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.

2 thoughts on “Time Constants, Half-Lives, and Modeling

  1. I think many politicians are panicking. Most of Virginia is virus-free. 90%+ of all cases are confined to a few counties. Yet the governor locked down the entire state. Over-reacting causes panic in the general population and before you know it, you have no soap, TP or food in stores. And 2.4 million guns sold in a month.

    I live in a densely populated area and I am taking precautions but asking people in SW Virginia to take the same measures doesn’t seem responsible.

  2. The main reason for the pre-emptive lockdown is because the virus has a long incubation period, and a pretty high rate of non-symptomatic carriers. Testing has increased, but the rate of positive tests is still coming out extremely high, well into double digits, the combination of which indicates there are a lot of people with the virus who do not know it yet or have been unable to get it confirmed.

    As for treatment options and progress on any potential vaccination, the best source I’ve found is Derek Lowe, and his blog In the Pipeline. He’s been a medical researcher for decades, and has been putting up the studies and going through them in detail.

    That said.. the line about ‘most’ of the place is virus free isn’t true. You’re just probably a few weeks behind, and the earlier you take precautions, the less hard the disease will be on you. The main goal of isolation is to prevent you from getting it. If you wait until you’ve got dead people, most of whom are dying weeks after getting infected, there are now many people with it, and you’re too late.

    ..Plus you might want to see how many people have been tested in your county. If there are, say, only 30 tests from your county, that’s not proof it isn’t there.

    Stay safe.

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