Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??

2. According to 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. ?? [Update. Mar 11.] ??On the other hand, 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 treat patients in Hubei. The rate would have been a lot higher otherwise.
3. 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.
4. 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.
5. 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. ??

6. 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. ??

1. Italy was forced to close all schools starting Mar 4, quarantine 16 million people starting Mar 8
2. [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.
3. [Update Mar 12].?? Italy close all shops except for food stores and pharmacies on Mar 12.
4. [Updated Mar 13]. ??On Mar 12, France declared closing of all schools starting Mar 16.
5. 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.

• [Update Mar 12.]?? It was pointed out to me that US has a population that is 5.4 times Italy???s. ??That means, in terms of the number of cases per million people, US is more likely 15 times behind Italy. ??That, doesn???t change the need to act sooner rather than later. ??I also hope that as we can see how is happening in Italy, and soon Spain, France, and Germany, US will act in stages earlier than Italy.

7. 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.??

Prediction and Justifications.

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.??

1. 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. ??
2. 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. 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. ??
4. 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. ??
5. 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. ??

[Updated Mar 14.] ??A lot of social distancing measures have been taken in the US over the last few days. ??Fortunately and unfortunately, exponential growth at the current rate will continue for at least 2 weeks, since many people already carry the virus and have not been identified. ??I say that this is fortunate because social distancing requires the effort of the whole society. ??The continued exponential growth will make more and more people realize the seriousness of the situation, and practice more aggressive social distancing, helping to shorten the period when such measures are needed.

The Paths Ahead.

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.

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.

• 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. It may be August or September before life can return to normal. And the economic damage will be a lot higher than Path A. ??
• Worst-case scenario is that spreading cannot be contained, and we are looking at situations predicted by some experts, with up to 70% of the population infected. ??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.

The Choice.

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.??

Every day of delaying means more people die in the end.

Any measure (economic or otherwise) not dealing with exponential growth is like treating gangrene with band-aid. ??

[Update on Mar 10] ??Is it Too Late Already?

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).

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.)

[Mar 14: Some contents that were here have been moved to my Open Letter 2.]

Who is the Author and Why is He Writing This? ??

I am a Professor of Computer Science at Purdue University. ??My research area is Security and Privacy. ??I am no medical expert, but I am familiar with the literature on the spreading of computer viruses (the mathematical modelling of which is similar to that of biological viruses), and I have worked with numbers a lot.

I started looking at COVID-19 numbers on Feb 27 because my son signed up for his school???s Spring break (Mar 14 to 21) trip to Orlando, FL, and I needed to decide whether I would allow him to go. ??While the numbers were low then, the exponential growth of COVID-19 case numbers was obvious. ??While I easily convinced my son that he should not go (he understands the power of exponential growth), I was worried about the trend, and has been following it since. ??Over the last week, my worst-case predictions on the case numbers have been met, and I have seen exponential growths in more and more countries. I have also been discussing these trends with others, and found that few people saw the same things as I did. ??I have resigned to simply sit back and watch the situation develop. ??However, after reading Testimony of a Surgeon working in Bergamo, I was deeply saddened by the suffering described there. ??The doctor???s first-person account turned the abstract numbers in my mind into vivid human suffering. ??I shared my frustration with my friends: ???I am watching a train wreck going to happen, yet can do nothing to help.??? ??Then I realized maybe there is something I could do. If this open letter achieves its goal, thousands of people do not have to die. ??Thus, even if the chance of having any impact is very low, I have to try. ??

Acknowledgements.

I thank the following and other friends and colleagues (some chose not to be named) for their valuable suggestions and advice regarding this letter: Hubo Cai, Songlin Fei, Susanne Hambrusch, Fritz Hartman, Faming Liang, Sarah Sellke. ??I emphasize that the opinions expressed in this open letter are entirely my own responsibility. ??

Originally written 2 am March 9, 2020

Minor edits were made throughout after the above time. ??Major edits are marked with ??[Update].

Open Letter 1 on COVID-19: The Urgent Need for Aggressive Social Distancing Actions

By Ninghui Li, Professor of Computer Science, Purdue University

Originally written 2am, March 9, 2020. ??Last updated March 14, 2020.

[March 14: I have written Open Letter 2 on COVID-19]

Goal. ??

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.

Executive Summary. [Added Mar 12]

COVID-19 is extremely contagious. ??Once community spread takes hold in a country or region (which happened in US by late February the latest), the number of cases starts exponential growth, doubling every 3 days or less, until either (1) infecting between 40% to 70% of the population, which should take less than 70 days in the US, or (2) aggressive social distancing practiced are enforced to curb or at least slow its spread. ??Based on current data, COVID-19 is 20 times as deadly as flu, and will result in a very high hospitalization rate. ??Even if just 0.1% of the population (330,000 in US) are infected, the health care system will be collapsing. ??When spreading reaches that point, society and governments will have no choice but to enforce drastic social distancing practices to curb its spread. This is inevitable. ??Acting earlier rather than later will lead to much smaller disruption and economic cost, shorter duration of drastic social distancing, and saving the life of thousands or more people. ??

Quote??from ???Young and Unafraid of the Coronavirus Pandemic? ??Good for you. ??Now stop killing people.??? ??[Added on Mar 12, the referenced article was published on Mar 11, when Italy has 0.02% infection rate.]

???Most of my childhood friends are now doctors working in north Italy. In Milan, in Bergamo, in Padua, they are having to choose between intubating a 40-year-old with two kids, a 40-year old who is fit and healthy with no co-morbidities, and a 60-year-old with high blood pressure, because they don't have enough beds. In the hallway, meanwhile, there are another 15 people waiting who are already hardly breathing and need oxygen.???

US Case Number Watch

[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.)

Facts.

1. 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.

1. See, e.g., number of cases outside China, and in France, Germany, Spain, Switzerland, UK, Netherlands, Sweden, Belgium, Norway.
2. [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, which leads to an increase by a factor of 10 in 10 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, 40 days to 1 million, 50 days to 10 millions, and 60 days to 100 millions.
3. [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??(almost every target has been infected), unless intervention stops the growth. ??

See figure. ??

2. 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.?? ??
3. [Added Mar 12] ??Starting with 388 on March 7, it needs to double 19 times to reach 203 millions, which would happen by May 3 when doubling every 3 days. ??(This will not actually happen because people will realize that they cannot afford to let it happen and will have take measures to curb its growth.)
4. 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.

1. A March 6 Testimony of a Surgeon working in Bergamo,Italy??uses first-hand experience to explain the stress on hospitals and that COVID-19 is not flu.
2. [Update Mar 12]. ??Doctors in Italy forced to choose who to treat and who to be left dying, and ??A doctor in Western Europe urges people not to kill others by spreading the virus.
3. [Update Mar 12]. The impending collapse of the medical system is the first thing that forces a government to take drastic actions, no matter how much they don???t want to take them.

5. 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. ??

1. [Update. Mar 10.] ??Comparison of age-based fatality rates of Flu vs. COVID-19. ??