How to decide if anybody should listen to your ideas on how and whether to re-open schools, or maybe you should just hush.

Peter Greene has provided a nice flow chart to let you decide whether you should open your mouth with your ideas on how and whether to re-open the public schools, or whether you should just be quiet and listen.

So, should you just hush, or do you have something valuable to contribute to this subject?

My wife and I each taught for 30 years or so, and so we would be in the ‘speak right up’ category, but I don’t really know how the USA can get public education to work next year, especially since the danger is not going away, but apparently once more growing at an exponential clip.

Nobody should be listening to billionaires or their bought-and-paid-for policy wonks who once spent a whole two years in a classroom.

A few quotes from Greene’s column. (He is a much better writer than me, and much more original as well.)

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

To everyone who was never a classroom teacher but who has some ideas about how school should be reopened in the fall:

Hush.

Just hush.

There are some special categories of life experiences. Divorce. Parenthood. Deafness. Living as a Black person in the US. Classroom teacher. They are very different experiences, but they all have on thing in common.

You can read about these things. But if you haven’t lived it, you don’t know. You can study up, read up, talk to people. And in some rare cases that brings you close enough to knowing that your insights might actually be useful.

But mostly, you are a Dunning-Krueger case study just waiting to be written up.

The last thirty-seven-ish years of education have been marked by one major feature– a whole lot of people who just don’t know, throwing their weight around and trying to set the conditions under which the people who actually do the work will have to try to actually do the work. Policy wonks, privateers, Teach for America pass-throughs, guys who wanted to run for President, folks walking by on the street who happen to be filthy rich, amateurs who believe their ignorance is a qualification– everyone has stuck their oar in to try to reshape US education. And in ordinary times, as much as I argue against these folks, I would not wave my magic wand to silence them, because 1) educators are just as susceptible as anyone to becoming too insular and entrenched and convinced of their own eternal rightness and 2) it is a teacher’s job to serve all those amateurs, so it behooves the education world to listen, even if what they hear is 98% bosh.

But that’s in ordinary times, and these are not ordinary times.

There’s a whole lot of discussion about the issues involved in starting up school this fall. The discussion is made difficult by the fact that all options stink. It is further complicated by the loud voices of people who literally do not know what they are talking about.

How the US States and Territories Compare on Covid Death Rates

I haven’t seen this sort of simple analysis done anywhere else, so I tallied the total number of reported deaths, and divided this by the population, and moved the decimal point six places so we get the death rates per million. The table below shows the results, in order from highest to lowest fatalities per million inhabitants.

Here is how Vietnam Stopped COVID-19, with ZERO fatalities

BBC had a detailed analysis of how Vietnam managed to prevent the coronavirus from causing massive fatalities: aggressive quarantining of anybody who came from abroad, lots of testing, and lots of contact tracing. All from the very beginning. The headline is “‘overreaction’ made Vietnam a virus success”

However, I doubt that most of the other nations with extremely low COVID death rates did what Vietnam did. Were they just lucky and/or isolated? This inquiring mind would like to know.

The article begins like this:

Despite a long border with China and a population of 97 million people, Vietnam has recorded only just over 300 cases of Covid-19 on its soil and not a single death.

Nearly a month has passed since its last community transmission and the country is already starting to open up.

Experts say that unlike other countries now seeing infections and deaths on a huge scale, Vietnam saw a small window to act early on and used it fully.

But though cost-effective, its intrusive and labour intensive approach has its drawbacks and experts say it may be too late for most other countries to learn from its success.

‘Extreme but sensible’ measures

“When you’re dealing with these kinds of unknown novel potentially dangerous pathogens, it’s better to overreact,” says Dr Todd Pollack of Harvard’s Partnership for Health Advancement in Vietnam in Hanoi.

Recognising that its medical system would soon become overwhelmed by even mild spread of the virus, Vietnam instead chose prevention early, and on a massive scale.

By early January, before it had any confirmed cases, Vietnam’s government was initiating “drastic action” to prepare for this mysterious new pneumonia which had at that point killed two people in Wuhan.

Will these ‘lost’ months of school really matter?

David Berliner explains that the academic topics untaught during these months of coronavirus shutdowns of schools aren’t really all that much to worry about — as long as kids have been engaged in useful or imaginative projects of their own choosing. This first appeared on Diane Ravitch’s blog. I found it at Larry Cuban’s blog.

Worried About Those “Big” Losses on School Tests Because Of Extended Stays At Home? They May Not Even Happen,
And If They Do, They May Not Matter Much At All!

David C. Berliner
Regents Professor Emeritus
Mary Lou Fulton Teachers College
Arizona State University
Tempe, AZ.

Although my mother passed away many years ago, I need now to make a public confession about a crime she committed year in and year out. When I was young, she prevented me from obtaining one year of public schooling. Surely that must be a crime!

Let me explain. Every year my mother took me out of school for three full weeks following the Memorial Day weekend. Thus, every single year, from K through 9th grade, I was absent from school for 3 weeks. Over time I lost about 30 weeks of schooling. With tonsil removal, recurring Mastoiditis, broken bones, and more than the average ordinary childhood illnesses, I missed a good deal of elementary schooling.
How did missing that much schooling hurt me? Not at all!

First, I must explain why my mother would break the law. In part it was to get me out of New York City as the polio epidemic hit U.S. cities from June through the summer months. For each of those summers, my family rented one room for the whole family in a rooming house filled with working class families at a beach called Rockaway. It was outside the urban area, but actually still within NYC limits.

I spent the time swimming every day, playing ball and pinochle with friends, and reading. And then, I read some more. Believe it or not, for kids like me, leaving school probably enhanced my growth! I was loved, I had great adventures, I conversed with adults in the rooming house, I saw many movies, I read classic comics, and even some “real” literature. I read series after series written for young people: Don Sturdy, Tom Swift, the Hardy Boys, as well as books by Robert Louis Stevenson and Alexander Dumas.

So now, with so many children out of school, and based on all the time I supposedly lost, I will make a prediction: every child who likes to read, every child with an interest in building computers or in building model bridges, planes, skyscrapers, autos, or anything else complex, or who plays a lot of “Fortnite,” or “Minecraft,” or plays non-computer but highly complex games such as “Magic,” or “Ticket to Ride,” or “Codenames” will not lose anything measurable by staying home. If children are cared for emotionally, have interesting stuff to play with, and read stories that engage them, I predict no deficiencies in school learning will be detectable six to nine months down the road.
It is the kids, rich or poor, without the magic ingredients of love and safety in their family, books to engage them, and interesting mind-engaging games to play, who may lose a few points on the tests we use to measure school learning. There are many of those kinds of children in the nation, and it is sad to contemplate that.

But then, what if they do lose a few points on the achievement tests currently in use in our nation and in each of our states? None of those tests predict with enough confidence much about the future life those kids will live. That is because it is not just the grades that kids get in school, nor their scores on tests of school knowledge, that predict success in college and in life. Soft skills, which develop as well during their hiatus from school as they do when they are in school, are excellent predictors of a child’s future success in life.

Really? Deke and Haimson (2006), working for Mathmatica, the highly respected social science research organization, studied the relationship between academic competence and some “soft” skills on some of the important outcomes in life after high school. They used high school math test scores as a proxy for academic competency, since math scores typically correlate well with most other academic indices. The soft skills they examined were a composite score from high school data that described each students’ work habits, measurement of sports related competence, a pro-social measure, a measure of leadership, and a measure of locus of control.

The researchers’ question, just as is every teacher’s and school counselor’s question, was this: If I worked on improving one of these academic or soft skills, which would give that student the biggest bang for the buck as they move on with their lives?

Let me quote their results (emphasis by me [-not me! GFB])

Increasing math test scores had the largest effect on earnings for a plurality of the students, but most students benefited more from improving one of the nonacademic competencies. For example, with respect to earnings eight years after high school, increasing math test scores would have been most effective for just 33 percent of students, but 67 percent would have benefited more from improving a nonacademic competency. Many students would have secured the largest earnings benefit from improvements in locus of control (taking personal responsibility) (30 percent) and sports-related competencies (20 percent). Similarly, for most students, improving one of the nonacademic competencies would have had a larger effect than better math scores on their chances of enrolling in and completing a postsecondary program.

​This was not new. Almost 50 years ago, Bowles and Gintis (1976), on the political left, pointed out that an individual’s noncognitive behaviors were perhaps more important than their cognitive skills in determining the kinds of outcomes the middle and upper middle classes expect from their children. Shortly after Bowles and Gintis’s treatise, Jencks and his colleagues (1979), closer to the political right, found little evidence that cognitive skills, such as those taught in school, played a big role in occupational success.

Employment usually depends on certificates or licenses—a high school degree, an Associate’s degree, a 4-year college degree or perhaps an advanced degree. Social class certainly affects those achievements. But Jenks and his colleagues also found that industriousness, leadership, and good study habits in high school were positively associated with higher occupational attainment and earnings, even after controlling for social class. It’s not all about grades, test scores, and social class background: Soft skills matter a lot!

Lleras (2008), 10 years after she studied a group of 10th grade students, found that those students with better social skills, work habits, and who also participated in extracurricular activities in high school had higher educational attainment and earnings, even after controlling for cognitive skills! Student work habits and conscientiousness were positively related to educational attainment and this in turn, results in higher earnings.

It is pretty simple: students who have better work habits have higher earnings in the labor market because they are able to complete more years of schooling and their bosses like them. In addition, Lleras’s study and others point to the persistent importance of motivation in predicting earnings, even after taking into account education. The Lleras study supports the conclusions reached by Jencks and his colleagues (1979), that noncognitive behaviors of secondary students were as important as cognitive skills in predicting later earnings.
So, what shall we make of all this? I think poor and wealthy parents, educated and uneducated parents, immigrant or native-born parents, all have the skills to help their children succeed in life. They just need to worry less about their child’s test scores and more about promoting reading and stimulating their children’s minds through interesting games – something more than killing monsters and bad guys. Parents who promote hobbies and building projects are doing the right thing. So are parents who have their kids tell them what they learned from watching a PBS nature special or from watching a video tour of a museum. Parents also do the right thing when they ask, after their child helps a neighbor, how the doing of kind acts makes their child feel. This is the “stuff” in early life that influences a child’s success later in life even more powerfully than do their test scores.

So, repeat after me all you test concerned parents: non-academic skills are more powerful than academic skills in life outcomes. This is not to gainsay for a minute the power of instruction in literacy and numeracy at our schools, nor the need for history and science courses. Intelligent citizenship and the world of work require subject matter knowledge. But I hasten to remind us all that success in many areas of life is not going to depend on a few points lost on state tests that predict so little. If a child’s stay at home during this pandemic is met with love and a chance to do something interesting, I have little concern about that child’s, or our nation’s, future.

Bowles, S., & Gintis, H. (1976). Schooling in Capitalist America. New York: Basic Books.

Deke, J. & Haimson, J. (2006, September). Expanding beyond academics: Who benefits and how? Princeton NJ: Issue briefs #2, Mathematica Policy Research, Inc. Retrieved May 20, 2009 from:http://www.eric.ed.gov:80/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/28/09/9f.pdfMatematicapolicy research Inc.

Lleras, C. (2008). Do skills and behaviors in high school matter? The contribution of noncognitive factors in explaining differences in educational attainment and earnings. Social Science Research, 37, 888–902.

Jencks, C., Bartlett, S., Corcoran, M., Crouse, J., Eaglesfield, D., Jackson, G., McCelland, K., Mueser, P., Olneck, M., Schwartz, J., Ward, S., and Williams, J. (1979). Who Gets Ahead?: The Determinants of Economic Success in America. New York: Basic Books.

 

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.

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* 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.

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