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The COVID-19 pandemic, an update

I needed to update my model through April 20. I have not changed the model parameters for two weeks, and I only had slight changes before. Thus, the model is stable and predictive, given the faulty, incomplete data at hand. The model points out that the reported number of deaths around the world is lagging. For the world, my cautious estimate is 30,000 missing COVID-19 deaths in late March and April, see Figures 1 and 2. My simple model points out clearly that the more complex models may not be predictive, while fitting the erratic data better.

My friend ecologist, Professor Bill Rees, just reminded me that his mentor, Crawford "Buzz" Holling, insisted on repeating to his teams whenever they got bogged down in disputes over accuracy vs precision: "It is better to be approximately correct than very precisely wrong."

Figure 1. My Gaussian model for the worldwide COVID-19 deaths as of April 20, 2020.  The difference between the magenta extrapolation of what the data ought to be and the reported data in black is ~30,000 unreported deaths.

Figure 2. The daily reports of COVID-19 deaths worldwide. The model has not changed, but the black data have been oscillating below the model prediction since the beginning of March 2020. The magenta line is a simple linear extrapolation of what the data ought to be to follow the Gaussian curve more-less. 

The New York Times just reported 28,000 of incremental deaths worldwide since January 2020.  Most of these deaths occurred in late March and April 2020, see Figure 3.  The Dutch and Belgian experiments with handling COVID-19 pandemic do not look as good as they did yesterday. Neither does the Swedish experiment, it appears.

Figure 3a. The missing deaths in Late March and April 2020, reported by the New York Times on April 21, 2020.  This is still work in progress.  China is missing, so is India, Nigeria, Egypt, Brazil, most of Indonesia, and  so on.  The true number of incremental deaths from or with the COVID-19 virus is several-fold higher, at least 100,000 people, who were not counted yet.

A note added on April 26, 2:53 pm CST:  Figure 3b shows the results of an analysis performed by the Financial Times:

"The death toll from coronavirus may be almost 60 per cent higher than reported in official counts, according to an FT analysis of overall fatalities during the pandemic in 14 countries. Mortality statistics show 122,000 deaths in excess of normal levels across these locations, considerably higher than the 77,000 official Covid-19 deaths reported for the same places and time periods. If the same level of underreporting observed in these countries was happening worldwide, the global Covid-19 death toll would rise from the current official total of 201,000 to as high as 318,000."

In other words, we could already be at the upper limit of the cumulative death curve in Figure 1.

Figure 3b. The Financial Times, "Global coronavirus death toll could be 60% higher than reported." 04/26/2020.

The data reporting is presumably better in the US. Ten days ago, or so, I decreased the height of the US Gaussian somewhat, so that the cumulative number of deaths would be about 60,000. I did not change the remaining two parameters: the time of the peak, and the initial rate of exponential growth I use as an approximation to guess the correct shape of the Gaussian. The results are shown in Figures 4 and 5.

Figure 4.  The cumulative number of COVID-19 deaths in the US follows more less my unchanged model. We are already four days after the single peak, unless a secondary Gaussian will emerge from the changing human behavior and too much social contact.  We shall see how the reopening of the US will work out.

Figure 5. The rate of the COVID-19 related deaths in the US. The model did not change.  The data lagged first in late March, then overshot when New York counted the number of deaths in nursing homes, houses, and apartments. 

In summary, as of April 21, 2020, at 12:30 pm CST, when I am writing this blog, the US reported 42,514 COVID-19 deaths and Germany 4,862 deaths. If one ratios the populations of both countries (the factor of four), the US should have had 19,500 deaths.  The difference is 23,000 more COVID-19 deaths in the US, relative to what these deaths would have been if the US had a central government, and was as advanced and well-organized as Germany.  If we scale up the German COVID-19 cases to the US population, we obtain 593,000 infections, while the US currently (at 6:13 pm CST) has 816,000 confirmed infections.  These excess 223,000 COVID-19 cases in the US may be attributed to lack of testing, governance, and social discipline.

The incremental deaths and COVID-19 cases in the US are the result of:
  1. The abysmal incompetence of the Trump administration and their Republican minions.
  2. The criminal inaction and denial of the Republican party and some Governors who aided and abetted President Trump in committing crimes against the American people (yes, it is time to replace the disastrous Senator Susan Collins and other ineffective Republicans).
  3. The dismal state of American medical system, hospitals in particular, that were optimized for the profits of private corporations, not for the good of the American people.
  4. The abominable ineffectiveness of the current federal government in securing and distributing medical supplies to prevent, test for, and treat the corona virus. Here is what Trump proposes instead.
  5. The criminal lack of medical coverage for at least 40 million people in America, especially the people of color.
  6. The bizarre social stratification in the US, with the runaway poverty, neglect and decreasing life expectations among tens of millions of Americans on one hand, and many of the richest people on the Earth on the other. 
  7. The criminal propaganda from the Fox "News" that influenced the millions of otherwise disoriented Americans to take actions that result in lives lost.
Let's send Senator Susan Collins to a political limbo, where she should remain for millenia.

In summary, thus far, I submit that the Trump administration bears direct responsibility for the unnecessary American death toll equal to eleven Twin Tower attacks on 9/11, and counting. When the initial phase of the pandemic is over in the US, the number of deaths over those scaled up from Germany might well be 40,000.

If this simple truth is not conveyed clearly to the disoriented Americans by November 2020, then the I shall name the Democratic party a clinically inapt, tepid organization that should be disbanded.  I call on Michael Moore to prepare several 2-4 minute film clips that will illustrate all key "achievements" of this historically incompetent White House. George Clooney is already doing his part. Now, Michael, here is my challenge for you: in your short pieces, top George's performance by a factor of four! You could actually ask George to star under your direction and tell the dumb@!$#asses what we think.

Here is a more serious view of Trump from the UK:

"A few things spring to mind. Trump lacks certain qualities which the British traditionally esteem. For instance, he has no class, no charm, no coolness, no credibility, no compassion, no wit, no warmth, no wisdom, no subtlety, no sensitivity, no self-awareness, no humility, no honour and no grace – all qualities, funnily enough, with which his predecessor Mr. Obama was generously blessed. So for us, the stark contrast does rather throw Trump’s limitations into embarrassingly sharp relief."

It is worth reading.

P.S. (04/21/2021, 21:09 CST)  Oh, what a difference a few hours make!  The spike in the US deaths has disappeared from the data, even though I recall vividly that it was linked to the unaccounted for deaths in New York.  The updated data and the same prediction are shown in Figure 6.  I guess, the new data are more presentable for the politicians.

Figure 6.  Figure 5 six hours later.  The raw data are downloaded automatically from the Worldometers website. It appears that the spike in US deaths was scrubbed down by this website. The incremental deaths were then distributed over the subsequent days, because the total number of reported deaths could not go down.  This version of the same old story of undercounting the COVID-19 deaths in the US is more presentable, I guess.
P.S.P.S. (04/22/2021) Because the record of US deaths has been changed upon the removal of the big New York spike, the additional deaths had to be redistributed over several days.  This caused the US peak to become somewhat broader, and the peak date modeled to April 20,2020.  The broader death rate Gaussian results in more cumulative deaths, 75,000 now.  The new results are shown in Figures 7 and 8.

Figure 7.  My April 22, 2020,  US prediction with the input data reshuffled on April 21.
Figure 8. My April 22, 2020, estimate of the cumulative COVID-19 deaths in the US. The num,ber of deaths has increased to 75,000.

P.S.^3 (04/26/2020) When a functional idiot leads the most powerful nation on the planet, there will be repercussions, way beyond the people here consistently voting against their self-interest, because they are deluded to think of themselves as the temporarily inconvenienced potential millionaires. Some of the difficulties with the US leadership in the post-COVID-19 world are described here.

P.S.^4 (04/29/2020)  Let's get real about the massive tests to confirm current or past presence of the COVID-19 virus in our bodies.  These tests are quite limited, as Michael T. Osterholm and Mark Olshaker explain in their 4/28/2020 editorial in the New York Times.


  1. "the US reported 42,514 COVID-19 deaths and Germany 4,862 deaths. If one ratios the populations of both countries (the factor of four), the US should have had 19,500 deaths. The difference is 23,000 more COVID-19 deaths in the US, relative to what these deaths would have been if the US had a central government, and was as advanced and well-organized as Germany. "

    I don't know how much sense it makes think about per capita deaths like this. Yes the US is four times the size of Germany, but from the point of view of the viral outbreak, both populations are approximately infinite. The virus is expanding into the populations and in neither country has it got anywhere close to being constrained by the size of the Petri dish.

    Rather than saying "23,000 more COVID-19 deaths in the US, relative to what these deaths would have been" so could say 37,000 more deaths from the outbreak in the US compared to the outbreak in Germany.

    1. Fair enough, Chris. But given all else, the pandemic has spread in the US much faster and killed - relatively speaking - many more people. We were in Germany, in Aachen, at the end of February, just to catch the end of the carnival, mix with huge crowds, and with the fastest growing cluster of COVID-19 infections in Germany. We left in March 3, when the Aachen railway station was already guarded by the police preventing people from buying tickets (I bought our online). Thus, with infinite populations or not, Germany reacted in two days, because they had testing, hospitals and government, and the US did not react for another 2-3 weeks, despite the origin of the pandemic being somewhat earlier here (US had first deaths reported on February 15), I think.

      As Brian just noted elsewhere, the first US case was identified on Jan 19 in WA state. The man came back from Wuhan on Jan 15, and thus had 3-4 days to infect others. COVID-19 was then "invisible" (ignored) in the region until the outbreak at the Life Care Center, which was genetically traced to that first case. By mid-March, when Gov. Inslee began shutdowns, WA had more identified cases and deaths than any other state. It has now slid to #15.

      In summary, Germans moved in swiftly and with forethought, tested and isolated the infected people just north of Aachen, and prevented the development of an explosive epidemic a la Seattle. We ignored the early warnings, mostly because there was way, way too little testing, and the outcome is well known today.

  2. Didier Van derslijenApril 22, 2020 at 1:29 AM

    Hello, just a small comment as someone who lives in Belgium.

    The government and experts here have decided to count all suspected deaths from both hospitals and care homes for the elderly in the statistics.

    At some points in the last weeks the daily deaths from care homes was twice that of the deaths in hospitals and it is possible that we have some overcounting here.

    As far as I understand, most countries only count confirmed deaths in hospitals. So it is likely that countries with similar demographics as Belgium (as in, a lot of elderly citizens) are severely undercounting their number of deaths.

    Personally I think the government here made the correct decision to go with this way of reporting numbers.

    1. Dear Didier,

      Thank you for this important clarification. Over the last two days there was an avalanche of new information about death undercounting, including the Santa Clara County. An unreviewed article from the Stanford and other doctors/researchers suggested that the rate of infection there was 80x the reported one. Therefore, many people who already died in the county, died from COVID-19, and in most cases we shall never know. I discounted the findings of that paper completely, based on the Bayesian conditional probabilities and the overwhelming number of false positives. But if the epidemic started a month earlier than we think and grew silently, we may be at 10%+ of the infected people and then the paper suddenly makes more sense.

      Your remark is particularly important in the US, where several governors have decided to govern by Trump's tweets to save their asses during the next election. The result will be opposite, but these political operatives are likely to commit crimes against the very people who stupidly voted for them.


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