Sunday, March 15, 2020

Surviving the Coronavirus

Deadly Peril Edition

Though I have been busy working to resolve wrongful convictions, I have not been posting about wrongful convictions on this once august site, due to priorities and time constraints.

Though I am now, as you can see with your own eyes, publishing a post on this once august site, it is not about wrongful convictions. Instead, as a public service, I am presenting my thoughts on how we, individually and as a society, might best survive the COVID-19 / Coronavirus pandemic.

I'll begin by pointing out that I am not an epidemiologist, a doctor, or a health care professional of any sort. Instead, I was once an engineer, and I now claim to be a recovering engineer. "Hello. My name is TSG, and I'm an engineer."

The Skeptical Spouse assures me that I will never recover. The fact that I am publishing this article weighs heavily in her favor.

Several recent technical articles have prompted me to think through the mathematics of surviving a pandemic. I will extract interesting and useful tidbits from some of the articles. I'll throw an itsy bitsy tiny weenie bit of math your way. I'll explain the math for those of you who are not recovering engineers. Hopefully, if I do this well, we might actually, in all seriousness, save a life or two. That's why I am resurrecting and redirecting this once reasonably well visited site.

The first article of interest is a pre-print, non-peer-reviewed paper enticingly titled, "Trends and prediction in daily novel coronavirus infection in China, Hubei Province and Wuhan City; an application of Farr's law." Dated 15 February this year, when 793 new cases were reported in Wuhan City, the authors predicted that new cases would drop to zero by 8 March, just three weeks out. According to a Reuter's article that I dug up, as of 5 March there were zero new cases in all of Hubei Province, which includes Wuhan City.

That was a spectacular prediction, certainly worthy of some consideration.

The authors made their prediction shortly after the rate of new cases each day had peaked. That allowed them to use Farr's Law to predict a "zero-new-cases" date. William Farr (1807-1883) was a British epidemiologist who observed that, during an epidemic, the rate of new cases tends to follow a normal bell-shaped curve. Since then, Farr's Law has been applied with reasonable success to analysis of a number of epidemics including smallpox, flu, and AIDS.

The authors who applied Farr's Law to the coronavirus outbreak at Wuhan city provided both tabulated data and plots for Wuhan City, the remainder of Hubei Province, and all of China. I show their plot for Wuhan City below. The blue line shows the actual number of new reported cases. The orange line is the author's best projection of how the future rate of new cases would develop in Wuhan City. The authors gave a 25% chance that new cases would develop more slowly than the comforting gray line, and a 25% chance that cases would explode faster than the scary yellow line.

The cases haven't peaked in the U.S., not by a long shot, so we can't yet apply Farr's Law of to make a guess at how bad things might become in our country, the good ol' US of A. What the plot does show is, that by applying extreme measures quickly, a country has some hope of limiting the damage that can result from the virus.

The second article provides the best quantified overview of the coronavirus pandemic that I have come across so far. It is by Our World in Data, which begins its article with the organization's mission statement: "The mission of Our World in Data is to make data and research on the world’s largest problems understandable and accessible." As a recovering engineer, I like that. I'll use some of their data as I describe a simplified mathematical model for the contagion, beginning ...


One of the most important numbers in epidemiology is the reproduction number, represented by the letter R. The number is defined as the average number of secondary cases generated by one primary case. If on average, one person infects two others, then R is equal to 2. If R is greater than 1, then the epidemic will spread. If it is much greater than 1, then the epidemic will spread quickly.

To get a sense of how serious the coronavirus might be when compared to other viral outbreaks that mankind has survived, we can compare their Ro values. (Ro is pronounced R zero or R naught, depending on your side of the pond.) Ro is the reproduction number at the beginning of the outbreak. For previous viral outbreaks, I rely on the classic paper by BMC Infectious Diseases, "Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature." From that august paper, I find the following:

The median Ro value for seasonal flu was 1.28. Seasonal flu kills between 3,000 and 49,000 people in the US each year.

The median Ro value for the 2009 swine flu was around 1.46. That animal named flu left 12,000 dead in the US.

The median Ro value for the 1957 Asian flu was 1.65. That non-geographically named flu left 115,000 dead in the US.

The median Ro value for the 1968 Hong Kong flu was 1.80. That non-geographically named flu left 110,000 dead in the US. 

The Ro value for the 1918 Spanish flu was also around 1.80. That non-geographically named flu left 675,000 dead in the US.

According to the International Journal of Infectious Diseases, the estimated Ro value for the Wuhan COVID-19 coronavirus, based on the Diamond Princess Cruise Ship trip to hell, is around 2.28.

According to the august medical journal The Lancet, the estimated Ro value for the Wuhan COVID-19 coronavirus, based on the China experience, is around 2.5. 


If you are not yet worried, you should be, at least a teeny weeny bit. You absolutely should not panic, but you absolutely should force yourself to read this lengthy august article to its dramatic conclusion.

For an epidemic to recede, its R value, its reproduction number, must somehow drop below 1.0. Anthony Farr's bell curve will peak when R falls to 1.0, and the rate of new cases will drop when R falls below 1.0. Because we need to keep R as low as possible, we should more carefully consider the reproduction number.

Left to its own evil devices, a pandemic will burn itself out by creating so many survivors that the entire society reaches a herd immunity threshold. At that point, R goes to 1. As still more and more people survive the infection and develop a natural immunity, then R falls below 1, the herd immunity becomes more robust, and pandemic blessedly withers.

Thanks to the wonders of mathematics, we can estimate the percentage of the population that must become immune to provide our entire herd with herd immunity. The equation is A = 1 - 1/Ro, where A is the herd immunity threshold (as a percentage of the population) and Ro is the reproduction number that you now understand so thoroughly and so well. Given that we have no vaccine, and probably will not soon have a vaccine, we are going to calculate the number of Americans who will have to get sick, survive, and develop a natural immunity.

The next paragraph is rated S, for shocking. Get ready. Brace yourself. Here we go.

If the starting R value for the coronavirus is indeed 2.28, as the poor folks aboard the Princess Cruise Line Ship have helped establish, then we will reach the herd immunity threshold once 56% of the population has been infected and has survived. Given there are 325 million of us here in the good ol' USA without a vaccine, then 182 million of us are going to have to get sick and survive. If the starting R value is 2.5, as the poor folks in Wuhan have helped establish, then 60% or us are going to have to take one for the team. That's 195 million of us.


There's an important caveat here. A really important caveat. We need people to survive to create our herd immunity. We don't need people to die. We don't want people to die. We want to minimize the number of people who die. And there is plenty within our power to do just that.

Pandemics are at their worst, by far, when the number of cases overwhelm the medical care capabilities of a country or community. China, obviously having prepared for a serious epidemic, built two temporary hospitals and put them into operation in slightly more than a week. Italy, far less prepared, was completely overwhelmed. The stories coming out of Italy are horrific beyond any words that I want to write.

The OECD (Organization for Economic Cooperation and Development) informs us that, at the outbreak, China had 4.3 hospital beds per 1,000 people; Italy had 3.2. South Korea and Japan had 12.3 and 13.1, respectively. The United States, by comparison, has 2.8.  Less than Italy!!


Now you can see why the strategy here, in the good ol' USA, is to "flatten the curve." Lots and lots and lots of people are going to contract the disease, but we don't want them to all contract the disease at once. We want to spread the infections out over time. Dr. Anthony Fauci, who appears to be the well-informed, calm, level-headed professional orchestrating the US response, explains it this way.
If you look at the curves of outbreaks, they go big peaks, and then come down. What we need to do is flatten that down. That would have less people infected. That would ultimately have less deaths. You do that by trying to interfere with the natural flow of the outbreak.
I think Dr. Fauci meant to say "fewer people" and "fewer deaths" rather than "less people" and "less deaths," but I quibble. More to the point, I think that Dr. Fauci was careful to follow "less infected" with a period rather than "at any point in time." It's not at all clear that the "flatten the curve" strategy is intended to lead to fewer infections. It is clear that the strategy is to spread those infections out over time, so that our hospitals can manage the most severe cases.

There are now many images out there showing the "flatten the curve" concept in graphical format. I offer one of them below.

Notice that the generic red and blue curves follow William Farr's Law. New cases appear slowly at first, intentionally, to lure the sleepy populace into a sense of complacency. Then the rate of new cases increases very rapidly, until the rate levels off because the stupid virus overdoes it and creates herd immunity. Thereafter the rate of new cases decreases rapidly. Finally, the rate of new cases approaches zero, and we tally the dead.

It is clear that, if our national strategy is to be successful, the peak of the blue zone will require fewer than 2.8 hospital beds per 1,000 people. What is left unsaid from the chart is how high the peak of the red curve might be. That peak might be very, very, excruciatingly high. As a recovering engineer, I suggest all such charts should, in the future, be labelled "Caution. Not drawn to scale." I'll go first.

For emphasis, I used red lettering, all caps, and exclamation marks. You can't miss it.

Also left unsaid by the chart, though suggested by it, is that the "flatten the curve" strategy will not necessarily reduce the total number of infections. Instead, the strategy is focused primarily on reducing the total number of deaths. By not overwhelming the healthcare system, we can reduce the number of deaths while the virus runs its course, but runs it more slowly.  The chart needs further clarification. I'll go first.

Warning! I may be wrong with my next observation. I might be way off base. If I am, I ask that any highly-qualified epidemiologist reading this post politely correct me in the comments.

I suspect that the "flatten the curve" strategy is actually the "best path to herd immunity since we won't have a vaccine for a while" strategy. The authorities simply refuse to use my more appropriate name for the strategy because it is a bit too long, not quite as snappy, and a whole lot scarier. I suspect they want to ease us into the herd immunity realization slowly, so that they can flatten the curve.

Flattening the curve is not the only strategy out there. There is, or at least was, what I'll call the impenetrable barrier strategy. Don't let any cases into the country and no one will get sick. In today's world though, that simply wasn't possible. The reason for restricting travel is not to prevent entry of the virus, but to slow it down, to flatten the curve.

There is one other strategy. I'll call it the "early mammal hunkering down" strategy. To explain it, we need to go back 65 million years to the age of the dinosaur. (You should keep in mind that your tour guide is neither a paleontologist nor an evolutionary biologist.) Way back then, the earth was very much like a giant, spherical Thomas's English Muffin with lots of nooks and crannies. Early mammals, with their disproportionately large brains, were smart enough to hide in the nooks and crannies, thus to keep from being eaten by the dinosaurs, with their disproportionately large teeth, small brains, and tiny arms. In this insightful analogy, the early mammals were today's humans and the dinosaurs were the coronavirus. Completing the analogy, the early mammals decided to hunker down and stay hunkered down until a vaccine, in the form of a giant meteorite, hit the planet and wiped out the the dinosaurs, a.k.a. the coronavirus. Then the early mammals unhunkered and evolved into us. That's the only reason you're able to read this. Q.E.D.

Again I may be wrong, but it seems to me that China is aggressively pursuing the "early mammal hunkering down" strategy. It's like Whac-A-Mole. Knock down every case that pops up. Don't let cases spread. You must literally bar people in their apartments, with metal bars outside their doors so they can't leave until some government official remembers them (with a bureaucratic "Oops!") and chooses to remove the bars.

You must literally drag people from their homes and families to quarantine locations, where they will be released only when and if the government decides you are to be released.


Under a government that assigns a social score to each of its citizens, it must be quite easy and socially responsible for panicky and vengeful individuals to see that any unwanted person is barricaded or extracted.

There are massive downsides to this early mammal hunkering down approach, even beyond the grave issue of social cost. Among the massive-est of downsides is the possible cratering of the economy, darkening the skies with gloom and impoverishment, increasing rather than decreasing the death and misery taxes, fees, and surcharges that will be extracted by the virus.

And, to top matters off, the early mammal hunkering down approach may have a fatal flaw. To the extent that the aggressive response rapidly shuts down the virus, the society that is being forcibly hunkered cannot develop herd immunity. Once the hunkering conditions are relaxed, and the mammals begin to reappear from their nooks and crannies, the virus is still out there, at least somewhere on the same planet, lurking, waiting, searching for the tiniest hole in the not-so-impenetrable barrier. The recently unhunkered populous will need to be forcibly hunkered down again, and again, and again. Rinse, lather, repeat. Over and over. Ad nauseam.

I suspect, therefore, that China's early mammal hunkering down strategy is coupled with some wishful thinking, which might come true. Their strategy may indeed lead to the minimum number of lives lost IF a vaccine or an effective treatment appears soon.

In the US, the strategy is to implement far less harsh measures that will flatten the curve. We don't want to drive the curve too quickly all the way back to zero. We want to flatten the curve. It's all about flattening the curve. Flatten the curve and save lives. Flatten the curve and develop herd immunity. Flatten the curve, but not at full speed ahead, rather at one-half or one-quarter speed ahead. If a vaccine or an effective treatment appears soon, that will be great. If not, we will develop herd immunity and move on with our lives without the dismal prospect of recurring infections.

Now, just in case the discussion has been insufficiently depressing, we will now plumb the depths of discouragement by considering how many of us might succumb as we develop our herd immunity. Bear in mind that it is not necessary that anyone at all die for us to achieve herd immunity. Sadly,  tragically, some people certainly will die of the disease, and many people may. Their deaths, however, will have little or no impact on the rate at which we develop herd immunity.

What we need to do, as individuals and as a society, is figure out how to minimize the number of deaths while we develop our herd immunity. I'll begin by using the wonders of math to estimate the worst case scenario, then we'll look at how we can improve on that number. Be forewarned, the worst case scenario is really bad. Also be fore-encouraged, because we can and will do much better than the worst case.

We already know, based on our deep understanding of Ro, that 60% of us must get infected and survive so that we, as a society, can develop herd immunity. We only need multiply our total population of 325 million by 60% and then by the case fatality rate (CFR) to get an estimate of how many of us will die along the way. To know the CFR, you have to know both the number of deaths cause by the disease (relatively easy to obtain) and the number of people who have survived or died of the infection (much harder to obtain).

Because South Korea has such an effective testing system in place, it is probably best to base a CFR on their numbers. As of 11 March 2020, South Korea had reported 7,755 cases and 60 deaths. That's a CFR of 0.77%. Multiply that by 60% of 325 million and were looking at 1.5 million dead.


We need to reduce that number, big time. Big, big, big time. We can begin by focusing on a coronavirus loophole. The coronavirus loophole is that it kills a disproportionately high number of old folks, such as your beloved Skeptical Juror and his beloved Skeptical Spouse. So widely recognized is this loophole that a few millennials have labelled the disease as a "boomer remover." While it's clever, it is not particularly helpful. Words can still hurt.

Business Insider has been more helpful and less hurtful. They published the Korean CFR by age group. I present that useful chart below.

covid 19 death rate by age south korea 3 11 20

There's very good news. Young children and adults seem to be at little risk of dying. That is not always the case with a pandemic. Children are frequently at greater risk than other groups. Furthermore, the 1819 Spanish flu took out young adults at a disproportionately high rate, just when World War I was taking them out almost exclusively on the battlefield and in military hospitals.

There's still more good news in the chart. Middle age adults seem to be faring reasonably well. Those people beneath fifty are no greater risk than the general population is during a regular seasonal flu.

Now, if we can determine the age distribution within the U.S., we can perform the dreadful task of distributing the 1.5 million deaths by age group, assuming each group was infected at the same rate. The good folks at provide a chart that gives us the insight we need.

The data are reportedly accurate as of 1 July 2018. The numbers in the horizontal bars are in millions for both men (blue) and women (black). The total population based on summing of all the values in each of the horizontal bars is 327.14 million. I've been assuming a population for the U.S. of 325 million.

So that you won't have to, I've aggregated the numbers into age ranges matching those used to report the South Korean CFR values by age range. Now, to serve you even better, I've put it all together, below, to calculate the number of U.S. deaths by age required to get us to herd immunity, assuming 60% of each population group will be infected.

0-29 years: 127.5 million x 60% for herd immunity x 0% CFR = 0 deaths
30-39 years: 43.69 million x 0.6 x 0.001 =   26,214 deaths
40-49 years: 40.46 million x 0.6 x 0.001 =   26,076 deaths
50-59 years: 42.83 million x 0.6 x 0.004 = 102,792 deaths
60-69 years: 37.41 million x 0.6 x 0.015 = 336,690 deaths
70-79 years: 22.66 million x 0.6 x 0.043 = 584,628 deaths
80 +   years: 12.68 million x 0.6 x 0.072 = 547,776 deaths

The not so grand total is 1,622,376 Americas dead of coronavirus. That number is reasonably close to the 1.5 million deaths calculated by multiplying 60% of our total population by the CFR for all of South Korea, 0.77%. The "slight" difference (of 122,376 deaths) is apparently due to slightly different age distributions between our two countries. I'm afraid that the higher number, the one based on population distribution, is more defensible from a mathematics standpoint.

From here, you can see the coronavirus loophole. If we somehow infected only the youngest among us, then the total number of deaths would be greatly diminished. We need 60% of 325 million to get infected and survive. We have 127.5 million with a CFR of zero, and 84 million with a CFR of a flu-like 0.1%. To ruthlessly reach our herd immunity level with the fewest number of deaths, we would ruthlessly infect everyone under 29 years of age and 81% of those between 30 and 49 years of age. The total number of people infected would be just over the magic number of 195 million. The number of deaths would be:

0-29 years: 127.5 million x 100% for herd immunity x 0% CFR = 0 deaths
30-39 years: 43.69 million x 0.81 x 0.001 =   35,389 deaths
40-49 years: 40.46 million x 0.81 x 0.001 =   32,772 deaths

The still not so grand total would be 71,161 Americans dead of coronavirus. That's only 4.4% of the 1.6 million that would die in the absence of such a ruthless loophole approach.

There are a number of assumptions involved with this ruthless loophole calculation, and the resulting 71,000 dead is almost certainly too low, even ignoring the moral implications.

In the real world, Americans are already beginning to recognize the coronavirus loophole. They can't quantify it, but they are nonetheless already acting on their intuitive feel. The older among us are more aggressively quarantining themselves than are the younger. The younger among us are stepping to the plate. They are, for example, the primary shoppers / drivers for services such as Instacart that bring groceries and supplies directly to one's doorstep. Some of them have taken to wearing masks and gloves, for the betterment of all involved, but their smile and enthusiasm is still obvious.

Yesterday, as the Skeptical Spouse and I returned from a safe outing, our younger neighbor approached us and volunteered to do any shopping we might need. I informed him that we were already well prepared. I thanked him. I asked him if he offered because he recognized that we (the Skeptical Spouse and I) are part of a high risk group. He acknowledged that was the case. I thanked him again for his thoughtfulness and compassion.

So ...

My prediction right now is that, in the absence of a vaccine or an effective treatment, somewhere between 75 thousand and 1.6 million of us Americans will succumb to the coronavirus, even if we flatten the curve. So too will too many others from other countries. We humans are an ingenious lot, though. When we cease our bickering and marshal our resources against a common enemy, we are formidable.

In upcoming posts, I will address the promise of vaccines and effective treatments. I will offer thoughts on how you, as an individual, can pitch in.

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