Crudely Modeling Herd Immunity

So what is this “herd immunity” that people keep talking about?

It works something like this:

Adam becomes infected with some disease. We’ll call it Batpox for this example. It turns out that the statistics of Batpox’s transmissibility are such that it is about as contagious as measles. Measles has a basic reproduction number (R0) of about 12. When Adam goes to visit his friends Betty and Chuck, the odds are high that they will both become infected as well—unless they are already immune because of a previous encounter with the disease or a vaccine. OTOH, if enough of the people Adam contacts while he’s sick are immune to Batpox, the disease isn’t likely to spread any further. A population has reached herd immunity for a disease when enough of the population is immune to prevent the disease from easily spreading.

The percentage of population required for herd immunity is greater for larger values of R0. The formula for the approximate percentage of immune individuals necessary for herd immunity is

X = (1 – 1/Ro) X 100

For measles X is about 92 %. That’s why it’s important for kids to be vaccinated in order to get the number of immune individuals as high as possible.

The initial estimate of R0 for the Wuhan virus was around 2.7. That would imply that we’d need about 63 % of the population to be immune in order to achieve herd immunity. However, the Real World data for Covid-19 shows much lower values for R0. That’s values, plural, because different places have different factors that affect transmissibility.

Take a look at these charts of how R0 has varied over time in various states. (Source: The solid lines represent the calculated values for R0 and the shaded areas around the lines show the confidence intervals for the calculations based on the amount and quality of the data. These plots are for entire states; the New York and Michigan numbers would be even lower with the effects of New York City and Detroit removed.

Note that these states have all achieved an R0 of about 1. Plugging that value into our formula for herd immunity gives a required immunity percentage of … pokes at calculator …  zero.

Now, I’ve been engaged in modeling here, and we know how problematic that can be, but I believe this gives us a hint about why people are ready to get back to their normal lives in large swaths of the country. Certainly, a value of R0 below 1 explains why the death toll hasn’t spiked in Georgia.

There are still places in the country struggling to contain the Wuhan virus outbreak, and they should be supported in their efforts. However, the data support letting the rest of the country get on with our lives.

Bending the Curve

I went over the the Maryland Department of Health’s coronavirus website and found the daily numbers for confirmed new Wuhan virus cases and deaths. Here’s the data. The green bars are the daily raw numbers. That data is rather noisy. The blue lines are the 5-day moving averages.

First, the confirmed new cases day by day—

Second, the daily deaths—Eamining the case data, it looks as if the number of cases hasn’t diverged far from a linear rising slope. Projecting the trend present around the first of this month onward yields about the same rate as we actually have now. If the was exponential growth, the exponent wasn’t much more than 1. Maryland hasn’t turned the corner on new cases yet, but it appears that we’ve kept the rate of increase from exploding as it did in New York City.

The downward bend in the death rate over the last few days is a hopeful sign.

Maryland’s response to the pandemic hasn’t been perfect, but we have achieved better results than some without having to go to full-tilt, nanny-state fascist as have some jurisdictions. Now comes the hard part. We need to reengage the economy without reinvigorating the virus.

Time Constants, Half-Lives, and Modeling

My podcasting partner Stacy McCain has a post up, MSNBC’s Doomsday Crisis Theme, that looks at the actual rate of increase in Wuhan virus infections and deaths in North Carolina and notes that they are increasing more slowly than the University of Washington’s Institute for Health Metrics and Evaluation model predicted.

Well, as someone who uses modeling as one of his principal professional tools, I’m not surprised. Mathematical models work well when they accurately describe the Real World system under study and they’re fed with data that represents the Real World system’s actual parameters. They’re like sewer pipes in that if you put garbage in, you’ll get garbage out.

Radioactive decay is a statistical process which is well described for every isotope of every element. Physicists speak of the half-life of an isotope meaning the time it takes for half of the atoms in a given sample of an isotope to undergo radioactive decay. Half-life doesn’t vary between two samples of the dame isotope.

Now, consider the discharge of an electrical capacitor. The voltage across a discharging capacitor will drop at an exponential rate, and the value of that exponent is determined by the reciprocal of the product of the capacitance in farads and resistance in ohms. Because farad X ohm = second, engineers refer to that exponent as the circuit’s time constant. If I’m analyzing an electrical network that might have widely varying values of capacitance and resistance, my model will give me a broad range of possible time constants. Knowing the possible range of part tolerances (and how they might vary over time, temperature, phase of the moon, or whatever) is important in predicting how a circuit will perform.

While the models used to predict the spread of viral disease are relatively straightforward and perform reasonably well when driven with good data, the Covid-19 pandemic is too new for sufficiently good data to have been acquired.

Here’s what we do know—1.) The disease is spread by person-to-person contact. 2.) Taking little or no protective measures produced disastrous results in China, Iran, Italy, and Spain. 3.) Thus far, it appears that several protective schemes work well. See, e.g., Taiwan and South Korea. 4.) In the U. S., densely populated areas with more opportunities for person-to-person contact have seen the majority of cases.

So, here’s what I’m doing—I have complicating factors (age and coronary artery disease) that make me high risk. I live in a state (Maryland) that’s under a mandatory stay-at-home order, but I’ve been telecommuting since it became an option. My son does my shopping for me, and if I do go out, it’s at odd hours when I’m likely to see fewer people.

Do I think the lockdown is necessary? I don’t know. There isn’t enough data yet.

Several people have spoken of the response to the Wuhan virus pandemic as if it were a war. It isn’t, but there is one bit of wartime ethics which may be applicable. When we are at war, we know that some people will suffer and some will die in order to save other lives. At some point, shutting down the economy will cause ongoing problems that will weaken our ability to maintain and improve our agricultural, transportation, medical, and other business and infrastructural systems. That impoverishment, in turn, may sentence more people to misery and possible death (in the long term) than might be saved by continuing economic disruption. That will be a difficult choice if it comes.

I hope and pray that the pandemic will not be so severe that we have to face that sort of ethical dilemma. It appears that drugs are being found for treatment, and a vaccine is possible.

Meanwhile, I’m being careful.

Math is Hard

Bernie Sanders is proposing a national health care system commonly referred to as Medicare for All. The low-side estimates of the program’s cost are around 3 trillion dollars a year.

Michael Bloomberg’s net worth is estimated to be about 62 billion dollars. If Bernie were to confiscate all of that wealth (and it could be liquidated as cash), he could pay for a week of his proposed program. If he could similarly liquidate the fortunes of the ten richest Americans, he wouldn’t find enough money to run Medicare for three months. And he would have destroyed productive assets that would generate further cash flow to fund the system. Even if he kept the seized assets as an investment portfolio (equivalent to a 100 percent income tax rate), a reasonable long-term rate of return would only provide for a week-and-half of Medicare for all each week.

The other 95 percent of the money required would exceed the government’s current income from taxes, so bringing Medicare for All online while maintaining something near the current level of other government services would require at least doubling the current total amount of federal taxation. If the billionaires have had their assets seized so that they have nothing left to be taxed, who do you think is left to be taxed? Cleaning out the millionaires won’t produce the same windfall as billionaires. If it’s still possible to pay wages at the current level after much of the productive investment in the economy is destroyed, then the average citizen’s share of the federal tax burden would likely rise to above 33 percent of personal income.

And then we’d have to figure out how to pay for the Green Nude Eel.

Math is Hard

Stephen Kruiser has a post over at PJ Media about Bernie Sanders’ careless attitude concerning the job losses that would result from his version of the Green Nude Eel. BTW, his version is larger and more voracious than She Guevara’s.

Bernie has admitted that “free” health care will cost more in taxes. And he wants to impose “free” college and other “free” stuff as well. What he and the other socialists running for President can’t seem to explain is where they’ll get all that other-peoples’s-money necessary to pay for the “free” goodies.

The people who call themselves the believers in science aren’t big believers in math. That lack of belief in math is where the socialist train always ends up going off the rails.

Eggs. Omelet. Some disassembly required.


Andrew Yang wants the government to give every adult in America a thousand bucks a month. There are around 250,000,000 of us, so that works out to about $3 trillion a year and would not quite double federal spending. (That’s roughly $3.8 trillion.) He would pay for it with a value added tax that he estimates would bring in less than a trillion dollars a year.

Math is hard, so I’m not sure how that works out in the real world, but I was able to do the math necessary to see the federal government already costs the average adult American over $15,000 a year.

Let’s assume that we’re willing to give kids a free ride until they reach 18. In that case, the average adult’s fair share (that is, the average tax rate) should be whatever proportion $15,000 is of the average income. Average income is about $47,000, so that implies a combined federal (FICA, income, excise, VAT, whatever) tax rate in the range of 32 percent. There aren’t enough rich to soak with the 70 percent max rate proposed by one of the B-Card Democrats won’t pull the average up that high.

Socialist governments traditionally do make a financial mess. They always run out of other people’s money. It’s quite a characteristic of them.

—Margaret Thatcher

Team Kimberlin Post of the Day

Yesterday’s TKPOTD dealt with one of The Dread Deadbeat Pro-Se Kimberlin’s failure to pay attention to details. So does today’s which originally ran five years ago. This was one of my favorites of his screwups.

* * * * *

Here’ another example of The Dread Pro-Se Kimberlin’s carelessness in his pleadings. It’s from the prayer for relief in his proposed second amended complaint.ECF 100-2k$2,000.000 is two-thousand dollars. The last time I checked, $2,000 does not exceed $75,000.

That math error is not the only consequential problem with that claim.


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Math is hard.

Don’t Know Much About History Meets Math Is Hard

Jeff Dunetz has a post over at The Lid about ¡Ocasio! She Guevara’s “tax fairness” proposal. He quotes her as saying.

You know, you look at our tax rates back in the ’60s, and when you have a progressive tax rate system, your tax rate let’s say from zero to $75,000 may be 10 percent or 15 percent, etc. But once you get to the tippy-tops on your 10 millionth dollar, sometimes you see tax rates as high as 60 or 70 percent …

Uh, wrong! The 70 precent top rate on incomes above $100,000 was a holdover from the ’40 and ’50s. One of the key accomplishments of the Kennedy Administration in the ’60 was to get the top rate lowered to 50 percent as a means of stimulating economic growth. Even corrected for inflation, her imagined threshold income for the top rate is an order of magnitude higher than the ’50s value. She’s set her definition of rich too high.

In any event, her numbers don’t add up with the current distribution of incomes. Jeff includes the following table—The top marginal rate is now about 40 percent. If doubling the rate didn’t result in the rich moving more of their their assets offshore and the taxman could take twice as much money from them, one could expect about a 20 percent increase in revenue. Personal income taxes would increase 40, but personal income taxes are only about half of the government’s take. That would provide roughly 800 billion dollars a year, which would not quite offset the deficit expected before implementing She Guevara’s Green New Deal. In fact, doubling everyone’s taxes wouldn’t provide enough money to fund her schemes.


UPDATE—With her congressional pay, Ms. Occasional-Cortex will be entering the upper 5 percent of income earners. Perhaps this will provide her with the same sort of practical education experienced by other who have climbed the income ladder.

Let’s Make a Deal

Sarah Hoyt has a long essay over at According to Hoyt very effectively demonstrating the stupidity of She Guevara’s proposed Green New Deal. Ms. Hoyt does this in a most unfair manner by using Real World data and numbers and math. For example, consider the cost of green energy upgrades to “every” residential and commercial building.

That estimate— which, frankly, for a full remodel of an average 2,500 square foot home to state-of-the-art anything is still probably small— would put the cost of this project at 1.36 trillion dollars. Oh, plus another 336 billion dollars if we assume renovating commercial buildings costs only about 6 times as much, per building, as private homes. Or, for convenient reference, a bit more than the 1.688 trillion the government is expected to make in personal income taxes. Again, by fairly conservative estimates. This could be way higher.

Read the whole thing. I did, and in the process I also found couple of useful new terms to use in reference to the young congresscritter-elect: ¡Ocasio! and kindercaucus.

A Bit of Fact Checking

She Guevara (aka Alexandria Ocasio-Cortez) was on CNN claiming that Medicare for all would be less expensive that our current healthcare because “incorporating the costs of all the funeral expenses of those who die because they can’t afford access to health care. That is part of the cost of our system.”

Speaking from my family’s experience, the cost of a funeral is generally a bargain compared to the cost of a few months of medical expenses for an elderly person, and downright cheap compared to the cost of a few months of cancer.

When the retirement age for Social Security was set at 65 back in the ’30s, that was slightly longer than average life expectancy. Increasing life expectancy has broken that system. I had to wait until I was 66 to collect a full-size Social Security check. If the system were now rigged as it originally was, I should be waiting to collect until I’m almost 80.

Putting us old folks on Medicare increases costs. Burying us would save money. Putting everyone on Medicare … if you think healthcare is expensive now, just wait till it’s “free.”

Math is hard.

Social Justice Math

Campus Reform reports that a professor at the University of Illinois-Chicago has contributed a chapter to a new textbook arguing that math teachers “have a responsibility” to adopt “social justice pedagogies.”

I have a bad feeling about that.

‘You are a slow learner, Winston,’ said O’Brien gently.

‘How can I help it?’ he blubbered. ‘How can I help seeing what is in front of my eyes? Two and two are four.’

‘Sometimes, Winston. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. You must try harder. It is not easy to become sane.’