The Math on WuFlu

 

I’m finding myself in a shrinking minority with respect to my view of the WuFlu.  To me, it still appears to be an irrational panic.  Heather MacDonald still seems to be on my side, at least as of yesterday (article here).  But even the Daily Wire guys have been convinced that there is something serious to fear, other than fear itself.  By Monday, MacDonald and I may be the only skeptics left standing.  (I would find her to be good company in such an event.)

I’ve done a bit of digging into the facts, and I still can’t understand the cause for alarm.  I would particularly value the input of our Ricochet docs and other medical professionals, as I certainly realize that I could be wrong.

I.  The Severity of the Symptoms

In round numbers, based on the Chinese experience thus far, it appears that about 80% of WuFlu cases are mild, about 15% are “serious,” and about 5% are “critical.”  The main problem with the WuFlu seems to be pneumonia. My impression is that “serious” cases might require hospitalization and oxygen treatment, while “critical” cases might require ICU treatment such as intubation.  My source is here, from the same Worldometer site that our friend Rodin is relying upon for his daily posts.  These estimates are based on information from China through Feb. 11.

Even these figures seem too high to me.  Rodin’s daily post today (here) generally shows lower rates of serious/critical cases than the 20% combined figure noted above.  In Italy, it is less than 10% (1,518 serious/critical out of 17,750 active).  In South Korea, it is less than 1% (59 serious/critical out of 7,300 active).  In the US, it is less than 0.5% (10 serious/critical out of 2,395 active).

My suspicion is that the rates of serious or critical illness is much lower, and that the rates appear high because very few people have been tested.  This makes sense, as I would expect that initial testing would be limited to people exhibiting WuFlu symptoms.  South Korea seems to have done the most extensive testing to date, and its very low rate of serious/critical cases is consistent with the hypothesis that wider testing will show a higher prevalence of the WuFlu, with the vast majority of cases being so mild as to be almost unnoticeable.

II.  The Math on the Hospital Bed Crisis

I’ve seen news reports that the WuFlu has overwhelmed the health care system, in Italy in particular.  Here is an article from The Atlantic on Wednesday, March 11, stating:

Today, Italy has 10,149 cases of the coronavirus. There are now simply too many patients for each one of them to receive adequate care. Doctors and nurses are unable to tend to everybody. They lack machines to ventilate all those gasping for air.

This NYT article from Thursday, March 12 similarly claims, in its headline:

We don’t have enough ventilators and I.C.U. beds if there’s a significant surge of new cases. As with Italy, the health system could become overwhelmed.

I know that I’m just a country lawyer, though I did once study math through the graduate level, with a focus on probability, statistics, and mathematical modeling.  But it doesn’t take grad-level math to question these figures.  It takes middle-school algebra.

The NYT article linked above says that Italy has 3.2 hospital beds per 1,000 people (and the US has only 2.8 beds per 1,000 people).  Italy has a population of about 60 million, so this implies about 192,000 hospital beds.

As noted above, the number of serious or critical WuFlu cases reported in Italy, according to Rodin’s post today, is 1,518.  That is 0.79% of the number of hospital beds in Italy.

Think about that.  We’re supposed to believe that an influx of about 1,500 new patients has overwhelmed the medical system of a nation that has 192,000 hospital beds.

Put this in perspective.  Let’s round up the Italian number to 1% — that is, assume that the number of serious or critical WuFlu cases in Italy is equal to 1% of the country’s hospital beds.  Imagine that you run a hospital with 200 beds.  This means that you can expect two (2) extra patients as a result of WuFlu.  Are people seriously suggesting that a 200-bed hospital will be “overwhelmed” if it has to take in an additional two patients?

You all can believe anything you like.  I’m staying in the skeptic camp with Heather MacDonald, at least for the moment.

Now let’s apply these figures to the US.  Recall that, according to the NYT article linked above, the US has 2.8 hospital beds per 1,000 people.  With a population of 327 million, that’s about 915,000 beds.

How many serious or critical cases are there in the US?  Ten (10), according to Rodin’s post today.  But let’s assume that the WuFlu spread rapidly in the US over the next month.  How rapidly?  Well, China has had 80,000 cases over several months, so let’s make the extreme assumption that the US has 100,000 new cases over the next month — a vastly faster spread than in China.  And let’s use the Chinese figures for serious and critical cases, rather than the much lower figures from South Korea (more than 20 times lower).

So if the US has 100,000 new cases over the next month, 15% will be serious (15,000) and 5% will be critical (5,000), for a total of 20,000.  This would be about 13 times the number of serious or critical cases currently existing in Italy.

20,000 new cases in the US would represent about 2.2% of the hospital beds in the country.  A hypothetical hospital with 200 beds would have to take in about 4 new patients over the next month.

Is the medical profession seriously maintaining that their capabilities are so marginal, their ability to adapt so limited, as to be unable to cope with an increase in their patient load of about 2%?

I fully understand the graph about the capacity of the health system.  Here is one example:

I do not dispute this graph in theory.  I dispute the dashed red line about the “healthcare system capacity.”  Based on my calculations above, the dashed red line is nowhere near as low as indicated.  It is far, far higher — literally off the chart, in this graph.

As noted above, I don’t just understand mathematical modeling.  I am a lawyer.  I know how to mislead — in my case, I endeavor not to mislead myself, but I am ever vigilant about how my opposition can mislead.  This is precisely the way that one can generate a panic — with a graph that is correct in theory, with just one small misleading element.

I see no evidence whatsoever of any serious danger that the WuFlu will overwhelm our healthcare system capacity, even with no protective measures.

Another way to mislead, incidentally, is to assume that the number of cases will continue to grow exponentially.  The very early stages seem exponential, but the number of cases eventually follows an S-curve.  Continuing to project an exponential growth rate — say for an entire month — is contrary to the facts, and will lead to a vast overestimate of the number of cases that we can expect.

 

III.  Expanding capacity

The calculations above assume that we have no ability to increase our capacity to handle patients needing hospitalization.  Obviously, we have such capacity.  I haven’t looked into the precise figures, but my recollection from the hospitalization of family and friends over the years is that most hospital rooms are either single or double occupancy.  In a crisis, it does not seem, to me, that it would be difficult to add an additional bed in each room.  This would probably increase the availability of hospital beds by 30-40%.

This would be enough to hospitalize every American needing it, even if the number of cases increased to about 900,000, and even assuming the very high, 20% rate of serious or critical cases based on reporting from China, and not the rate of about 1% in South Korea and 10% in Italy.

This suggests that we could handle, without too much trouble, the health care needs of Americans even if the WuFlu spreads 10 or 20 times faster in the US than it has spread in China.

And we haven’t even talked about setting up emergency medical facilities.  You know, schools are closing.  Why not set up temporary hospitals in school gyms or auditoriums?  How hard could it be?  Bring in about 100 beds and some oxygen masks.  Have 4 nurses or orderlies monitor the patients, administering oxygen when necessary.  They could check each patient every 30 minutes or so.  If there aren’t enough pulse oximeters for each patient, have the nurse carry it around.  Patients who need critical care could be sent to a hospital.

As I understand it, even the serious WuFlu cases are essentially moderate-grade pneumonia.  Patients may need an oxygen mask, but they won’t immediately die without it.  They can take the mask off to eat, or to go to the bathroom.  They can basically lie there, in relative comfort with an oxygen mask, and watch TV.  Except that they can’t watch March Madness.

IV.  About That March Madness

Actually, perhaps these hypothetical WuFlu patients will be able to watch March Madness.  Because, it seems to me, the term is being redefined. 

I was expecting to watch March Madness on CBS Sports and ESPN.  It was going to involve a bunch of college basketball players.  Now, I seem to be watching a different kind of March Madness on CNN, MSNBC, and Fox News.  It involves a bunch of talking heads, politicians, and medical experts telling me that we’re all going to die unless we shut down the world.  I find this extremely unlikely.

I would appreciate any corrections to my analysis.

If I turn out to be correct, I am going to prepare a huge plate of crow for everyone who disagreed.  :)

 

 

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  1. Saint Augustine Member
    Saint Augustine
    @SaintAugustine

    Rodin (View Comment):

    Got to be someone testing a revision to the database/spreadsheet.

    From the site now:

    We apologize for the temporary disservice that you may have experienced. For about 20 minutes, our site showed clearly incorrect data due to a malicious act. We have investigated the issue and we’re now implementing protective measures to prevent this from happening again. The other day we got hit with a big DDoS attack. Now this. We’ll continue with our daily efforts and we’ll not give up.

    • #121
  2. Rodin Member
    Rodin
    @Rodin

    Saint Augustine (View Comment):

    Rodin (View Comment):

    Got to be someone testing a revision to the database/spreadsheet.

    From the site now:

    We apologize for the temporary disservice that you may have experienced. For about 20 minutes, our site showed clearly incorrect data due to a malicious act. We have investigated the issue and we’re now implementing protective measures to prevent this from happening again. The other day we got hit with a big DDoS attack. Now this. We’ll continue with our daily efforts and we’ll not give up.

    Fascinating that someone thought it would be fun to mess with the database. I wonder if they screwed with anything other than adding absurd and obviously erroneous numbers for Vatican City?

    • #122
  3. Marjorie Reynolds Coolidge
    Marjorie Reynolds
    @MarjorieReynolds

    The Reticulator (View Comment):

    Marjorie Reynolds (View Comment):
    so even though they only have 40 reported cases they have taken great measures to prevent spread like banning private car use etc.

    That’s strange. I’d think private cars should be preferred over mass public transit.

    I know that’s what I thought too. 

    • #123
  4. Bryan G. Stephens Thatcher
    Bryan G. Stephens
    @BryanGStephens

    Ontheleftcoast (View Comment):

    Bryan G. Stephens (View Comment):
    If we have 100,000 cases, we would require 2,000 ventilators, which seems well within capabilities

    Not quite. For every 100,000 cases we would require an additional 2,000 ventilators (and 500 or so more qualified therapists) over and above the day in, day out utilization before the epidemic.

    Also, in many cases, ventilators are necessary but not sufficient. If all COVID-19 cases have been triaged to locations where the necessary level of total care is not possible (which is likely if an epidemic reaches mass casualty levels.) If appropriate care levels are possible but the number of staffable ventilators is the limiting factor, likely prognosis will be a triage factor and those unlikely to survive may not be put on ventilators.

    In order to permit the use of unapproved equipment (several comments have suggested this in various ways) and/or unqualified staff, there will also need to be emergency regulations promulgated to allow this without incurring legal liability.

    If they haven’t done it, states will need to pass enabling legislation to permit hospitals to provide patients to be admitted for care in wards set up in tents, gyms, hotels, etc.

     

    So, I am quoted but that was not me. That links back to me saying Amen. Please correct. 

    • #124
  5. Phil Turmel Coolidge
    Phil Turmel
    @PhilTurmel

    The Reticulator (View Comment):

    Phil Turmel (View Comment):

    The Reticulator (View Comment):

    Phil Turmel (View Comment):

    OldPhil (View Comment):
    OK, but I never understood “exponential” to mean “doubling.” An exponent was always the teeny little number (I know, technical) next to the base number. So 100 to the 2nd power would be 10,000. And 10,000 to the second power would be 100,000,000. Pretty soon we’d be into Michael Bloomberg-type money and we’d all get a million dollars.

    You’ve got it backwards. It is the exponent that is rising. Try 100 to the 3rd power => 1,000,000, then the 4th power => 100,000,000, then the fifth power => 10,000,000,000.

    But thinking in terms of powers of 100 is hard to reason with. The same curve can be scaled to be powers of two. The growth is 2 to the n’th power, where n is steadily growing.

    Um, I don’t think so. Not in the usual equations to model these things.

    Yes, yes they are. Tim did a better job than me in #94. One must remember that exponents don’t have to be integers.

    If following OldPhil’s pattern, the curve is parabolic, not exponential. Parabolic curves are much less dramatic than exponential.

    When people speak of exponential growth, the exponent is usually the growth rate, and is a constant (although in real life, growth rate is not a constant forever). Tim’s example doesn’t express it that way, though the growth rate (doubling time) is in the exponent, as the denominator of the exponent. And in Tim’s example, the exponent is not rising. It’s falling as t gets larger, which it usually does except where time flows backwards. But I’m not quite sure what you were getting at when you were saying the exponent is rising, so maybe I’m missing something.

    In Tim’s excellent example, t itself is in the numerator of the exponent, and is divided by the (constant) doubling time, yielding an increase of “+1” in the exponent for every doubling time that passes.  You missed that and/or mis-understood.

    As a quick check of your premise, note that if the exponent was declining as time passed, the numerical result of the operation would also be declining.  And it isn’t, so your premise is wrong.

    • #125
  6. The Reticulator Member
    The Reticulator
    @TheReticulator

    Phil Turmel (View Comment):
    In Tim’s excellent example, t itself is in the numerator of the exponent, and is divided by the (constant) doubling time, yielding an increase of “+1” in the exponent for every doubling time that passes. You missed that and/or mis-understood.

    Ah, that’s right.

    • #126
  7. Jules PA Inactive
    Jules PA
    @JulesPA

    Mendel (View Comment):

    Jerry Giordano (Arizona Patrio… (View Comment):
    The vast majority of those who die in the US from the WuFlu will be the elderly and infirm, chiefly people vulnerable to opportunistic infections, and likely to have died of something else in the near future (like the regular flu).

    I imagine this attitude goes a long way toward explaining your belief that the entire reaction to corona is overblown.

    This is obviously a subjective and not a scientific topic, but I think it’s not getting anywhere near enough attention. Based on fairly consistent data from around the world, it’s safe to say that the fight against corona is indeed really a fight to save old people with already-weak bodies. What price are we willing to pay to protect them?

    I’m sure you read Prof. Rahe’s post a few days ago in which he essentially said “I’m heavily at risk and I don’t want to die yet; please do whatever you can”. Would you be willing to tell him your son’s robot fair is more important than trying to prevent him from dying somewhat earlier than he otherwise might? I’m not trying to provoke or troll you, there’s no clear answer to this question. But it’s one we shouldn’t sweep under the table.

    Wow, that’s nicer than I would have put it. Both of my grandparents are dead 20 years, but my mom is healthy for a 76 year old. 

    Her life, as a parent and a grandparent, is more valuable than the entire NBA. And yes your darn robotics event is cancelled. Yes it’s inconvenient.  I’m sorry. 

    I don’t understand what is happening, I really don’t, but the end of this insanity is about which door we choose. 

    I think choosing for the health and future of many is important. Some might say, “Choose Life.”

    What profit a man if he gains the whole world but loses his soul. 

     

    • #127
  8. kedavis Member
    kedavis
    @kedavis

    Marjorie Reynolds (View Comment):

    The Reticulator (View Comment):

    Marjorie Reynolds (View Comment):
    so even though they only have 40 reported cases they have taken great measures to prevent spread like banning private car use etc.

    That’s strange. I’d think private cars should be preferred over mass public transit.

    I know that’s what I thought too.

    And I wonder if the Left, especially, will realize what this says about Uber and Lyft and other ride-sharing services of their adoration, and even self-driving cars?

    • #128
  9. Darin Johnson Member
    Darin Johnson
    @user_648569

    Jules PA (View Comment):

    [My mom’s] life, as a parent and a grandparent, is more valuable than the entire NBA. And yes your darn robotics event is cancelled. Yes it’s inconvenient. I’m sorry.

    I think choosing for the health and future of many is important. Some might say, “Choose Life.”

    What profit a man if he gains the whole world but loses his soul.

    I can definitely understand this perspective, especially when it’s your mom in question.  But before you worry too much about Jerry’s soul, please remember that cost/benefit questions — including those related to fatalities — are a necessary part of life.   There are two ways to think about this.

    First, part of the cost of these decisions is to dramatically slow the economy, and there will be life and death consequences associated with this.  They won’t be seen, like the death of a loved one from corona virus, but they’re real nonetheless. 

    Second, we cavalierly take risks with our lives and the lives of others for trivial reasons like basketball games and robot fairs, all the time.  It’s true that the risk is higher now than normal, but it’s not the case that deciding to attend a public gathering had zero risk in normal circumstances.  And it’s not the case that we “choose life” at every turn.

    The numbers matter.  I’m not arguing for or against cancelling the NBA.  I’m just pointing out that it isn’t a binary question.  The NBA was never “safe,” and it isn’t “unsafe” now.

    • #129
  10. Jerry Giordano (Arizona Patrio… Member
    Jerry Giordano (Arizona Patrio…
    @ArizonaPatriot

    Darin Johnson (View Comment):

    Jules PA (View Comment):

    [My mom’s] life, as a parent and a grandparent, is more valuable than the entire NBA. And yes your darn robotics event is cancelled. Yes it’s inconvenient. I’m sorry.

    I think choosing for the health and future of many is important. Some might say, “Choose Life.”

    What profit a man if he gains the whole world but loses his soul.

    I can definitely understand this perspective, especially when it’s your mom in question. But before you worry too much about Jerry’s soul, please remember that cost/benefit questions — including those related to fatalities — are a necessary part of life. There are two ways to think about this.

    First, part of the cost of these decisions is to dramatically slow the economy, and there will be life and death consequences associated with this. They won’t be seen, like the death of a loved one from corona virus, but they’re real nonetheless.

    Second, we cavalierly take risks with our lives and the lives of others for trivial reasons like basketball games and robot fairs, all the time. It’s true that the risk is higher now than normal, but it’s not the case that deciding to attend a public gathering had zero risk in normal circumstances. And it’s not the case that we “choose life” at every turn.

    The numbers matter. I’m not arguing for or against cancelling the NBA. I’m just pointing out that it isn’t a binary question. The NBA was never “safe,” and it isn’t “unsafe” now.

    Thanks, Darin.

    Jules, I have a mom, too, about to turn 75 this week.  And a mother-in-law, 86.  And an entire Bible study class a good generation older than me, including two dear friends who just celebrated their 60th wedding anniversary.  But your comment exemplifies the hysterical overreaction to which I am objecting.  You have no idea about the extent of the danger to your mom — or mine, or you, or me, or anyone else.  The trend seems to be toward the WuFlu being something like 10% of the typical annual flu, and neither of us would dream of shutting down the world for such a thing.

    If you’re serious, then we should shut down the darned NBA — and everything else — each and every year, because of the regular flu.  Oh, and the schools, which are now shut down.  And all of the restaurants (just shut down in Tucson, apparently).  These are all a danger to your mom, and mine, each and every year.  Perhaps we should all live in a plastic bubble.

    And if I question it, you say that I have lost my soul.  I dissent.  I think that others are losing their minds, temporarily I hope.

    • #130
  11. Jules PA Inactive
    Jules PA
    @JulesPA

    So where is the balance? What choices will create a balance between insane options that include the eat drink be merry approach and what I will completely ackowledge as hysterical isolation?

     

    • #131
  12. Saint Augustine Member
    Saint Augustine
    @SaintAugustine

    Jules PA (View Comment):

    So where is the balance? What choices will create a balance between insane options that include the eat drink be merry approach and what I will completely ackowledge as hysterical isolation?

    Hong Kong?

    • #132
  13. kedavis Member
    kedavis
    @kedavis

    Jerry Giordano (Arizona Patrio… (View Comment):

    If you’re serious, then we should shut down the darned NBA — and everything else — each and every year, because of the regular flu. Oh, and the schools, which are now shut down. And all of the restaurants (just shut down in Tucson, apparently). These are all a danger to your mom, and mine, each and every year. Perhaps we should all live in a plastic bubble.

    And if I question it, you say that I have lost my soul. I dissent. I think that others are losing their minds, temporarily I hope.

    Not shutting down anything is only serious if some of the estimates prove out to be correct.  If they don’t, things could be much worse than a regular flu season.

    Meanwhile, I don’t see anyone who’s claiming that current measures are way overboard, volunteering to be the ones who become possibly jobless, possibly homeless, and possibly life-less if they turn out to be wrong.  Just playing the odds with everyone else doesn’t seem to be sufficient.  It’s not like just not using a seatbelt yourself.  That’s really only gambling with your own life, not anyone else’s.

    • #133
  14. iWe Coolidge
    iWe
    @iWe

    kedavis (View Comment):
    Meanwhile, I don’t see anyone who’s claiming that current measures are way overboard, volunteering to be the ones who become possibly jobless, possibly homeless, and possibly life-less if they turn out to be wrong.

    I am betting my family and my business that the current measures are way overboard. If I am wrong I will indeed threaten my livelihood. I continue to circulate, so I am putting my self at risk of contracting sooner rather than later.

    Just playing the odds with everyone else doesn’t seem to be sufficient. It’s not like just not using a seatbelt yourself. That’s really only gambling with your own life, not anyone else’s.

    I am responsible for a lot of people – both family and shareholders and people who work with and for my company.

     

    • #134
  15. kedavis Member
    kedavis
    @kedavis

    iWe (View Comment):

    kedavis (View Comment):
    Meanwhile, I don’t see anyone who’s claiming that current measures are way overboard, volunteering to be the ones who become possibly jobless, possibly homeless, and possibly life-less if they turn out to be wrong.

    I am betting my family and my business that the current measures are way overboard. If I am wrong I will indeed threaten my livelihood. I continue to circulate, so I am putting my self at risk of contracting sooner rather than later.

    Just playing the odds with everyone else doesn’t seem to be sufficient. It’s not like just not using a seatbelt yourself. That’s really only gambling with your own life, not anyone else’s.

    I am responsible for a lot of people – both family and shareholders and people who work with and for my company.

    Not equivalent at all.  If you can’t see that, well, I’m sorry.  For you, and for them.

    • #135
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