captainpatriot
2020-03-10T22:00:21+00:00
Open Letter on COVID-19
关于COVID-19的一封公开信
By Ninghui Li, Professor of Computer Science, Purdue University
作者:李宁辉，普渡大学计算机科学教授
This letter aims at convincing the US Governments and the public about the urgent need to immediately adopt aggressive social distancing policies to contain the spreading of COVID-19.
这封信的目的是说服美国政府和公众，迫切需要立即采取积极的社会疏远政策，以遏制COVID-19的传播。
Facts.
事实
Once community spread takes hold in a country or region, the number of cases increases exponentially, doubling every 3 days or so, unless aggressive social distancing policies are enforced.
一旦一个国家或地区出现社区传播，病例数就会呈指数级增长，大约每3天翻一番，除非实施积极的社会疏远政策。
See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
请看，例如，中国境外的病例数，以及法国、德国、西班牙、瑞士、英国、荷兰、瑞典、比利时、挪威的病例数。
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-az7wZdT1kShs-dc.jpg.medium.jpg[/img]
Update. March 10.
Exponential growth occurs because the number of newly infected people is proportional to the number of people already carrying it. In a simplified model, if each person carrying the virus on average transmits to 0.26 persons per day, the total number of patients will be multiplied by 1.26 each day, and will double every 3 days. Starting from 100, it takes 10 days to go to 1000, 20 days to go to 10,000, 30 days to go to 100,000, etc.
指数增长是因为新感染的人数与已经感染的人数成正比。在一个简化的模型中，如果每个携带病毒的人平均每天传播0.26人，那么患者总数将乘以每天1.26人，每3天翻一番。从100开始，10天到1000,20天到10000,30天到100000。
Update. March 10
The spreading of communicative diseases follows the same mathematical models as the spreading of computer worms. See studies on how code-red worm, the SQL slammer worm spreads. Once exponential growth starts, it slows down only when getting close to saturation (every target has been infected), unless intervention stops the growth.
传播疾病的传播遵循与计算机蠕虫传播相同的数学模型。参见关于代码红色蠕虫、SQL slammer蠕虫如何传播的研究。一旦指数增长开始，它只有在接近饱和(每个目标都被感染)时才会减慢，除非干预停止增长。
See figure.
见图
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-l2ipK4T1kShs-dc.gif.medium.jpg[/img]
The US case number has been growing exponentially for over a week. On Saturday Feb 29, the total number of US cases is 69, including 47 cases originated from the Diamond Princess cruise ship or Wuhan evaluation, and 22 local cases. By Saturday Mar 7, the number of local cases rose to 388. Within 7 days, the number of local cases increased more than 16 folds, doubling more than 4 times.
一周多以来，美国的病例数呈指数增长。2月29日星期六，美国的病例总数为69例，其中47例来自钻石公主号游轮或武汉评估，22例来自当地。截至3月7日星期六，当地病例增至388例。7天内，局部病例数增加16倍以上，增加4倍以上。
When the number of cases reaches thousands, the sheer volume of patients will overwhelm the healthcare system. Hundreds or more people (mostly older citizens) die, and medical workers will suffer greatly. See reports on this in S. Korea, Italy on Mar 2, Italy on Mar 7, Europe.
当病例数达到数千时，庞大的患者数量将使医疗系统不堪重负。数百人或更多的人(大部分是老年人)死亡，医务工作者将遭受巨大的痛苦。参见3月2日在韩国、3月7日在意大利、欧洲的报道。
A March 6 3月6Testimony of a Surgeon working in Bergamo,Italy uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
一名在意大利贝加莫工作的外科医生的证词。用第一手的经验来解释医院的压力和新冠病毒肺炎并不是流感。
Update. Mar 11
By locking down Hubei province, China limited the numbers of COVID-19 cases in other provinces to be relatively small. When hospitals in Hubei are overwhelmed, China mobilized the medical resources of the whole country to help.
通过封锁湖北省，中国将其他省份的病例数量限制在相对较小的范围内。当湖北的医院不堪重负时，中国动员全国的医疗资源来帮助他们。
COVID-19 has a significantly higher fatality rate than Flu appears to be about 20 times as deadly as Flu for every age group. Flu is estimated to have fatality of 0.1%. Estimation of the fatality rate of COVID-19 varies, some numbers are 2.3% according China’s CDCP, 3.4% according to the WHO.
COVID-19的致死率明显高于流感，在每个年龄组的致死率是流感的20倍左右。据估计，流感的致死率为0.1%。对covt -19致死率的估计各不相同，中国疾病预防控制中心的数字是2.3%，世界卫生组织的数字是3.4%。
Update. Mar 10.
Comparison of age-based fatality rates of Flu vs. COVID-19
在不同年龄人群中，流感和新冠病毒肺炎的死亡率对比
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-ank0ZfT3cSuk-z6.jpg.medium.jpg[/img]
According to worldometer worldometer, among 66,106 closed cases, there are 3828 deaths, translating to a 5.8% fatality rate. This is dominated by data from China. It could be too high, as many people with mild symptoms in China may be self-quarantined and not discovered. On the other hand, this is achieved because China can mobilize medical resources of the whole country to treat patients in Hubei. The rate would be a lot higher otherwise.
在66106宗已完结的病例中，有3828宗死亡，即5.8%的病死率。这主要是来自中国的数据。这可能太高了，因为在中国，许多有轻微症状的人可能被自我隔离，而没有被发现上报。另一方面，这是因为中国可以调动全国的医疗资源来治疗湖北的病人。否则死亡率会高得多。
The numbers from the other countries with more than 5000 cases are worrisome. As of March 5, S. Korea tested 140,000 cases, with 6000 positive cases, and 33 deaths. However, using 33/6000 to claim 0.6% fatality rate is utterly wrong, since the vast majority of the 6000 cases are still active, and the number of deaths will increase. As of March 8, S. Korea has 51 deaths, 166 recovered cases, and 7165 cases being treated. S. Korea’s thorough testing means that even patients with mild symptoms are included, yet this yields a tentative fatality rate of 51/(51+166) = 23.5%, which is alarmingly high.
来自其他国家超过5000例的数字令人担忧。截至3月5日，韩国检测了14万例，其中6000例为阳性，33人死亡。然而，用33/6000来声称0.6%的致死率是完全错误的，因为6000个病例中的绝大多数病程仍在发展，死亡人数还会增加。截至3月8日，韩国已有51人死亡，166人痊愈，7165人得到治疗。年代。韩国的全面检测意味着即使有轻微症状的患者也包括在内，但这得出的暂定病死率为51/(51+166)= 23.5%，这一数字高得惊人。
Similarly, as of March 8,Italy has 366 deaths, and only 622 recovered cases. Iran has 194 deaths for 2134 recovered cases. These are the most critical numbers to be watched in the next few days. Some scientists claim that there are two strains with one deadlier, but there is no consensus. Even for a very conservative estimation of fatality rate of 1%, it would mean 5% to 10% of patients need hospital care, which cannot be provided when it is a pandemic. Without adequate medical care, the fatality rate will be higher.
同样，在3月8日，意大利有366人死亡，只有622人康复。伊朗有194人死亡，2134人康复。这些是未来几天需要关注的最关键的数据。一些科学家声称有两种毒株, 但目前还没有达成共识。即使非常保守地估计死亡率为1%，这也意味着5%到10%的病人需要住院治疗，而在流感大流行时，医院是无法提供这种治疗的。如果没有足够的医疗护理，死亡率会更高。
Strong social distancing measures, taken by S. Korea and China, have effectively slowed down, and are on path to stop the spreading of the virus in China and S. Korea.
韩国和中国采取了强有力的社会疏离措施，有效地减缓了病毒在中国和韩国的传播速度，并正在阻止病毒在两国的蔓延。
Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
意大利被迫于3月4日起关闭所有学校。自3月8日起，将有1600万人被隔离.
Update, Mar 9
Italy finally lock down the whole country on Mar 9. Had Italy taken decisive action one week ago, it could have avoided locking down the whole country, just as China’s locking down Hubei avoided the need for locking down the whole country.
意大利终于在3月9日锁定了整个国家。如果意大利在一周前采取果断行动，它本可以避免封锁整个国家，就像中国封锁湖北避免了封锁整个国家一样。
The number of cases in the US is about the same as Italy’s numbers 10 days ago. What Italy is doing now, the US is likely to have to follow in 10 days.
美国的病例数量与10天前意大利的患者数量基本相同。意大利现在所做的，美国可能不得不在10天内效仿。
The risk to each individual at this time (i.e., Mar 9) remains low. Even if one million people within US are infected, the chance that one person gets it is 1 out of a few hundreds. Also, the fatality rates for young people are known to be low. [Correction on Mar 10: see the updated fatality analysis earlier.] However, the risk to everyone increases exponentially over time as the number of cases rises, and the risk to society is very high.
此时每个个体的风险(即3月9日仍然很低。即使我们有100万人被感染，一个人感染的几率是几百分之一。此外，众所周知，年轻人的死亡率很低。[3月10日更正:请参阅之前更新的病死率分析。]然而，随着病例数量的增加，对每个人的风险也会随着时间呈指数增长，对社会的风险也非常高。
Prediction and Justifications.
预测和理由
Without new decisive containment efforts, the number of confirmed cases in US will increase at least 10 folds in 10 days, to 4000 or more (and possibly as high as 10,000) by Mar 17.
如果不采取新的决定性遏制措施，到3月17日，美国确诊病例数将在10天内至少增加10倍，达到4000例或更多(可能高达1万例)。
Every region with cases reaching 400 has been on exponential growth until reaching 4000. To go from around 400 to 4000, it took China 6 days, S. Korea 8 days, Italy 9 days, Iran 7 days.
每个病例达到400例的地区在达到4000例之前一直呈指数增长。从400到4000，中国用了6天，韩国用了8天，意大利用了9天，伊朗用了7天。
In 3 days (from Mar 5 to Mar 8),France case number grows from 423 to 1126, and Germany grows from 349 to 847, both significantly more than doubling.
3天内(3月5日至3月8日) ，法国的感染人数从423人增长到1126人。与此同时，德国的感染人数从349人增长到847人，几乎都是原来的两倍多。
So far, the number of persons tested in the US is low. According to the Atlantic, less than 2000 persons were tested as of Mar 6, with 10% positive rate. On the Grand Princess cruise ship, out of the first group of 46 tested, 21 were positive. These indicate that many people with the virus have not been tested.
到目前为止，在美国接受检测的人数很少。截至3月6日，共有不到2000人接受测试，阳性率为10%。在大公主号游轮上，第一批46名测试者中，有21人呈阳性。这表明许多携带病毒的人没有接受过检测。
The virus is highly contagious. In New York, one patient leads to dozens of cases. Out of 3700 passengers and crew members quarantined on Diamond Princess, the number of confirmed cases grew from 10 on Feb 4 to 542 on Feb 18.
这种病毒传染性很强。在纽约，一个病人导致了几十个病例。在“钻石公主号”上被隔离的3700名乘客和船员中，确诊病例从2月4日的10例增至2月18日的542例。
The situation will be dire by the end of March, before warm weather arrives in the northern part of the country. And experts say the expectation that COVID-19 will disappear in summer like flu is false hope .
到3月底，在温暖的天气到来之前，美国北部的形势将依然非常严峻。同时专家也声称，预期COVID-19将像流感一样在夏季消失是一种虚假的希望.
[UPDATE, added 9pm on 3/9] US case number watch, using only non-repatriated cases. Prediction starts from number on 3/7, and is based on 27% daily growth, which results in slightly more than doubling every 3 days. (The wiki page lowered the number for 3/7 from 388 to 352 after I entered the predictions; I am keeping the original predictions based on starting from 388.)
观察美国的病例，仅考虑未修正的病患人数。预测从3/7开始，以27%的日增长率为基础，结果是每3天翻一番多一点。(在我输入预测结果后，维基页面把3/7的数字从388降到了352；我保留了最初的预测，从388开始。)
见图
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-cvybZjT3cS1vn-i8.jpg.medium.jpg[/img]
The Paths Ahead.
未来的道路。
Path A. The US government takes decisive and proactive actions today and leads all countries fighting the potential devastation by COVID-19 in a coordinated effort to enforce aggressive social distancing measures to contain the spread. Looking at situations in China, this should be able to contain the virus in 4 to 6 weeks. Life should be able to return to normal by June or July. Economy should be able to quickly recover in a few months after that. Total number of cases in the US may be in the tens of thousands, with hundreds of deaths. There will be economic and other kinds of pains and suffering, but these are unavoidable.
策略A：美国政府今天采取了果断和积极的行动，领导所有国家与潜在的Covid-19灾难作斗争，协调努力，实施积极的社会疏远措施，以控制传播。看看中国的情况，应该能在4到6周内控制住病毒。到6月或7月，生活应该可以恢复正常。在那之后的几个月里，经济应该能够迅速复苏。美国的病例总数可能达到数万，其中数百人死亡。会有经济上和其他方面的痛苦和折磨，但这些都是不可避免的。
Path B. Continue the current course of action. In no more than two weeks (by Mar 22), the number of confirmed cases will top 10 thousands. Health care systems in states starting with Washington, California, New York will be strained like Northern Italy today. US government may have to adopt drastic social distancing measures similar to locking down entire cities.
策略B：继续当前的行动。在不到两周的时间内(到3月22日)，确诊病例将超过1万例。从华盛顿、加利福尼亚、纽约开始的各州的医疗保健系统将会像今天的意大利北部一样紧张。美国政府可能不得不采取极端的社会疏远措施，类似于封锁整个城市。
The best case scenario is that the spreading can still be contained by these measures to be about 10 to 50 times the size as under Path A, i.e., with hundreds of thousands or a few millions of people infected, and thousands or more deaths. It will take longer for the lockdown effort to be effective because of the scale of spreading. t may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A.
最理想的情况是，通过这些措施，病毒仍然可以将传播在路径A下的10到50倍。即在美国，成千上万甚至几百万的人被感染，成千上万甚至更多的人死亡。由于扩散的规模，封锁措施需要更长的时间才能生效。生活可能要到八月或九月才能恢复正常。经济损失将比路径A严重得多。
Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to of the population infected
最坏的情况是传播无法被控制，我们正在观察一些专家预测的情况70% 的人会被感染。
Local communities will still try any conceivable containment method. Economic and social activities will be greatly disrupted. At least 20% of the population over the age of 70, as well as significant fractions of other age groups, will die while waiting for medical care, with family members desperately looking on. The situation looks to be at least as bad as the Spanish flu. We may be looking at the worst humanity and economic disaster since World War 2. The remaining hope after the devastation is that either virus mutates to a milder form, or effective vaccines can be developed before the next wave hits.
当地社区仍将尝试任何可能的遏制措施。经济和社会活动将受到严重干扰。至少有20%的70岁以上的人口，以及相当一部分其他年龄段的人，将在等待医疗护理期间死亡，而家人则在一旁绝望地看着。情况看起来至少和西班牙流感一样糟糕。我们可能正面临自二战以来最严重的人类和经济灾难。在这次灾难之后，剩下的希望是，要么病毒变异成一种更温和的形式，要么在下一波袭击之前开发出有效的疫苗。
The Choice.
抉择
It appears that US officials have admitted failure in containment and moved to mitigation; however, it is unclear what is the mitigation strategy. The only rational choice is Path A. While this brings the disruption to the broader society earlier, the magnitude of the disruption will be less and it will pass quicker. Without decisive and aggressive actions now, the government will have to take these or even more drastic measures later, when the virus is much more widespread, which leads to thousands of preventable deaths, health care systems straining to the point of breaking, longer disruption of social and economic activities, and bigger scale of damage to the society and the economy.
美国官员似乎已承认在遏制方面的失败，并采取了缓解措施;然而，目前还不清楚什么是缓解策略。唯一理性的选择是a路。虽然这将更早地给更广泛的社会带来破坏，但破坏的程度将会更小，而且会更快过去。现在没有决定性的和积极的行动,政府将不得不采取这些甚至更严厉的措施后,当病毒更广泛,导致成千上万的可预防的死亡,卫生保健系统竭力打破,再破坏社会和经济活动,和更大的规模,损害社会和经济。
Every day of delaying means more people die in the end. Any measure (economic or otherwise) not curbing the exponential spreading of the virus is like treating gangrene with band-aid.
每耽搁一天，就意味着最终会有更多的人死去。任何措施(无论是经济上的还是其他方面的)如果不能遏制病毒的指数级传播，就像用创可贴治疗坏疽一样。
Is it Too Late Already?
是否已经太迟了?
Some argued that it is already too late to try to contain the spread COVID-19. I believe that this is wrong because at any point during the spreading of the virus before saturation (i.e., around 50% of the population infected), the total cost of aggressive social distancing will be much lower than the alternative. This is true no matter 0.001%, 0.01%, 0.1%, 1%, or 10% of the population have already been infected. The cost of total social distancing is largely fixed, but the cost of letting the virus spread will increase proportionally with the size of the infected population. The benefit of preventing the infection percentage to go from 10% to 20%, based on 5% fatality rate (which is very conservative because the vast majority of patients can receive no medical care at that point), means saving the life of 1.65 million people in the US (330M * 0.1 * 0.05).
一些人认为，现在试图遏制这种蔓延已经太晚了。我认为这是错误的，因为在病毒传播的任何时候，在病毒饱和之前(大约有50%的人感染了这种病毒)。主动与他人保持距离的总成本将比另一种选择低得多。不管是0.001%，0.01%，0.1%，1%还是10%的人已经被感染了。总的社会距离的成本在很大程度上是固定的，但让病毒传播的成本将随着受感染人口的规模成比例地增加。预防感染的比例从10%到20%,基于5%的死亡率(这是非常保守的,因为绝大多数患者可以接受没有医疗这一点),意味着拯救165万人的生命在美国(3.3亿* 0.1 * 0.05)。
My estimate is that currently between 0.001% and 0.01% of the population carry COVID-19, while 0.0002% has been tested positive. When the number of confirmed cases reaches 0.01% (33,000), which should happen in 3 to 4 weeks if no strong social distancing action is taken, the government and most of the society will realize that the cost of letting the virus spread is not what the society can bear. Drastic social distancing is the only way to go. My hope is to wake up the Administration and the public before we reach that point. (If one disagrees with my 3 to 4 weeks time estimation, feel free to replace it with 1 to 2 months. It doesn’t change the need to act earlier rather than later.)
我估计目前有0.001%到0.01%的人携带covid19，而0.0002%的人被检测为阳性。当确诊病例数达到0.01%(3.3万)时，如果不采取强有力的社会距离行动，3 - 4周内就会发生，政府和大多数社会将认识到，让病毒传播的代价不是社会所能承受的。激烈的社交距离是唯一的出路。我的希望是在我们到达那个点之前唤醒政府和公众。(如果有人不同意我对3到4周时间的估计，你可以用1到2个月来代替它。这并没有改变早做而不是晚做的必要性。
[Q/A. Added Mar 11]
问答：
Question. What is the end game? If 1% of the population are infected, why would social distancing/lockdown work? Wouldn’t COVID-19 be with us forever, like flu does?
问题：疫情发展最终结局会是什么？如果有1%的人被感染了，为什么社会疏远/封锁会起作用?COVID-19不会像流感那样永远与我们同在吗?
Answer. Each patient has a period of time during which s/he is contagious. Assume that it is 2 weeks for COVID-19. Suppose that intervention measures can reduce the average number of new patients infected by one existing patient to 0.02 person, which means on average 1 patient infecting 0.28 new patients. After one cycle of 14 days, the original patient is no longer a patient (either recovered or dead), and the patient population size is 0.28 that of the original.
的答案。每个病人都有一段传染期。假设COVID-19是2周。假设干预措施可以将1名现有患者平均感染新患者数降低到0.02人，即平均1名患者感染0.28名新患者。经过一个14天的循环，原患者不再是患者(恢复或死亡)，患者人数为原患者人数的0.28。
This is when exponential growth (or shrinking) is our brightest hope, instead of our worst fear. Starting from a infected population of 3.3 million, see the following table:
在这个时候，指数增长(或萎缩)是我们最光明的希望，而不是最糟糕的担忧。从330万感染人口开始，见下表:
Somewhere around Day 60, when there are less than 20000 patients, if people at risk are thoroughly tested, and the public can clearly identify almost all patients, then only the patients need to be isolated, the rest of the public can go back to normal life. After Day 96, it would take 3 more cycles for the number of patients to be in single digits. But very few people’s life needs to be affected in that phase. 在第60天左右，当患者不到2万的时候，如果对处于危险中的人进行彻底的检测，并且公众可以清楚地识别出几乎所有的患者，那么只有患者需要被隔离，其余的公众可以恢复正常生活。在第96天之后，需要3个以上的周期，每日增长患者人数才能达到个位数。但是很少人的生活需要在那个阶段受到影响。
If we start now, assuming that the true number of virus carriers is 72,000, it would take 2 to 3 cycles, e.g., 4 to 6 weeks for the spreading in the US to be contained. If we wait, the period of containment will be longer.
如果我们现在开始，假设病毒携带者的真实数量是72000人，那么需要2到3个周期，例如，4到6周，美国的传播才会得到控制。如果我们一味等待，遏制的时间会更长。
Note that seasonal flu can be eliminated in the same fashion, but the fatality rate and hospitalization rate for flu are too low to compensate for the huge cost of the required social distancing efforts. And depending on how prevalent flu viruses are with animals, flu can easily come back to humans.
请注意，季节性流感可以以同样的方式被控制，但流感的致死率和住院率很低，不足以弥补所需的社会距离努力的巨大成本。根据流感病毒在动物身上的流行程度，流感很容易传染给人类。
COVID-19, with about 20 times higher fatality rate, is very different. If hospitals can become strained to handle a bad flu season, imagine how it can deal with demand that is 20 times larger. When patients cannot receive hospital care, they die at much higher rate.
COVID-19的致死率大约比流感高出20倍，所以情况大不相同。如果医院在应对一个严重的流感季节时会感到紧张，那么请想象一下它如何应对比现在大20倍的需求。当病人不能得到医院照顾时，他们的死亡率会高得多。
关于COVID-19的一封公开信
By Ninghui Li, Professor of Computer Science, Purdue University
作者:李宁辉，普渡大学计算机科学教授
This letter aims at convincing the US Governments and the public about the urgent need to immediately adopt aggressive social distancing policies to contain the spreading of COVID-19.
这封信的目的是说服美国政府和公众，迫切需要立即采取积极的社会疏远政策，以遏制COVID-19的传播。
Facts.
事实
Once community spread takes hold in a country or region, the number of cases increases exponentially, doubling every 3 days or so, unless aggressive social distancing policies are enforced.
一旦一个国家或地区出现社区传播，病例数就会呈指数级增长，大约每3天翻一番，除非实施积极的社会疏远政策。
See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
请看，例如，中国境外的病例数，以及法国、德国、西班牙、瑞士、英国、荷兰、瑞典、比利时、挪威的病例数。
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-az7wZdT1kShs-dc.jpg.medium.jpg[/img]
Update. March 10.
Exponential growth occurs because the number of newly infected people is proportional to the number of people already carrying it. In a simplified model, if each person carrying the virus on average transmits to 0.26 persons per day, the total number of patients will be multiplied by 1.26 each day, and will double every 3 days. Starting from 100, it takes 10 days to go to 1000, 20 days to go to 10,000, 30 days to go to 100,000, etc.
指数增长是因为新感染的人数与已经感染的人数成正比。在一个简化的模型中，如果每个携带病毒的人平均每天传播0.26人，那么患者总数将乘以每天1.26人，每3天翻一番。从100开始，10天到1000,20天到10000,30天到100000。
Update. March 10
The spreading of communicative diseases follows the same mathematical models as the spreading of computer worms. See studies on how code-red worm, the SQL slammer worm spreads. Once exponential growth starts, it slows down only when getting close to saturation (every target has been infected), unless intervention stops the growth.
传播疾病的传播遵循与计算机蠕虫传播相同的数学模型。参见关于代码红色蠕虫、SQL slammer蠕虫如何传播的研究。一旦指数增长开始，它只有在接近饱和(每个目标都被感染)时才会减慢，除非干预停止增长。
See figure.
见图
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-l2ipK4T1kShs-dc.gif.medium.jpg[/img]
The US case number has been growing exponentially for over a week. On Saturday Feb 29, the total number of US cases is 69, including 47 cases originated from the Diamond Princess cruise ship or Wuhan evaluation, and 22 local cases. By Saturday Mar 7, the number of local cases rose to 388. Within 7 days, the number of local cases increased more than 16 folds, doubling more than 4 times.
一周多以来，美国的病例数呈指数增长。2月29日星期六，美国的病例总数为69例，其中47例来自钻石公主号游轮或武汉评估，22例来自当地。截至3月7日星期六，当地病例增至388例。7天内，局部病例数增加16倍以上，增加4倍以上。
When the number of cases reaches thousands, the sheer volume of patients will overwhelm the healthcare system. Hundreds or more people (mostly older citizens) die, and medical workers will suffer greatly. See reports on this in S. Korea, Italy on Mar 2, Italy on Mar 7, Europe.
当病例数达到数千时，庞大的患者数量将使医疗系统不堪重负。数百人或更多的人(大部分是老年人)死亡，医务工作者将遭受巨大的痛苦。参见3月2日在韩国、3月7日在意大利、欧洲的报道。
A March 6 3月6Testimony of a Surgeon working in Bergamo,Italy uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
一名在意大利贝加莫工作的外科医生的证词。用第一手的经验来解释医院的压力和新冠病毒肺炎并不是流感。
Update. Mar 11
By locking down Hubei province, China limited the numbers of COVID-19 cases in other provinces to be relatively small. When hospitals in Hubei are overwhelmed, China mobilized the medical resources of the whole country to help.
通过封锁湖北省，中国将其他省份的病例数量限制在相对较小的范围内。当湖北的医院不堪重负时，中国动员全国的医疗资源来帮助他们。
COVID-19 has a significantly higher fatality rate than Flu appears to be about 20 times as deadly as Flu for every age group. Flu is estimated to have fatality of 0.1%. Estimation of the fatality rate of COVID-19 varies, some numbers are 2.3% according China’s CDCP, 3.4% according to the WHO.
COVID-19的致死率明显高于流感，在每个年龄组的致死率是流感的20倍左右。据估计，流感的致死率为0.1%。对covt -19致死率的估计各不相同，中国疾病预防控制中心的数字是2.3%，世界卫生组织的数字是3.4%。
Update. Mar 10.
Comparison of age-based fatality rates of Flu vs. COVID-19
在不同年龄人群中，流感和新冠病毒肺炎的死亡率对比
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-ank0ZfT3cSuk-z6.jpg.medium.jpg[/img]
According to worldometer worldometer, among 66,106 closed cases, there are 3828 deaths, translating to a 5.8% fatality rate. This is dominated by data from China. It could be too high, as many people with mild symptoms in China may be self-quarantined and not discovered. On the other hand, this is achieved because China can mobilize medical resources of the whole country to treat patients in Hubei. The rate would be a lot higher otherwise.
在66106宗已完结的病例中，有3828宗死亡，即5.8%的病死率。这主要是来自中国的数据。这可能太高了，因为在中国，许多有轻微症状的人可能被自我隔离，而没有被发现上报。另一方面，这是因为中国可以调动全国的医疗资源来治疗湖北的病人。否则死亡率会高得多。
The numbers from the other countries with more than 5000 cases are worrisome. As of March 5, S. Korea tested 140,000 cases, with 6000 positive cases, and 33 deaths. However, using 33/6000 to claim 0.6% fatality rate is utterly wrong, since the vast majority of the 6000 cases are still active, and the number of deaths will increase. As of March 8, S. Korea has 51 deaths, 166 recovered cases, and 7165 cases being treated. S. Korea’s thorough testing means that even patients with mild symptoms are included, yet this yields a tentative fatality rate of 51/(51+166) = 23.5%, which is alarmingly high.
来自其他国家超过5000例的数字令人担忧。截至3月5日，韩国检测了14万例，其中6000例为阳性，33人死亡。然而，用33/6000来声称0.6%的致死率是完全错误的，因为6000个病例中的绝大多数病程仍在发展，死亡人数还会增加。截至3月8日，韩国已有51人死亡，166人痊愈，7165人得到治疗。年代。韩国的全面检测意味着即使有轻微症状的患者也包括在内，但这得出的暂定病死率为51/(51+166)= 23.5%，这一数字高得惊人。
Similarly, as of March 8,Italy has 366 deaths, and only 622 recovered cases. Iran has 194 deaths for 2134 recovered cases. These are the most critical numbers to be watched in the next few days. Some scientists claim that there are two strains with one deadlier, but there is no consensus. Even for a very conservative estimation of fatality rate of 1%, it would mean 5% to 10% of patients need hospital care, which cannot be provided when it is a pandemic. Without adequate medical care, the fatality rate will be higher.
同样，在3月8日，意大利有366人死亡，只有622人康复。伊朗有194人死亡，2134人康复。这些是未来几天需要关注的最关键的数据。一些科学家声称有两种毒株, 但目前还没有达成共识。即使非常保守地估计死亡率为1%，这也意味着5%到10%的病人需要住院治疗，而在流感大流行时，医院是无法提供这种治疗的。如果没有足够的医疗护理，死亡率会更高。
Strong social distancing measures, taken by S. Korea and China, have effectively slowed down, and are on path to stop the spreading of the virus in China and S. Korea.
韩国和中国采取了强有力的社会疏离措施，有效地减缓了病毒在中国和韩国的传播速度，并正在阻止病毒在两国的蔓延。
Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
意大利被迫于3月4日起关闭所有学校。自3月8日起，将有1600万人被隔离.
Update, Mar 9
Italy finally lock down the whole country on Mar 9. Had Italy taken decisive action one week ago, it could have avoided locking down the whole country, just as China’s locking down Hubei avoided the need for locking down the whole country.
意大利终于在3月9日锁定了整个国家。如果意大利在一周前采取果断行动，它本可以避免封锁整个国家，就像中国封锁湖北避免了封锁整个国家一样。
The number of cases in the US is about the same as Italy’s numbers 10 days ago. What Italy is doing now, the US is likely to have to follow in 10 days.
美国的病例数量与10天前意大利的患者数量基本相同。意大利现在所做的，美国可能不得不在10天内效仿。
The risk to each individual at this time (i.e., Mar 9) remains low. Even if one million people within US are infected, the chance that one person gets it is 1 out of a few hundreds. Also, the fatality rates for young people are known to be low. [Correction on Mar 10: see the updated fatality analysis earlier.] However, the risk to everyone increases exponentially over time as the number of cases rises, and the risk to society is very high.
此时每个个体的风险(即3月9日仍然很低。即使我们有100万人被感染，一个人感染的几率是几百分之一。此外，众所周知，年轻人的死亡率很低。[3月10日更正:请参阅之前更新的病死率分析。]然而，随着病例数量的增加，对每个人的风险也会随着时间呈指数增长，对社会的风险也非常高。
Prediction and Justifications.
预测和理由
Without new decisive containment efforts, the number of confirmed cases in US will increase at least 10 folds in 10 days, to 4000 or more (and possibly as high as 10,000) by Mar 17.
如果不采取新的决定性遏制措施，到3月17日，美国确诊病例数将在10天内至少增加10倍，达到4000例或更多(可能高达1万例)。
Every region with cases reaching 400 has been on exponential growth until reaching 4000. To go from around 400 to 4000, it took China 6 days, S. Korea 8 days, Italy 9 days, Iran 7 days.
每个病例达到400例的地区在达到4000例之前一直呈指数增长。从400到4000，中国用了6天，韩国用了8天，意大利用了9天，伊朗用了7天。
In 3 days (from Mar 5 to Mar 8),France case number grows from 423 to 1126, and Germany grows from 349 to 847, both significantly more than doubling.
3天内(3月5日至3月8日) ，法国的感染人数从423人增长到1126人。与此同时，德国的感染人数从349人增长到847人，几乎都是原来的两倍多。
So far, the number of persons tested in the US is low. According to the Atlantic, less than 2000 persons were tested as of Mar 6, with 10% positive rate. On the Grand Princess cruise ship, out of the first group of 46 tested, 21 were positive. These indicate that many people with the virus have not been tested.
到目前为止，在美国接受检测的人数很少。截至3月6日，共有不到2000人接受测试，阳性率为10%。在大公主号游轮上，第一批46名测试者中，有21人呈阳性。这表明许多携带病毒的人没有接受过检测。
The virus is highly contagious. In New York, one patient leads to dozens of cases. Out of 3700 passengers and crew members quarantined on Diamond Princess, the number of confirmed cases grew from 10 on Feb 4 to 542 on Feb 18.
这种病毒传染性很强。在纽约，一个病人导致了几十个病例。在“钻石公主号”上被隔离的3700名乘客和船员中，确诊病例从2月4日的10例增至2月18日的542例。
The situation will be dire by the end of March, before warm weather arrives in the northern part of the country. And experts say the expectation that COVID-19 will disappear in summer like flu is false hope .
到3月底，在温暖的天气到来之前，美国北部的形势将依然非常严峻。同时专家也声称，预期COVID-19将像流感一样在夏季消失是一种虚假的希望.
[UPDATE, added 9pm on 3/9] US case number watch, using only non-repatriated cases. Prediction starts from number on 3/7, and is based on 27% daily growth, which results in slightly more than doubling every 3 days. (The wiki page lowered the number for 3/7 from 388 to 352 after I entered the predictions; I am keeping the original predictions based on starting from 388.)
观察美国的病例，仅考虑未修正的病患人数。预测从3/7开始，以27%的日增长率为基础，结果是每3天翻一番多一点。(在我输入预测结果后，维基页面把3/7的数字从388降到了352；我保留了最初的预测，从388开始。)
见图
[img]https://img.nga.178.com/attachments/mon_202003/12/-7Q5-cvybZjT3cS1vn-i8.jpg.medium.jpg[/img]
The Paths Ahead.
未来的道路。
Path A. The US government takes decisive and proactive actions today and leads all countries fighting the potential devastation by COVID-19 in a coordinated effort to enforce aggressive social distancing measures to contain the spread. Looking at situations in China, this should be able to contain the virus in 4 to 6 weeks. Life should be able to return to normal by June or July. Economy should be able to quickly recover in a few months after that. Total number of cases in the US may be in the tens of thousands, with hundreds of deaths. There will be economic and other kinds of pains and suffering, but these are unavoidable.
策略A：美国政府今天采取了果断和积极的行动，领导所有国家与潜在的Covid-19灾难作斗争，协调努力，实施积极的社会疏远措施，以控制传播。看看中国的情况，应该能在4到6周内控制住病毒。到6月或7月，生活应该可以恢复正常。在那之后的几个月里，经济应该能够迅速复苏。美国的病例总数可能达到数万，其中数百人死亡。会有经济上和其他方面的痛苦和折磨，但这些都是不可避免的。
Path B. Continue the current course of action. In no more than two weeks (by Mar 22), the number of confirmed cases will top 10 thousands. Health care systems in states starting with Washington, California, New York will be strained like Northern Italy today. US government may have to adopt drastic social distancing measures similar to locking down entire cities.
策略B：继续当前的行动。在不到两周的时间内(到3月22日)，确诊病例将超过1万例。从华盛顿、加利福尼亚、纽约开始的各州的医疗保健系统将会像今天的意大利北部一样紧张。美国政府可能不得不采取极端的社会疏远措施，类似于封锁整个城市。
The best case scenario is that the spreading can still be contained by these measures to be about 10 to 50 times the size as under Path A, i.e., with hundreds of thousands or a few millions of people infected, and thousands or more deaths. It will take longer for the lockdown effort to be effective because of the scale of spreading. t may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A.
最理想的情况是，通过这些措施，病毒仍然可以将传播在路径A下的10到50倍。即在美国，成千上万甚至几百万的人被感染，成千上万甚至更多的人死亡。由于扩散的规模，封锁措施需要更长的时间才能生效。生活可能要到八月或九月才能恢复正常。经济损失将比路径A严重得多。
Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to of the population infected
最坏的情况是传播无法被控制，我们正在观察一些专家预测的情况70% 的人会被感染。
Local communities will still try any conceivable containment method. Economic and social activities will be greatly disrupted. At least 20% of the population over the age of 70, as well as significant fractions of other age groups, will die while waiting for medical care, with family members desperately looking on. The situation looks to be at least as bad as the Spanish flu. We may be looking at the worst humanity and economic disaster since World War 2. The remaining hope after the devastation is that either virus mutates to a milder form, or effective vaccines can be developed before the next wave hits.
当地社区仍将尝试任何可能的遏制措施。经济和社会活动将受到严重干扰。至少有20%的70岁以上的人口，以及相当一部分其他年龄段的人，将在等待医疗护理期间死亡，而家人则在一旁绝望地看着。情况看起来至少和西班牙流感一样糟糕。我们可能正面临自二战以来最严重的人类和经济灾难。在这次灾难之后，剩下的希望是，要么病毒变异成一种更温和的形式，要么在下一波袭击之前开发出有效的疫苗。
The Choice.
抉择
It appears that US officials have admitted failure in containment and moved to mitigation; however, it is unclear what is the mitigation strategy. The only rational choice is Path A. While this brings the disruption to the broader society earlier, the magnitude of the disruption will be less and it will pass quicker. Without decisive and aggressive actions now, the government will have to take these or even more drastic measures later, when the virus is much more widespread, which leads to thousands of preventable deaths, health care systems straining to the point of breaking, longer disruption of social and economic activities, and bigger scale of damage to the society and the economy.
美国官员似乎已承认在遏制方面的失败，并采取了缓解措施;然而，目前还不清楚什么是缓解策略。唯一理性的选择是a路。虽然这将更早地给更广泛的社会带来破坏，但破坏的程度将会更小，而且会更快过去。现在没有决定性的和积极的行动,政府将不得不采取这些甚至更严厉的措施后,当病毒更广泛,导致成千上万的可预防的死亡,卫生保健系统竭力打破,再破坏社会和经济活动,和更大的规模,损害社会和经济。
Every day of delaying means more people die in the end. Any measure (economic or otherwise) not curbing the exponential spreading of the virus is like treating gangrene with band-aid.
每耽搁一天，就意味着最终会有更多的人死去。任何措施(无论是经济上的还是其他方面的)如果不能遏制病毒的指数级传播，就像用创可贴治疗坏疽一样。
Is it Too Late Already?
是否已经太迟了?
Some argued that it is already too late to try to contain the spread COVID-19. I believe that this is wrong because at any point during the spreading of the virus before saturation (i.e., around 50% of the population infected), the total cost of aggressive social distancing will be much lower than the alternative. This is true no matter 0.001%, 0.01%, 0.1%, 1%, or 10% of the population have already been infected. The cost of total social distancing is largely fixed, but the cost of letting the virus spread will increase proportionally with the size of the infected population. The benefit of preventing the infection percentage to go from 10% to 20%, based on 5% fatality rate (which is very conservative because the vast majority of patients can receive no medical care at that point), means saving the life of 1.65 million people in the US (330M * 0.1 * 0.05).
一些人认为，现在试图遏制这种蔓延已经太晚了。我认为这是错误的，因为在病毒传播的任何时候，在病毒饱和之前(大约有50%的人感染了这种病毒)。主动与他人保持距离的总成本将比另一种选择低得多。不管是0.001%，0.01%，0.1%，1%还是10%的人已经被感染了。总的社会距离的成本在很大程度上是固定的，但让病毒传播的成本将随着受感染人口的规模成比例地增加。预防感染的比例从10%到20%,基于5%的死亡率(这是非常保守的,因为绝大多数患者可以接受没有医疗这一点),意味着拯救165万人的生命在美国(3.3亿* 0.1 * 0.05)。
My estimate is that currently between 0.001% and 0.01% of the population carry COVID-19, while 0.0002% has been tested positive. When the number of confirmed cases reaches 0.01% (33,000), which should happen in 3 to 4 weeks if no strong social distancing action is taken, the government and most of the society will realize that the cost of letting the virus spread is not what the society can bear. Drastic social distancing is the only way to go. My hope is to wake up the Administration and the public before we reach that point. (If one disagrees with my 3 to 4 weeks time estimation, feel free to replace it with 1 to 2 months. It doesn’t change the need to act earlier rather than later.)
我估计目前有0.001%到0.01%的人携带covid19，而0.0002%的人被检测为阳性。当确诊病例数达到0.01%(3.3万)时，如果不采取强有力的社会距离行动，3 - 4周内就会发生，政府和大多数社会将认识到，让病毒传播的代价不是社会所能承受的。激烈的社交距离是唯一的出路。我的希望是在我们到达那个点之前唤醒政府和公众。(如果有人不同意我对3到4周时间的估计，你可以用1到2个月来代替它。这并没有改变早做而不是晚做的必要性。
[Q/A. Added Mar 11]
问答：
Question. What is the end game? If 1% of the population are infected, why would social distancing/lockdown work? Wouldn’t COVID-19 be with us forever, like flu does?
问题：疫情发展最终结局会是什么？如果有1%的人被感染了，为什么社会疏远/封锁会起作用?COVID-19不会像流感那样永远与我们同在吗?
Answer. Each patient has a period of time during which s/he is contagious. Assume that it is 2 weeks for COVID-19. Suppose that intervention measures can reduce the average number of new patients infected by one existing patient to 0.02 person, which means on average 1 patient infecting 0.28 new patients. After one cycle of 14 days, the original patient is no longer a patient (either recovered or dead), and the patient population size is 0.28 that of the original.
的答案。每个病人都有一段传染期。假设COVID-19是2周。假设干预措施可以将1名现有患者平均感染新患者数降低到0.02人，即平均1名患者感染0.28名新患者。经过一个14天的循环，原患者不再是患者(恢复或死亡)，患者人数为原患者人数的0.28。
This is when exponential growth (or shrinking) is our brightest hope, instead of our worst fear. Starting from a infected population of 3.3 million, see the following table:
在这个时候，指数增长(或萎缩)是我们最光明的希望，而不是最糟糕的担忧。从330万感染人口开始，见下表:
Somewhere around Day 60, when there are less than 20000 patients, if people at risk are thoroughly tested, and the public can clearly identify almost all patients, then only the patients need to be isolated, the rest of the public can go back to normal life. After Day 96, it would take 3 more cycles for the number of patients to be in single digits. But very few people’s life needs to be affected in that phase. 在第60天左右，当患者不到2万的时候，如果对处于危险中的人进行彻底的检测，并且公众可以清楚地识别出几乎所有的患者，那么只有患者需要被隔离，其余的公众可以恢复正常生活。在第96天之后，需要3个以上的周期，每日增长患者人数才能达到个位数。但是很少人的生活需要在那个阶段受到影响。
If we start now, assuming that the true number of virus carriers is 72,000, it would take 2 to 3 cycles, e.g., 4 to 6 weeks for the spreading in the US to be contained. If we wait, the period of containment will be longer.
如果我们现在开始，假设病毒携带者的真实数量是72000人，那么需要2到3个周期，例如，4到6周，美国的传播才会得到控制。如果我们一味等待，遏制的时间会更长。
Note that seasonal flu can be eliminated in the same fashion, but the fatality rate and hospitalization rate for flu are too low to compensate for the huge cost of the required social distancing efforts. And depending on how prevalent flu viruses are with animals, flu can easily come back to humans.
请注意，季节性流感可以以同样的方式被控制，但流感的致死率和住院率很低，不足以弥补所需的社会距离努力的巨大成本。根据流感病毒在动物身上的流行程度，流感很容易传染给人类。
COVID-19, with about 20 times higher fatality rate, is very different. If hospitals can become strained to handle a bad flu season, imagine how it can deal with demand that is 20 times larger. When patients cannot receive hospital care, they die at much higher rate.
COVID-19的致死率大约比流感高出20倍，所以情况大不相同。如果医院在应对一个严重的流感季节时会感到紧张，那么请想象一下它如何应对比现在大20倍的需求。当病人不能得到医院照顾时，他们的死亡率会高得多。