USA: Highest COVID Death toll in the entire world; One of the highest infection rates per capita; and highest number of cases

Making America Great Again – was it really intended to make the USA have the highest Covid-19 death toll in the entire world, PLUS the highest infection rate? What a record!!

Please look at this table, which I compiled from data I found here and here. I have sorted it by the total number of reported Covid-19 deaths and left off almost all of the nations with less than three thousand cases, except for Taiwan and Vietnam.

If you look, you will see that the US (with 105 thousand deaths) is way ahead of every other country — in fact, it’s about the same as the next three or four nations combined (UK, Italy, Brazil, and France).

The US also has the highest number of reported cases in the entire world, with about 1.8 million; that’s roughly the same amount as the next seven nations combined (Brazil, Russia, UK, Spain, Italy, Germany, and India).

No Herd Immunity

People have been talking about herd immunity and low fatality rates. My calculations tell me that we are a long, long way from herd immunity anywhere, and that the fatality rates are rather high.

To get herd immunity, you need to have 70% to 90% of the population that has antibodies – either from a vaccine or from having contracted the disease and recovered by their own body producing the necessary antibodies. I simply divided the total number of reported cases (which is probably too low in every case, but I have no idea by what factor) by the population of each country. What I find is that not a single nation has reached even 1% of their population having been infected and recovered. The highest such rates are in the small nations of Bahrain, Kuwait, and Luxembourg, which have about 7 people diagnosed as having been positive per THOUSAND, that’s 0.7%. The US has about 0.55% positive.

No herd immunity there.

High Fatality Rates

If we divide the number of coronavirus deaths by the total number of cases, we get rather large percentages. For the world as a whole, it’s about 6%, and for the very worst-off nations like France, Belgium, Italy, the UK, Netherlands, Sweden, Spain, and Mexico, your chances of dying if diagnosed positive [EDIT] are over 10%.*

Scary.

Total Reported Cases Total Reported Deaths Calculated fatality rate Population, millions Infection rate so far
World 6,104,980 370,078 6.06% 7594 0.080%
United States 1,811,016 105,295 5.81% 327 0.554%
United Kingdom 274,762 38,489 14.01% 66 0.416%
Italy 233,019 33,415 14.34% 60 0.388%
Brazil 501,985 28,872 5.75% 209 0.240%
France 151,496 28,771 18.99% 67 0.226%
Spain 239,429 27,127 11.33% 46 0.520%
Mexico 87,512 9,779 11.17% 126 0.069%
Belgium 58,381 9,467 16.22% 11 0.531%
Germany 183,411 8,602 4.69% 83 0.221%
Iran 151,466 7,797 5.15% 82 0.185%
Canada 90,516 7,092 7.84% 37 0.245%
Netherlands 46,442 5,956 12.82% 17 0.273%
India 182,143 5,164 2.84% 10 1.821%
Russia 405,843 4,693 1.16% 144 0.282%
China 83,001 4,634 5.58% 1393 0.006%
Turkey 163,103 4,515 2.77% 82 0.199%
Sweden 37,542 4,395 11.71% 10 0.375%
Peru 155,671 4,371 2.81% 32 0.486%
Ecuador 38,571 3,334 8.64% 17 0.227%
Switzerland 30,862 1,657 5.37% 9 0.343%
Ireland 24,990 1,652 6.61% 5 0.500%
Indonesia 26,473 1,613 6.09% 268 0.010%
Pakistan 70,868 1,519 2.14% 212 0.033%
Chile 94,858 997 1.05% 19 0.499%
Philippines 18,086 957 5.29% 107 0.017%
Egypt 23,449 913 3.89% 98 0.024%
Colombia 28,236 890 3.15% 50 0.056%
Japan 16,804 886 5.27% 127 0.013%
Ukraine 23,672 708 2.99% 46 0.051%
Austria 16,731 668 3.99% 9 0.186%
Algeria 9,394 653 6.95% 42 0.022%
Bangladesh 47,153 650 1.38% 161 0.029%
South Africa 30,967 643 2.08% 58 0.053%
Denmark 11,633 571 4.91% 6 0.194%
Argentina 16,201 528 3.26% 44 0.037%
Hungary 3,876 526 13.57% 10 0.039%
Saudi Arabia 85,261 503 0.59% 34 0.251%
Dominican Republic 16,908 498 2.95% 11 0.154%
Panama 13,018 330 2.53% 4 0.325%
Finland 6,859 320 4.67% 5.5 0.125%
Czech Republic 9,233 319 3.45% 11 0.084%
Bolivia 9,592 310 3.23% 11 0.087%
Moldova 8,251 295 3.58% 3.5 0.236%
Israel 17,024 284 1.67% 9 0.189%
Nigeria 9,855 273 2.77% 196 0.005%
South Korea 11,468 270 2.35% 52 0.022%
Sudan 4,800 262 5.46% 42 0.011%
United Arab Emirates 33,896 262 0.77% 10 0.339%
Afghanistan 15,205 257 1.69% 37 0.041%
Serbia 11,381 242 2.13% 7 0.163%
Norway 8,437 236 2.80% 5 0.169%
Belarus 42,556 235 0.55% 9.5 0.448%
Kuwait 27,043 212 0.78% 4 0.676%
Morocco 7,783 204 2.62% 36 0.022%
Honduras 5,094 201 3.95% 9.6 0.053%
Iraq 6,179 195 3.16% 38 0.016%
Cameroon 5,904 191 3.24% 25 0.024%
Bosnia & Herzegovina 2,510 153 6.10% 3 0.084%
Bulgaria 2,453 140 5.71% 7 0.035%
North Macedonia 2,226 133 5.97% 2 0.111%
Armenia 9,282 131 1.41% 3 0.309%
Malaysia 7,819 115 1.47% 32 0.024%
Luxembourg 4,016 110 2.74% 0.6 0.669%
Croatia 2,246 103 4.59% 4 0.056%
Australia 7,193 103 1.43% 25 0.029%
Guatemala 4,739 102 2.15% 17 0.028%
Cuba 2,025 83 4.10% 11 0.018%
DR Congo 3,046 72 2.36% 84 0.004%
Azerbaijan 5,494 63 1.15% 10 0.055%
Thailand 3,081 57 1.85% 69 0.004%
Tajikistan 3,807 47 1.23% 9 0.042%
Oman 11,437 46 0.40% 5 0.229%
Senegal 3,535 41 1.16% 16 0.022%
Kazakhstan 10,858 40 0.37% 18 0.060%
Ghana 7,881 36 0.46% 30 0.026%
Ivory Coast 2,799 33 1.18% 25 0.011%
Guinea 3,706 23 0.62% 12 0.031%
Singapore 34,884 23 0.07% 5.6 0.623%
Djibouti 3,194 22 0.69% 1 0.319%
Bahrain 10,793 18 0.17% 1.5 0.720%
Uzbekistan 3,554 14 0.39% 33 0.011%
Taiwan 442 7 1.58% 24 0.002%
Vietnam 328 0 0.00% 96 0.000%

* EDIT: The divisor here is the number of people who have been formally and medically diagnosed as positive. The number of people who have actually been exposed to COVID-19 is probably considerably higher than the number of people who have tested positive, since no country is testing every single citizen, and the technicians are not testing people randomly.

By what factor is the reported positive rate in the various nation’s populations too low? I cannot say, and I’m positive it varies a lot from nation to nation and even within any country or state or region.

CDC gives a much lower fatality rate than I do – they estimate it to be under 1%, which would mean that every single reported positive case represents about 10 to 60 people who got the infection and fought it off unknowingly. That’s the only way you can lower a 6% fatality rate to 0.6% or 0.1%. Does that sound reasonable to you? It would be nice if that were true, but I rather doubt it.

There is NO Herd Immunity in the US but we have a High Fatality Rate

covid cases reported each day, USA

Notice from this pink graph that in the USA, technicians are still detecting twenty to 25 THOUSAND new cases of COVID-19 per day. These folks didn’t all get sick; they just all tested positive for antigens and/or antibodies. Some did get sick, some less so, and some more so, and some died.

One of the key questions is, what is the fatality rate? We now have some idea, which we can get by comparing the total number of cases reported so far with the total number of deaths. This yellow graph shows the cumulative ECDC-reported number of cases in the USA. Right now it’s a bit over 1.7 million people – roughly one half of one percent of the population, which is roughly 330 million.

One half of one percent of the population is nothing like herd immunity! You need 70 to 90% or more of the people to have been exposed to reach that level according to JHU.

total covid cases to date, may 30

Now let’s compare that to the total deaths each day and cumulative.

covid deaths per day

As you can see from the white graph above, the US is recording something like 1000 to 1500 deaths from COVID every day. (My guess as to why it’s going down has to do with the fact that the vast majority of the population is engaging in social distancing.)

Total, cumulative deaths can be seen below:

TOTAL COVID DEATHS TO DATE, MAY 30

The above graph shows that at present, a bit over a hundred thousand people have been killed in the United States so far by this virus at this writing. Now let’s compare that total number of deaths, namely 102,836, with the total number of detected cases, which is 1,747,087. Get out your favorite calculator and divide. If you divide the big one (~1.7 million) by the smaller one (~103 thousand), you get roughly 17 — which means that about ONE OUT OF EVERY 17 PEOPLE IN THE USA WHO HAS TESTED POSITIVE, HAS DIED.

Let that sink in.

If you are infected, it looks like you have a one-in-seventeen chance of dying.

And there is neither a vaccine, nor a cure, nor herd immunity, nor any contact tracing to speak of. Testing is still rationed tightly, or else you have to pay a LOT for it. Will that ratio continue to hold in the future? I don’t know, but it’s alarming all the same.

If you divide the little one by the big one, you will get about 0.05886. That means 5.886% chance of dying – nearly 6% fatality rate!

That is one hell of a lot more lethal than the flu.

If we open up again without contact tracing and effective and humane quarantine and/or medical care of those who test positive, I am really afraid of what will happen.

5.886% of the population of the USA is over 19 million people.

I’ve checked about a dozen other countries, and their fatality rates range from about 2% (Taiwan) up to 19% (France).

 

How Dutch Schools are Re-Opening

Schools in The Netherlands are opening back up with no social distancing for the littlest students. A Dutch writer describes the details at Larry Cuban’s site. She says one ingredient for success with younger kids was bubbles.

I hope it all works.

https://larrycuban.wordpress.com/2020/05/30/how-dutch-schools-reopened-with-no-pupil-distancing-linda-van-druijten/

The best way to re-open the economy is to defeat the virus. Not by yelling slogans.

By Alex Tabarrok and Puja Ahluwalia Ohlhaver in the Washington Post

May 15, 2020 at 10:06 a.m. EDT

With the unemployment rate at its highest level since the Great Depression — 14.7 percent and climbing — many Americans are clamoring to reopen the economy, even if it means that thousands of daily covid-19 deaths become part of the backdrop to life. It’s time to move on as “warriors,” President Trump has said, because “we can’t keep our country closed down for years.” We, too, favor markets and share the president’s eagerness to stop economically ruinous shutdowns. But the choice between saving lives and saving the economy, the latter of which Trump has endorsed implicitly, is a false one.

In fact, framing the issue that way could kill many Americans and kill the economy.

The dangers of reopening without disease control — or a coronavirus vaccine or therapeutic breakthrough — are illustrated by events at the Smithfield Foods meatpacking plant in Sioux Falls, S.D. Smithfield offered workers a bonus if they showed up every day in April. Normally, bonus pay would increase attendance. But in a pandemic, encouraging the sick to haul themselves into work can be disastrous. The plan backfired. Hundreds of Smithfield employees were infected, forcing the plant to shut down for more than three weeks. If we stay the current course, we risk repeating the same mistake across the whole economy.

The economy consists of people who have hopes and fears. As long as they are afraid of a lethal virus, they will avoid restaurants, travel and workplaces. (According to a Washington Post-Ipsos poll last week, only 25 percent of all Americans want to “open businesses and get the economy going again, even if that means more people will get the coronavirus.”) The only way to restore the economy is to earn the confidence of both vulnerable industries and vulnerable people through testing, contact tracing and isolation.

As covid-19 spreads through Nebraska meat plants, workers feel helpless and afraid

There is already a bipartisan plan to achieve this; we helped write it. The plan relies on frequent testing followed by tracing the contacts of people who test positive (and their contacts) until no new positive cases are found. It also encourages voluntary isolation, at home or in hotel rooms, to prevent further disease spread. Isolated patients would receive a federal stipend, like jurors, to discourage them from returning to workplaces too soon.

But our plan also recognizes that rural towns in Montana should not necessarily have to shut down the way New York City has. To pull off this balancing act, the country should be divided into red, yellow and green zones. The goal is to be a green zone, where fewer than one resident per 36,000 is infected. Here, large gatherings are allowed, and masks aren’t required for those who don’t interact with the elderly or other vulnerable populations. Green zones require a minimum of one test per day for every 10,000 people and a five-person contact tracing team for every 100,000 people. (These are the levels currently maintained in South Korea, which has suppressed covid-19.) Two weeks ago, a modest 1,900 tests a day could have kept 19 million Americans safely in green zones. Today, there are no green zones in the United States.

 

What antibody tests can teach us about potential coronavirus immunity

Most Americans — about 298 million — live in yellow zones, where disease prevalence is between .002 percent and 1 percent. But even in yellow zones, the economy could safely reopen with aggressive testing and tracing, coupled with safety measures including mandatory masks. In South Korea, during the peak of its outbreak, it took 25 tests to detect one positive case, and the case fatality rate was 1 percent. Following this model, yellow zones would require 2,500 tests for every daily death. To contain spread, yellow zones also would ramp up contact tracing until a team is available for every new daily coronavirus case. After one tracer conducts an interview, the team would spend 12 hours identifying all those at risk. Speed matters, because the virus spreads quickly; three days is useless for tracing. (Maryland, Virginia and Washington, D.C., are all yellow zones.)

 

A disease prevalence greater than 1 percent defines red zones. Today, 30 million Americans live in such hot spots — which include Detroit, New Jersey, New Orleans and New York City. In addition to the yellow-zone interventions, these places require stay-at-home orders. But by strictly following guidelines for testing and tracing, red zones could turn yellow within four weeks, moving steadfastly from lockdown to liberty.

 

Getting to green nationwide is possible by the end of the summer, but it requires ramping up testing radically. The United States now administers more than 300,000 tests a day, but according to our guidelines, 5 million a day are needed (for two to three months). It’s an achievable goal. Researchers estimate that the current system has a latent capacity to produce 2 million tests a day, and a surge in federal funding would spur companies to increase capacity. The key is to do it now, before manageable yellow zones deteriorate to economically ruinous red zones.

 

States can administer these “test, trace and supported isolation” programs — but Congress would need to fund them. The total cost, we estimate, is $74 billion, to be spent over 12 to 18 months. That sum would cover wages and training for contract tracers, the cost of building voluntary self-isolation facilities, stipends for those in isolation and subsidies to manufacture tests.

 

That amount is a lot, but not compared to the cost of a crippled economy. In Congress’s latest relief package, $75 billion went to struggling hospitals alone, $380 billion to help small businesses and $25 billion toward testing. But hospitals and businesses will continue to hemorrhage money and seek bailouts as long as they can’t open safely. Not spending on disease control means new waves of infection followed by chaotic spikes in disease and death, followed by more ruinous cycles of economic openings and closures. Economists talk about “multipliers” — an injection of spending that causes even larger increases in gross domestic product. Spending on testing, tracing and paid isolation would produce an indisputable and massive multiplier effect.

 

States have strong economic incentives to become — and remain — green zones. Nations that have invested the most in disease control have suffered the least economic hardship: Taiwan grew 1.5 percent in the first quarter, whereas the United States’ gross domestic product contracted by 4.8 percent, at an annual adjusted rate. (Taiwan was fortunate to have its vice president, Chen Chien-Jen, a U.S.-trained epidemiologist; under his guidance, the island acted quickly with masks, temperature checks, testing and tracing.) The second quarter will be worse: The projected decline for U.S. GDP, at an annualized rate, is an alarming 40 percent.

 

Looking forward, we will see stark economic contrasts across states, depending on their investment in disease control. With $74 billion, Congress could close the gap between states and relieve pressure on state budgets hamstrung by collapsing revenues. In the spirit of federalism, states would then become laboratories for discovering the best ways to implement testing, tracing and isolation. States might choose to form interstate compacts that pool and move testing resources across state lines as the disease travels and surges; county health officials might tap firefighters or other municipal workers to build regional contact-tracing workforces (as is happening in Tyler, Tex.). When local and state governments become accountable for adopting strategies that work, we can expect more innovation.

 

How do we know that testing, tracing and supported isolation would work? It already has worked in New Zealand, South Korea and Taiwan — where there have been few to no new daily cases recently. Taiwan never had to shut down its economy, while New Zealand and South Korea are returning to normal. It would work here, too. Since March, Congress has passed relief bills totaling $3.6 trillion to support an economy devastated by a virus — and $3 trillion more is on the table. We should attack the disease directly so we can stop spending to alleviate symptoms. Following this road map, we can defeat the coronavirus and be celebrating life, liberty and livelihood by the Fourth of July.

Slight Downward Trend in Daily US Covid-19 Deaths After More Than 90 Thousand Die

This graph shows the daily reported number of deaths from COVID-19 in the US since March 10. As you can see, the daily reported death numbers fluctuate rather wildly from day to day, but that’s probably because of the bureaucratic hurdles involved in reporting a death (and many offices are closed on weekends, so it’s probably not because fewer people die on Sundays and Mondays).

But overall there seems to be a slight downward trend since a high point near April 15. Most of that longed-for reduction seems to be from massive numbers of people practicing self-isolation, washing hands, wearing masks, and so forth, rather than because of a vaccine (none yet) or highly effective drugs that aid in recovery (only in experimental phases so far), or because of any skilled, consistent, and scientific help from the lying megalomaniac currently residing in the White House. (Nobody has seen any skills, consistency, or knowledge of science emanating from Mango Mussolini, except for his breathtaking abilities to swindle and fool a large subset of the American voting public.)

daily COVID deaths, USA, from ECDC

This second graph shows the cumulative numbers of Americans who have died from this pandemic. It is clearly not an example of exponential growth, but it also has clearly not leveled off.

total covid deaths to date

I got this data from the European Center for Disease Control and Prevention, which has a website with both daily Covid-19 cases and Covid-19 deaths for just about every country in the world. You can find it here.

 

Perhaps a slight downward trend in new COVID cases?

Prompted by a former colleague, I did some tedious work at the CDC site on the numbers of COVID-19 cases each day, going back to January. I found what looks like a weekly up-and-down oscillation pattern that might have to do with whether offices are open and whether reports are made promptly, or might have to be delayed until the end of the weekend. However, it does appear to me that there might be a slow, but real, downward trend over the last few weeks — mostly because the vast majority of us are practicing self-isolation. Here is the graph I made:

new covid cases in the US, per day

Clearly, we are no longer seeing either a steady increase in the number of new cases each day as we were seeing from week 6 to week 10 nor (God forbid!) exponential growth as we were seeing back in March. If we were having exponential growth, it would show up as a horizontal line in the graph below.

daily rate of increases

However, if we stop the social distancing, if we all stop wearing masks and washing hands, if we all start going to movies and restaurants and museums and bars as if this is all over, and if kids go play on playgrounds and go back to school as normal, then exponential growth will raise its ugly, feverish head, and perhaps millions will die.

By the way, I cannot easily find equivalent data on the CDC website for daily deaths; just new diagnosed cases. The COVID death data may be there, but it’s really difficult to dig out. Maybe someone has a source?

The Pandemic Is Far From Over

While the rate of increase per day in the number of deaths is generally down, the COVID-19 pandemic is far from over. In general, more people are still dying each day in the US from this disease than the day before, as you can see from this data, which is taken from the CDC. The very tall bar on day 27 is when New York City finally added thousands of poor souls who had in fact died from this virus. (Day 27 means April 9, and Day 41 means April 30, which is today.)

Opening up the economy and encouraging everybody to go back to work, play, and school will mean a rebirth of exponential growth in deaths and in diagnosed cases after about 2 weeks, since this disease takes about that long to be noticed in those who have been exposed. And once everybody is back on the streets and in the stores and schools, the disease WILL spread exponentially. Opening wide right now, when we still can’t test or follow those who may be infected, would be a huge mistake.

us covid deaths per day

Only somebody as clueless as our current Grifter-In-Chief and his brainless acolytes could be recommending something so irresponsible, against the advice of every medical expert. Maybe they think that only the poor, the black, and the brown will get this disease. Wrong.

The shutdown, while painful, appears to have saved a LOT of lives so far

If you recall, the growth of the new corona virus disease in the US (and many other countries) at first looked to be exponential, meaning that the number of cases (and deaths) were rising at an alarming, fixed percent each and every single day.

Even if you slept through your high school or middle school math lessons on exponential growth, the story of the Shah and the chessboard filled with rice may have told you that the equation 2^x gets very, very hairy after a while. Pyramid schemes eventually run out of suckers people. Or perhaps you have seen a relatively modest credit-card bill get way out of hand as the bank applies 8 percent interest PER MONTH, which ends up multiplying your debt by a factor of 6 after just 2 years!

(If the total number of deaths were still increasing by 25 percent per day, as they were during the middle of March, and if that trend somehow continued without slowing down, then every single person residing inside America’s borders would be dead before the end of May. Not kidding! But it’s also not happening.)

However, judging by numbers released by the CDC and reported by my former colleague Ron Jenkins, I am quite confident that THE NUMBER OF CASES AND DEATHS FROM COVID-19 ARE NO LONGER following a fixed exponential curve. Or at least, the daily rate of increase has been going down. Which is good. But it’s still not zero.

Let me show you the data and fitted curves in a number of graphs, which often make complex things easier to visualize and understand.

My first graph is the total reported number of deaths so far in the US, compared to a best-fit exponential graph:

Deaths in US are not growing exponentially

During the first part of this pandemic, during the first 40 or so days, the data actually fit an exponential graph pretty well – that is, the red dotted line (the exponential curve of best fit) fit the actual cumulative number of deaths (in blue). And that’s not good. However, since about day 50 (last week) the data is WAY UNDER the red dots. To give you an idea of how much of a victory that is: find day 70, which is May 9, and follow the vertical line up until it meets the red dotted line. I’ll wait.

Did you find it? If this pandemic were still following exponential growth, now and into the future, at the same rate, we would have roughly a MILLION PEOPLE DEAD BY JUNE 9 in just the US, just from this disease, and 2 million the week after that, and 4 million the next week, then 8 million, then 16 million, and so on.

THAT AIN’T HAPPENIN’! YAY! HUZZAH!

As you can see — the blue and red graphs have diverged. Ignore the relatively high correlation value of 0.935 – it just ain’t so.

But what IS the curve of best fit? I don’t know, so I’ll let you look for yourself.

Is it linear?

Deaths in US are not growing in a linear fashion

This particular line of best doesn’t fit the data very well; however, if we start at day 36 or thereabouts, we could get a line that fits the data from there on pretty well, like so:

maybe this purple line

 

The purple line fits the blue dots quite well after about day 37 (about April 6), and the statistics algorithms quite agree. However, it still calls for over 80,000 Americans dead by May 8. I do not want the slope of that line to be positive! I want it to turn to the right and remain horizontal – meaning NOBODY ELSE DIES ANY MORE FROM THIS DISEASE.

Perhaps it’s not linear? Perhaps it’s one of those other types of equations you might remember from some algebra class, like a parabola, a cubic, or a quartic? Let’s take a look:

Deaths might be growing at a 2nd degree polynomial rate - still not good

This is a parabolic function, or a quadratic. The red dots do fit the data pretty well. Unfortunately, we want the blue dots NOT to fit that graph, because that would, once again, mean about a hundred thousand people dead by May 8. That’s better than a million, but I want the deaths to stop increasing at all. Like this piecewise function (which some of you studied). Note that the purple line cannot go back downwards, because generally speaking, dead people cannot be brought back to life.

maybe this purple line - nah, prefer horizontal

Well, does the data fit a cubic?

deaths fit a cubic very well

Unfortunately, this also fits pretty well. If it continues, we would still have about a hundred thousand dead by May 8, and the number would increase without limit (which, fortunately, is impossible).

How about a quartic (fourth-degree polynomial)? Let’s see:

4th degree polynomial is impossible - people do NOT come back to life

I admit that the actual data, in blue, fit the red calculated quartic red curve quite well, in fact, the best so far, and the number of deaths by Day 70 is the lowest so far. But it’s impossible: for the curve to go downwards like that would mean that you had ten thousand people who died, and who later came back to life. Nah, not happening.

What about logarithmic growth? That would actually be sweet – it’s a situation where a number rises quickly at first, but over time rises more and more slowly. Like this, in red:

logarithmic growth

I wish this described the real situation, but clearly, it does not.

One last option – a ‘power law’ where there is some fixed power of the date (in this case, the computer calculated it to be the date raised to the 5.377 power) which explains all of the deaths, like so:

no sign of a power law

I don’t think this fits the data very well, either. Fortunately. It’s too low from about day 38 to day 29, and is much too high from day 50 onwards. Otherwise we would be looking at about 230,000 dead by day 70 (May 8).

But saying that the entire number of deaths in the US is no longer following a single exponential curve doesn’t quite do the subject justice. Exponential growth (or decay) simply means that in any given time period, the quantity you are measuring is increasing (or decreasing) by a fixed percentage (or fraction). That’s all. And, as you can see, for the past week, the daily percentage of increase in the total number of deaths has been in the range of three to seven percent. However, during the first part of March, the rate of increase in deaths was enormous: 20 to 40 percent PER DAY. And the daily percent of increase in the number of cases was at times over A HUNDRED PERCENT!!! – which is off the chart below.

daily percentages of increases in covid 19 cases and deaths, USA, thru April 25

The situation is still not good! If we are stuck at a daily increase in the number of deaths as low as a 3%/day increase, then we are all dead within a year. Obviously, and fortunately, that’s probably not going to happen, but it’s a bit difficult to believe that the math works out that way.

But it does. Let me show you, using logs.

For simple round numbers, let’s say we have 50,000 poor souls who have died so far from this coronavirus in the USA right now, and that number of deaths is increasing at a rate of 3 percent per day. Let’s also say that the US has a population of about 330 million. The question is, when will we all be dead if that exponential growth keeps going on somehow? (Fortunately, it won’t.*) Here is the first equation, and then the steps I went through. Keep in mind that a growth of 3% per day means that you can multiply any day’s value by 1.03, or 103%, to get the next day’s value. Here goes:

in 10 months we are all dead

Sound unbelievable? To check that, let us take almost any calculator and try raising the expression 1.03 to the 300th power. I think you’ll get about 7098. Now take that and multiply it by the approximate number of people dead so far in the US, namely 50,000. You’ll get about 355,000,000 – well more than the total number of Americans.

So we still need to get that rate of increase in fatalities down, to basically zero. We are not there yet. With our current highly-incompetent national leadership, we might not.

===================================================================

* what happens in cases like this is you get sort of an s-shaped curve, called the Logistic or logit curve, in which the total number levels off after a while. That’s shown below. Still not pleasant.

I have no idea how to model this sort of problem with a logistic curve; for one thing, one would need to know what the total ‘carrying capacity’ – or total number of dead — would be if current trends continue and we are unsuccessful at stopping this virus. The epidemiologists and statisticians who make models for this sort of thing know a lot more math, stats, biology, and so on than I do, but even they are working with a whole lot of unknowns, including the rate of infectiousness, what fraction of the people feel really sick, what fraction die, whether you get immunity if you are exposed, what is the effect of different viral loads, and much more. This virus has only been out for a few months…

logistic curve again

 

What’s the best approach – should we lock down harder, or let people start to go back to work? Some countries have had lockdowns, others have not. How will the future play out? I don’t know. I do know that before we can decide, we need to have fast, plentiful, and accurate tests, so we can quarantine just the people who are infected or are carriers, and let everybody else get back on with their lives. We are doing this lockdown simply because we have no other choice.

How do we fix the CV19 testing problem? By re-testing everybody who tested positive!

I guess I’ve re-discovered a form of Bayes’ Theorem  regarding the problem that is posed by the high numbers of false negatives and false positives when testing for the feared coronavirus.  What I found is that it doesn’t really even matter whether our tests are super-accurate or not. The solution is to assume that all those who test negative, really are negative, and then to give a second test to all those who tested positive the first time. Out of this group, a larger fraction will test positive. You can again forget about those who test negative. But re-test again, and if you like, test again. By the end of this process, where each time you are testing fewer people, then you will be over 99% certain that all those who test positive, really have been exposed.

Let me show you why.

Have no fear, what I’m gonna do is just spreadsheets. No fancy math, just percents. And it won’t really matter what the starting assumptions are! The results converge to almost perfect accuracy, if repeated!

To start my explanation, let’s start by assuming that 3% of a population (say of the US) has antibodies to CV19, which means that they have definitely been exposed. How they got exposed is not important for this discussion. Whether they felt anything from their exposure or not is not important in this discussion. Whether they got sick and died or recovered, is not going to be covered here. I will also assume that this test has a 7% false positive rate and a 10% false negative rate, and I’m going to assume that we give tests AT RANDOM to a hundred thousand people (not people who we already think are sick!) I’m also assuming that once you have the antibodies, you keep them for the duration.

This table represents that situation:

math of CV19 testing

If you do the simple arithmetic, using those assumptions, then of the 100,000 people we tested, 3%, or three thousand, actually do have those antibodies, but 97%, or ninety-seven thousand, do not (white boxes, first column with data in it).

Of the 3,000 folks who really do have the antibodies – first line of data – we have a false  negative rate of 10%, so three hundred of these poor folks are given the false good tidings that they have never been exposed (that’s the upper orange box). The other 90% of them, or two thousand seven hundred, are told, correctly, that they have been exposed (that’s the upper green box).

Now of the 97,000 people who really do NOT have any antibodies – the second line of data – we have a false positive rate of 7%, so you multiply 0.07 times 97000 to get six thousand, seven hundred ninety of them who would be told, incorrectly, that they DID test positive for Covid-19 – in the lower orange box. (Remember, positive is bad here, and negative is good.) However, 90,210 would be told, correctly, that they did not have those antibodies. (That’s in the lower green box.)

Now let’s add up the folks who got the positive test results, which is the third data column. We had 2,700 who correctly tested positive and 6,790 who wrongly tested positive. That’s a total of 9,490 people with a positive CV19 antibody test, which means that of that group of people, only 28.5% were correctly so informed!! That’s between a third and a fourth! Unacceptable!

However, if we look at the last column, notice that almost every single person who was told that they were negative, really was negative. (Donno about you, but I think that 99.7% accuracy is pretty darned good!)

However, that 28.5% accuracy among the ‘positives’ (in the left-hand blue box) is really worrisome. What to do?

Simple! Test those folks again! Right away! Let’s do it, and then let’s look at the results:

math of CV19 testing - round 2

Wowser! We took the 9490 people who tested positive and gave them another round of tests, using the exact same equipment and protocols and error rates as the first one. The spreadsheet is set up the same; the only thing I changed is the bottom two numbers in the first data column. I’m not going to go through all the steps, but feel free to check my arithmetic. Actually, check my logic. Excel doesn’t really make arithmetic errors, but if I set up the spreadsheet incorrectly, it will spit out incorrect results.

Notice that our error rate (in blue) is much lower in terms of those who tested positive. In fact, of those who test positive, 83.7% really ARE positive this time around, and of those who test negative, 95.9% really ARE negative.

But 84% isn’t accurate enough for me (it’s either a B or a C in most American schools). So what do we do? Test again – all of the nearly three thousand who tested positive the first time. Ignore the rest.

Let’s do it:

math of CV19 testing - round 3

At this point, we have much higher confidence, 98.5% (in blue), that the people who tested ‘positive’, really are ‘positive’. Unfortunately, at this point, of the people who tested negative, only about 64% of the time is that correct. 243 people who really have the antibodies tested negative. So perhaps one should test that subgroup again.

The beautiful thing about this method is that it doesn’t even require a terribly exact test! But it does require that you do it repeatedly, and quickly.

Let me assure you that the exact level of accuracy, and the exact number of exposed people, doesn’t matter: If you test and re-test, you can find those who are infected with almost 100% accuracy. With that information you can then discover what the best approaches are to solving this pandemic, what the morbidity and mortality rates are, and eventually to stop it completely.

Why we don’t have enough tests to do this quickly and accurately and repeatedly is a question that I will leave to my readers.

Addendum:

Note that I made some starting assumptions. Let us change them and see what happens. Let’s suppose that the correct percentage of people with COVID-19 antibodies is not 3%, but 8%. Or maybe only 1%. Let’s also assume a 7% false positive and a 10% false negative rate. How would these results change? With a spreadsheet, that’s easy. First, let me start with an 8% infection rate and keep testing repeatedly. Here are the final results:

Round Positive accuracy rating Negative accuracy rating
1 52.8% 99.1%
2 93.5% 89.3%
3 99.5% 39.3%

So after 3 rounds, we have 99.5% accuracy.

Let’s start over with a population where only 1% has the antibodies, and the false positive rate is 7% and the false negative rate is 10%.

Round Positive accuracy rating Negative accuracy rating
1 11.5% 99.9%
2 62.6% 98.6%
3 95.6% 84.7%
4 99.6% 30.0%

This time, it took four rounds, but we still got to over 99.6% accuracy at distinguishing those who really had been exposed to this virus. Yes, towards the end our false negative rate rises, but I submit that doesn’t matter that much.

So Parson Tommy Bayes was right.

More on the “false positive” COVID-19 testing problem

I used my cell phone last night to go into the problem of faulty testing for COVID-19, based on a NYT article. As a result, I couldn’t make any nice tables. Let me remedy that and also look at a few more assumptions.

This table summarizes the testing results on a theoretical group of a million Americans tested, assuming that 5% of the population actually has coronavirus antibodies, and that the tests being given have a false negative rate of 10% and a false positive rate of 3%. Reminder: a ‘false negative’ result means that you are told that you don’t have any coronavirus antibodies but you actually do have them, and a ‘false positive’ result means that you are told that you DO have those antibodies, but you really do NOT. I have tried to highlight the numbers of people who get incorrect results in the color red.

Table A

Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 50,000 10% 45,000 5,000
Actually Negative 950,000 3% 28,500 921,500
Totals 1,000,000 73,500 926,500
Percent we assume are actually positive 5% Accuracy Rating 61.2% 99.5%

As you can see, using those assumptions, if you get a lab test result that says you are positive, that will only be correct in about 61% of the time. Which means that you need to take another test, or perhaps two more tests, to see whether they agree.

The next table assumes again a true 5% positive result for the population and a false negative rate of 10%, but a false positive rate of 14%.

Table B

Assume 5% really exposed, 14% false positive rate, 10% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 50,000 10% 45,000 5,000
Actually Negative 950,000 14% 133,000 817,000
Totals 1,000,000 178,000 822,000
Percent we assume are actually positive 5% Accuracy Rating 25.3% 99.4%

Note that in this scenario, if you get a test result that says you are positive, that is only going to be correct one-quarter of the time (25.3%)! That is useless!

Now, let’s assume a lower percentage of the population actually has the COVID-19 antibodies, say, two percent. Here are the results if we assume a 3% false positive rate:

Table C

Assume 2% really exposed, 3% false positive rate, 10% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 20,000 10% 18,000 2,000
Actually Negative 980,000 3% 29,400 950,600
Totals 1,000,000 47,400 952,600
Percent we assume are actually positive 2% Accuracy Rating 38.0% 99.8%

Notice that in this scenario, if you get a ‘positive’ result, it is likely to be correct only a little better than one-third of the time (38.0%).

And now let’s assume 2% actual exposure, 14% false positive, 10% false negative:

Table D

Assume 2% really exposed, 14% false positive rate, 10% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 20,000 10% 45,000 2,000
Actually Negative 980,000 14% 137,200 842,800
Totals 1,000,000 182,200 844,800
Percent we assume are actually positive 2% Accuracy Rating 24.7% 99.8%

Once again, the chances of a ‘positive’ test result being accurate is only about one in four (24.7%), which means that this level of accuracy is not going to be useful to the public at large.

Final set of assumptions: 3% actual positive rate, and excellent tests with only 3% false positive and false negative rates:

Table E

Assume 3% really exposed, 3% false positive rate, 3% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 30,000 3% 45,000 900
Actually Negative 970,000 3% 29,100 940,900
Totals 1,000,000 74,100 941,800
Percent we assume are actually positive 3% Accuracy Rating 60.7% 99.9%

Once again, if you test positive in this scenario, that result is only going to be correct about 3/5 of the time (60.7%).

All is not lost, however. Suppose we re-test all the people who tested positive in this last group (that’s a bit over seventy-four thousand people, in Table E). Here are the results:

Table F

Assume 60.7% really exposed, 3% false positive rate, 3% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 45,000 3% 43,650 1,350
Actually Negative 29,100 3% 873 28,227
Totals 74,100 44,523 29,577
Percent we assume are actually positive 60.7% Accuracy Rating 98.0% 95.4%

Notice that 98% accuracy rating for positive results! Much better!

What about our earlier scenario, in table B, with a 5% overall exposure rating, 14% false positives, and 10% false negatives — what if we re-test all the folks who tested positive? Here are the results:

Table G

Assume 25.3% really exposed, 14% false positive rate, 10% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 45,000 14% 38,700 6,300
Actually Negative 133,000 10% 13,300 119,700
Totals 178,000 52,000 126,000
Percent we assume are really positive 25.3% Accuracy Rating 74.4% 95.0%

This is still not very good: the re-test is going to be accurate only about three-quarters of the time (74.4%) that it says you really have been exposed, and would only clear you 95% of the time. So we would need to run yet another test on those who again tested positive in Table G. If we do it, the results are here:

Table H

Assume 74.4% really exposed, 14% false positive rate, 10% false negative
Group Total Error rate Test says they are Positive Test says they are Negative
Actually Positive 38,700 14% 33,282 5,418
Actually Negative 13,300 10% 1,330 11,970
Totals 52,000 34,612 17,388
Percent we assume are really positive 74.4% Accuracy Rating 96.2% 68.8%

This result is much better, but note that this requires THREE TESTS on each of these supposedly positive people to see if they are in fact positive. It also means that if they get a ‘negative’ result, that’s likely to be correct only about 2/3 of the time (68.8%).

So, no wonder that a lot of the testing results we are seeing are difficult to interpret! This is why science requires repeated measurements to separate the truth from fiction! And it also explains some of the snafus committed by our current federal leadership in insisting on not using tests offered from abroad.

 

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EDIT at 10:30 pm on 4/25/2020: I found a few minor mistakes and corrected them, and tried to format things more clearly.

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