Flattening The Curve

<chirp chirp> My phone’s non-business ring-tone. “Moire here.”

“Hi, Mr Moire, it’s me, Jeremy, again. Sorry for the hold-up. My phone’s on the charger now so we can keep going about the Logistics Curve and all.”

“Logistic Curve, Jeremy, singular. Logistics plural has to do with managing the details of a military or business operation. That’s quite different from population growth which is what the Logistic Curve is about. Though come to think of it, these days we’re seeing a tie‑in. So where were we?”

“We had that S-shaped Logistic Curve with exponential growth at the beginning but then it plateaus and you showed me a humpy curve that’s the slope of the other one and you said the humpy curve is like R = K*S*(N‑S) if N is everybody and S is how many are susceptible to the virus. But you kind of skipped over K.”

“True and I’ll get to K, but that ‘humpy’ curve is important. In the context of the pandemic, it’s people per day — how many catch the virus, how many show up for medical care, how many need ventilators or even mortuary care — there’s a different K for each question. The hump is what we’re trying to get control of. The K factors summarize a whole pipeline of ifs and maybes. Some of them are knobs that we may be able to use to flatten the hump.”

“We can do that? How?”

“Good question. Here, let me send your phone another image. Let me know when you receive it.”

“It’s here, Mr Moire. Looks like you’ve got three Logistic Curves but they’re stretched out different amounts.”

“Stretched out on the time axis, and that’s crucial. I generated those three plots by using different values for K. Sooner or later in all three models everyone catches the bug. In the blue-line case, though, that happens over a much longer time interval than in the red-line case. If you’re a public health official or hospital administrator you pray for the blue-line case — the slow initial rise gives you a heads-up and more time to get ready for future incoming cases. Better yet, because the cases-per-day peak is flatter you don’t need as many masks and ventilators to take of the patients and your front-line people are less likely to be over‑extended. Assuming you’ve hired enough in the first place.”

“So the government wants to reduce the K numbers to get to the blue-line case.”

“Absolutely. Keep in mind, K is such a complicated summary of things that realistic models are complex. Experienced modelers know that the more factors you put into a model, the riskier the predictions become. Anyway some of the things that go into K we can’t control, we can only measure or estimate them and try to account for what’d happen if something changes.”

“Like what?”

“Suppose you’re exposed to the virus. What’s the probability that you’ll come down with symptoms bad enough to need medical care? Current data suggests those odds depend a lot on uncontrollable things like your age and medical history. A model for a retirement community almost certainly needs a different set of K-values then a model for a college town full of teens and twenty-somethings. But that gets into a different cluster of factors.”

“That’s for sure. My grandparents are a lot more careful about their health than my crew is.”

“Which gets us into the K-factors we can at least try to manage. Simple example — you can’t catch the virus if you’re not exposed to it. That’s what Social Distancing is all about and that’s why you’re staying at home, thank you very much. Typically, models gauge that piece by surveying what fraction of the population is complying with the stay-at-home, masking and 6-feet-away rules. We need to get to 70% or better to keep the patients-per-day rate down to what the hospitals can cope with. A vaccine, when we get one, will have the same effect but that’s a year away.”

“Yeah, and if someone invents a good treatment so people don’t have to go on ventilators, that’d help the K for that end of the pipeline.”

“Get to work on it, Jeremy.”

~~ Rich Olcott

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