COVID-19 (Coronavirus Disease) is a dangerous global pandemic. The likely fatality rate for COVID-19 is between 1% and 4%. It is caused by the virus SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2).
In the U.S., the spread of SARS-CoV-2 has not been brought under control. In fact, numerous states and several of our largest metropolitan areas are reporting exponential increases in the number of confirmed COVID-19 cases.
In China, the spread of SARS-CoV-2 has been brought under control. For the past several days, all provinces in China have reported zero or near-zero new domestically-transmitted confirmed cases.
That is, in China, the spread of the pandemic been stopped. In the U.S., the pandemic is spreading exponentially. The World Health Organization (WHO) is now warning that the U.S. may become the epicenter of the pandemic.
China is the only country in the world that has stopped COVID-19. Societal response stopped the spread in China.
The difference between China, which has stopped the pandemic, and the U.S., where the pandemic is spreading exponentially, is societal measures, including government efforts, media efforts, and societal mobilization. The necessary public health measures, also known as non-pharmaceutical interventions (NPIs), are well known. Implementing NPIs requires the concerted efforts of government, media, and society.
The total number of deaths from COVID in China is now about 3,300, and will likely not increase significantly. The most recent authoritative analysis estimates that with societal measures, deaths in the U.S. could eventually reach one million; without societal measures, deaths could reach about two million, and even more if our health system is overwhelmed. These numbers are similar to the worst-case scenario in a U.S. Centers for Disease Control and Prevention (CDC) study, which has not been released to the public, according to a report published in the New York Times. White House coronavirus task force member Dr. Anthony S. Fauci, whose statements are often carefully calibrated to correct misinformation from the administration, estimates between 100,000 to 200,000 deaths. A survey of experts averages estimates to 246,000 deaths in 2020. Admittedly, much remains unknown about the spread of the pandemic.
COVID-19 can be stopped by societal response, and in fact it has been stopped in China. The total number of deaths we suffer in the U.S., whether tens of thousands, hundreds of thousands, or millions of lost American lives, depends on the choices we collectively make in the coming days, weeks, and months.
Exponential increase, as I explain below, lies outside our ordinary experience. It is incomparably rapid. It is responsible for the enormous destructive power of nuclear weapons.
In numerous areas in the U.S., the number of confirmed COVID-19 cases is currently increasing exponentially, doubling every two to seven days in many areas.
In the near term (the next week or two), this will have the following consequences:
The estimated number of eventual deaths from one hundred thousand cases is one to several thousand Americans. This means that by the end of March, the number of American lives that will eventually be lost to COVID-19 will be the same order of magnitude of the number of American lives lost in 9/11, and the same order of magnitude as the total number of deaths in China to date, about 3300.
In the medium term (the next one to several months), the pandemic may become considerably worse. Epidemiologists have warned, based on complex computational models, that in worst-case scenarios, the U.S. may eventually have more than one hundred million cases.
Currently President Trump is stating that the U.S. will loosen the limited societal measures by Easter.
The simple mathematical model I present here, based on the actual number of cases to date, confirms that the current exponential increase in COVID-19 is consistent with worst-case scenarios. The projections I present below are speculative, and depend on a considerable number of factors, many unknown, but especially on the efficacy of social policy measures taken, such as social distancing. As of March 23, there is little evidence at this point of a marked slowdown in the rate of exponential increase. The exponential increase in the U.S. could result in the following consequences:
One million cases would mean deaths in the range of ten to several tens of thousands of Americans. Ten million cases would mean deaths in the range of one hundred to several hundreds of thousands of Americans. One hundred million cases would mean deaths between one and several million Americans.
In particular, what has been euphemistically called "herd immunity," allowing the infection of between 30% to 60% of the population, would result in the death of several million Americans, and is in reality a genocidal proposal that would decimate infirm, elderly, and economically disadvantaged Americans, many of whom may have inadequate or no medical insurance. This would also likely overwhelm medical capacities, resulting in considerable additional unnecessary deaths.
China has, as of this writing, stopped the spread of COVID-19. That is, in China, after initial exponential increase, using the societal measures, the pandemic was contained, exponential increase was halted, and the pandemic was then suppressed in areas it had spread, with the result that for the past several days, the number of new confirmed cases of domestically-transmitted in the entire nation of 1.4 billion has been near zero. Currently almost all confirmed cases are from travellers from outside China; in response, China is currently requiring travellers to quarantine for fourteen days. The number of total number of cases is about 82000. The number of fatalities, now at 3270, will likely eventually remain under 5000.
In the coming months, in the U.S., responses to the exponential spread in COVID-19 are primarily societal, not scientific. That is, ultimately we may hope to find solutions to the COVID-19 pandemic through scientific medicine. These solutions are not available for the medium term: vaccines are a year or more away; and two months of worldwide effort has failed to yet discover an effective treatment.
As an example, let me first offer one very simple example of health policy measures where China succeeded but the U.S. has inexplicably failed:
Today, in the United States, many of our health care providers (HCP) do not have adequate personal protective equipment (PPE) to protect themselves from COVID-19. Many do not even have face masks. Worse, some medical providers are not even permitted to wear PPE. That is, many HCP--our physicians, nurses, and medical workers--are not just working to save our lives but at the same time they are being asked to put their own lives and those of their families at risk because of our failures as a society.
Indeed, the CDC is now allowing HCP to use scarves and bandanas in place of masks, and allowing medical providers to remain at work after exposure to COVID-19.
In contrast, today China is sending face masks to countries around the world. Chinese physicians are mailing face masks to their colleagues here in the U.S.
Individuals and all levels of government must immediately demand that all medical providers be protected with masks and PPE, and immediately demand that our federal government do everything possible including invoking emergency powers to procure and produce them.
The central point of this webpage is to urge all levels of government in the United States along with all Americans to immediately adopt as many societal measures as possible to slow the pandemic and reduce the loss of life. The U.S. unfortunately has been very slow to do so, and has taken few of the societal measures necessary to slow or stop COVID-19. Any measures adopted, whether by governments or individuals, contribute to slowing the pandemic and ultimately saving lives.
The remainder of this webpage explains in detail the following key points :
This section presents simple mathematical models that confirm the possibility that between one to two hundred million Americans may become infected with SARS-CoV-2; the resulting cases of COVID-19 could result in deaths ranging from one to several million Americans.
Exponential increase is perhaps difficult to understand because it is for the most part beyond our ordinary experiences. This section will compare linear, polynomial, and exponential increases.
Linear increase, that is, increase proportional to the indepentdent variable, is probably the easiest to understand. For example, if I travel at a constant speed, the distance I cover is proportional to the time, d ∝ t.
Polynomials, such as a quantity squared x2 (that is, a quantity multiplied by itself), describe many other processes in nature with which we are familiar. For example, in gravity free-fall, velocity increases linearly with time v ∝ t, and thus distance increases with the square of time, d ∝ t2. Many disasters involve polynomial increases: falling rocks, avalanches, runaway vehicles all gain speed roughly linearly proportional to time, v ∝ t, and the energy of the crash is proportional to the square of the velocity, E ∝ v2.
Exponential increase is incomparably faster than any polynomial increase, as the following table illustrates:
|Linear: y = n||1||2||3||4||5||6||7||8||9||10||11||12||13||14||15||...||20||...||25||...||30|
|Polynomial: y = n2||1||4||9||16||25||36||49||64||81||100||121||144||169||196||225||...||400||...||625||...||900|
|Exponential: y = 2(n-1)||1||2||4||8||16||32||64||128||256||512||1024||2048||4096||8192||16384||...||524288||...||16777216||...||536870912|
From the above table, it can be seen that an exponential increase at the outset may seem slow: for n = 1, 2, 3, exponential increase is approximately the same as linear increase; for n = 1, 2, 3, 4, 5, 6, exponential increase is slower than the polynomial increase. Exponential increase eventually becomes incomparably faster than any polynomial nk, no matter how large the exponent k.
Exponential increase is largely beyond our ordinary experience, and many of the examples with which we may be familiar double over periods of years or generations, such as compounded interest or population growth.
An more relevant example of a process in nature that is exponential is nuclear reactions: at critical mass, the nuclear reaction becomes exponential, leading to the enormous destructive power of nuclear explosions. This should help serve as a reminder destructive power of exponential processes.
To expand this analogy, our current situation might be likened to a nuclear reactor accident:
Three Mile Island was shutdown in just 8 seconds; any delay would have resulted in a considerably worse disaster, possibly including nuclear explosion.
Suggestions to ignore scientists, such as that made by Fox personality Tucker Carlson, "You can't just let epidemiologists run a country of more than 320 million people," could be likened to suggesting that we not listen to nuclear scientists in a nuclear accident.
To give a concrete example of what the exponential increase of COVID-19 means for a large metropolitan area with several million Americans, assume we begin with just 100 cases. Assume that the number of cases increases exponentially, so that the number doubles every three days. After three days, the first doubling of 100 gives 200. After three more days, doubling that 200 gives 400. After three more days, doubling that 400 gives 800, then 1600, 3200, 6400, 12800, 25600, 51200, 102400, 204800, 409600, 819200, and 1638400. So, assuming no effective societal measures are taken, and if for the sake of this example we ignore other factors that might reduce the rate of increase, an initial infection of about one hundred cases could in a worst-case scenario grow in a period of about 45 days to about one million cases. At the outset, the numbers are small and the increase seems small, but soon the numbers are catastrophic.
For the entire U.S., the implications are equally grim, as the number of confirmed cases doubles approximately every two days. On February 28, the first day of exponential increase, we had 19 confirmed cases, up from 15 the previous day. That 19 doubled two days later to 42 on March 1, doubling again two days later to 85 on March 3, doubling again two days later to 175 on March 5, doubling again two days later to 353 on March 7, doubling again two days later to 645 on March 9, doubling again two days later to 1205 on March 11, nearly doubling again two days later to 2163 on March 13, doubling again three days later to 4372 on March 16, nearly doubling again two days later to 8074 on March 18, doubling again three days later to 17235 on March 20, nearly doubling again tow days later to 33767 on March 22, nearly doubling again three days later to 64107 on March 25.
Beginning with the onset on February 28 of exponential increase in the U.S., up until today, the number of confirmed cases of COVID-19 has doubled approximately every two days. If exponential increase continued at about that rate, for example doubling every three days, the resulting numbers would be as follows:
March 28: 125,000
March 31: 250,000
April 3: 500,000
April 6: 1,000,000
April 9: 2,000,000
April 12: 4,000,000
April 15: 8,000,000
April 18: 16,000,000
April 21: 32,000,000
April 24: 64,000,000
April 27: 128,000,000
At some point, the rate of exponential increase gradually slows. The following section will use a simple mathematical model based to make more accurate projections into the near future.
The graph below shows the rapid increase in confirmed cases in the United States and several other Western democracies, up to March 23..
While the plots appear to differ, they share a fundamental feature, which becomes apparent when we use a log scale, as in the graph below..
The log scale graph shows that the increase is indeed exponential. As can be seen, most of the graphs begin with periods of little increase, and then at a certain point begin to increase exponentially. The exponential increase in the U.S. began on February 28. The following graph plots the periods of exponential increase..
The following graph focuses on the number of cases only for further clarity..
What news reports have often omitted—with few exceptions—are future projections, the implications of this exponential increase. That is, even articles published in our most reputable news sources, when they show exponential increase, do so without a scale indicating the actual number of cases.
The following graph shows the result of exponential increase projected over the following three months..
As can be seen from this log scale graph, the rate of the exponential increase gradually slows.
The following graph shows the numbers of projected COVID-19 cases in the United States and other countries..
The mathematical model used here is simple (see below for a further description). As can be seen, there is a wide range of possible outcomes.
The remainder of this webpage is still under construction. I will be updating this section and adding information daily.
The four main responses employed in China that have been recommended by the World Health Organization (WHO) for all countries are the following:
A more complete list of these responses taken in China include the following:
Some of the measures taken by China in response to COVID-19 are described in the following article: "Inside China’s All-Out War on the Coronavirus" 疫中访问中国，WHO专家组组长看到了什么？ New York Times, March 5, 2020.
As a historian, I present these measures adopted in China not to endorse any particular one, but for evaluation of the extent to which they might be scientific, efficacious, and implementable in the U.S.
The U.S. response to the COVID-19 pandemic has been severely crippled by disinformation. The comedy program “The Daily Show” has compiled a brief (i.e., very incomplete) montage of misleading and false statements about COVID-19.
National Institutes of Health: Coronavirus (COVID-19)
New England Journal of Medicine
Science, "Coronavirus: Research, Commentary, and News"
Centers for Disease Control and Prevention: Coronavirus (COVID-19)
World Health Organization: Coronavirus disease (COVID-19) Pandemic
Coronavirus COVID-19 Global Cases by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University
The COVID Tracking Project
Coronavirus Disease (COVID-19) – Statistics and Research
New York Times, "Coronavirus in the U.S.: Latest Map and Case Count""
PanCAP Adapted U. S. Government COVID - 19 Response Plan March 13, 2020
Center for Infection & Immunity
Tedros Adhanom Ghebreyesus, Director-General of the World Health Organization.
Github: New York Times: covid-19-data
Github: New York Times: us-counties.csv
NYT, What 5 Coronavirus Models Say the Next Month Will Look Like
Reich Lab COVID-19 Forecast Hub
IHME, COVID-19 projections: predicting the next phase of the epidemic
COVID Analytics, DELPHI Epidemiological Case Predictions
Dr. Amesh Adalja on Fox News "Mar. 28, 2020 - 5:39 - Infectious disease expert Dr. Amesh Adalja joins Eric Shawn to discuss how the coronavirus may impact smaller communities outside the infected areas of the U.S."
This page is dedicated to all those throughout the world--the doctors, nurses, care providers, scientists, and so many others--who are fighting to save our lives, and too often, because of our failures, risking their own lives for ours.
Several physicians in Wuhan (including Li Wenliang 李文亮, below) who were reprimanded by Wuhan police for warning of an outbreak of viral pneumonia. Ironically, on the same day, the Hubei government honored Zhang Dingyu 张定宇 and Zhang Jixian 张继先 for being the first to report the virus.
Pamella Brown-Richardson and over one dozen nurses in New York, who filed lawsuits against the state health department and two hospitals, as reported by the Washington Post.
Jhonna Porter，registered nurse, who was suspended without pay for posting concerns about a lack of PPE on Facebook, as reported in the HuffPost.
Michael Gulick and nine other coronavirus-unit nurses, suspended for refusing to work without N95 masks, asreported by CNN
Dr. Ming Lin, an emergency room physician at PeaceHealth St. Joseph Medical Center, who was fired for decrying inadequate testing and safety procedures, according to a Seattle Times report.
Capt. Brett Crozier, captain, commanding officer of the U.S. nuclear aircraft carrier Theodore Roosevelt. Whistleblower. Acting Navy Secretary Thomas Modly announced that Crozier was relieved "at my direction," adding "this decision is not one of retribution," according to a San Francisco Chronicle article. The article further reports that, in the view of former Reagan administration assistant secretary of defense Lawrence Korb, Crozier's letter to the Navy "shows that this is a person who is putting the welfare of his sailors ahead of his career." Capt. Crozier later tested positive for COVID-19.
Rebekah Jones, the scientist who created Florida's COVID-19 data dashboard, was fired for refusing to, in her words, "manually change data to drum up support for the plan to reopen," according to a report by Florida Today and other media sources.
Fighting to keep us safe, some of the world's most eminent epidemiologists have contracted COVID-19:
Dr. Ian Lipkin, Professor of Epidemiology, Professor of Neurology, Professor of Pathology & Cell Biology, and Director of the Center for Infection and Immunity, Mailman School of Public Health, Columbia University. Dr. Lipkin states, “If it can hit me, it can hit anybody. That’s the message I want to convey.”
Li Wenliang 李文亮, ophthalmologist, Wuhan Central Hospital. After Mr. Li alerted colleagues via social media about a SARS-like virus, he was accused of disrupting social order and reprimanded by Wuhan police. He died on February 7, 2020, at age 33, from COVID-19. Posthumously, Li was exonerated, an official apology was issued, and two Wuhan police officers were disciplined.
Kious Jordan Kelly, nurse, Mount Sinai Hospital. Mr. Kelly died on March 24, 2020, at age 48, from COVID-19, possibly because of inadequate personal protective equipment. NBC News reports, “Mount Sinai Hospital did not respond to specific questions about how Kelly was exposed to the virus, but it insisted that it has provided workers with the necessary protective equipment.”
Dr. Frank Gabrin, ER physician. Dr. Gabrin died on March 31, 2020 from COVID-19, apparently due to inadequate protective gear. East Orange General Hospital stated, "We are committed to ensuring the safety of our patients, staff and physicians. We currently have sufficient staffing, supplies and equipment – including N95 respirators and facemasks – on hand to care for patients," according to a report by CBS News.
In protest, nurses have read the names of colleagues who have died from COVID-19, as reported in the Washington Post.
Italy, National Federation of Orders of Surgeons and Dentists, names of more than 60 healthworkers who have died from COVID-19.
The following website honors healthcare workers who have sacrificed their lives for us in the fight against COVID-19:
In Memoriam: Healthcare Workers Who Have Died of COVID-19.
On a personal note, I want to thank my best friends, and express to them my enormous admiration: one is a physician in the U.S. who has been treating patients without protective gear or even a face mask; one is a physician in China, who, at a time when too little was known about the possible risks, established the hospital's PCR testing laboratory, which completed testing of thousands, including all outpatients, inpatients, and staff, in just three days.
© Roger Hart 2020.
Background: I earned my B.S. in mathematics from MIT and my M.S. in mathematics from Stanford. I earned my M.A. in Chinese Literature and my Ph.D. in Chinese history and history of science from UCLA. I have held the following positions: Postdoctoral Fellow, Fairbank Center for East Asian Studies, Harvard University; Postdoctoral Fellow, Center for Chinese Studies, UC Berkeley; Andrew W. Mellon Postdoctoral Fellow and Visiting Assistant Professor in the Program in History and Philosophy of Science, Stanford University; National Endowment for the Humanities Fellow at the School of Historical Studies, Institute for Advanced Study, Princeton; Visiting Assistant Professor, Department of History, University of Chicago, in the Fishbein Center for the History of Science; Assistant Professor, Department of History, University of Texas at Austin; Visiting Professor, Templeton “Science and Religion in East Asia” Project, Science Culture Research Center, Seoul National University. I am currently Professor of Chinese History and Director of the China Institute at Texas Southern University. I have spent a total of six years teaching, studying and researching in China. My research and teaching interests include contemporary China, Chinese history, history of science, and critical theory. My published reseearch includes The Chinese Roots of Linear Algebra (Johns Hopkins UP, 2010) and Imagined Civilizations: China, the West, and Their First Encounter (Johns Hopkins UP, 2013). My current research project is Quantum States: Science and U.S-China Relations in the Global Twenty-First Century (in progress).
I am solely responsible for all information presented here. In particular, the information presented here does not represent Texas Southern University, the Texas Southern University China Institute, or any other institution. This site has no governmental, corporate, political, religious, ideological, or institutional affiliation or purpose.