expecting to open up a news page and see a headline that just says “We’re Fucked”
Original question:
Is the worst yet to come with Covid-19 in the U.S.?
Michael Feely, 我在美國生活了大半生，瞭解了一些美國的歷史。
答案是肯定的。
美國只是勉強開始壓制這條曲線，而且幾乎一直以來，美國的曲線上的傳播速度都比意大利快。我們知道有多少人死於意大利的感染曲線。在我們這個人口眾多的大國，需要大量的絕對人口才能使醫院床位的巨大容量不堪重負，但我們沒有理由相信，美國總體上不會達到這一目標，而紐約現在正開始達到這一目標。再加上美國實施的檢測數量相對較少，這一曲線實際上甚至比已知陽性結果的曲線更為陡峭。通常需要5-9天左右的時間才會出現症狀，再過一兩個星期才會恢復(或不恢復)，所以在各州開始簽發禁閉令之前就已經有很多病患和死亡了。
所以情況會變得更糟。更糟。特別是當越來越多的前線人員在醫院、診所和救護車上為我們拼命戰鬥的時候。
我一直等著打開一個新聞頁面，看到一個標題，上面寫著“我們完蛋了”。
Franklin Veaux, Professional Writer
Answered Sun · Upvoted by Robert Hampton, MD Medicine and Healthcare, Emory University (1976) and Aishik Kundu, MBBS Medical School & Medicine and Healthcare, Medinipore Medical College (2022)
Here’s a quick riddle to illustrate how most people really, really don’t understand exponential growth:
Lilly pads are growing on a pond. Every day, the amount of pond they cover doubles. It takes 30 days for the lily pads to cover the entire pond. How long does it take them to cover half the pond?
Answer: 29 days.
They double every day. On day 29 they cover half the pond; on day 30 they double and cover the whole pond.
That’s how exponential growth works. It starts out very small. So small you don’t notice. Doo bee doo, nothing happening, nothing to see here, nothing happening, then all of a sudden, wham! It’s everywhere.
Human beings are used to living in a world where things happen more or less linearly, not exponentially. Our intuition doesn’t work for exponential growth.
Here’s another example: Take a chess board. Put a penny on one square. Put two pennies on the second square, then four pennies on the third square, then eight pennies, then 16, then 32, then 64, then 128 (at this point you’re only up to a dollar and twenty-eight cents), then 256, 512, then 1024.
It takes eleven squares just to hit $10. But here’s the thing…when you get to the last square, you have more money than exists in all the world’s economies combined…by five orders of magnitude.
Yes, the worst is yet to come.
Franklin Veaux, 職業作家
人們是真的不理解指數增長:
莉莉家的浮葉長在池塘裡。每一天，它們所覆蓋的池塘面積都會翻倍。浮葉需要30天才能覆蓋整個池塘，那它們要花多長時間才能覆蓋半個池塘呢?
答：29天。
他們每天翻倍。第29天，他們覆蓋了半個池塘，到了第30天，它們翻了一倍，覆蓋了整個池塘。這就是指數增長的原理。它一開始很小。小到你都沒注意到。什麼都沒發生，這裡什麼都沒看到，什麼都沒發生，然後突然，砰!它無處不在。
人類習慣於生活在一個事物或多或少是線性而不是指數的世界裡。我們的直覺並不適用於指數增長。
這是另一個例子:拿一個棋盤。把一便士放在一個方框。第二格放兩枚便士，第三格放四枚便士，然後是八枚便士，然後是16枚，32枚，64枚，128枚(此時你只剩下1美元28美分)，然後是256,512枚，最後是1024枚。
需要11個方塊才能得到10美元。但……當你到最後一格時，你的錢比世界上所有經濟體的錢加起來還要多，甚至高了五個數量級。
所以，是的，最糟的還在後頭。
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