The good news in the Imperial College of London COVID-19 report

This detailed model of COVID-19 transmission shows that it may be possible for US and UK public health authorities to apply the basic ideas of feedback control systems to prevent hospitals from being overwhelmed, for as long as it takes for the vaccine cavalry to arrive. And the solution doesn't require an unrealistic degree of compliance on the part of the general public in an open society. It can even be applied on a local scale, wherever there's a public health officer with nerves of steel.

I wrote this analysis on March 18th, two days after the report came out, by the request of a doctor that I've known for many years. She replied the next day that she has passed it to the county health officer, with an explicit request that it be passed up the chain to Sacramento. She observed that there aren't many people in the medical field with the sort of engineering background needed to recognize a control feedback loop. I elaborated on the thermostat example because I think it's easier for a non-specialist to understand how things like the lag between the cooling kicking in and the measurement at the thermostat changing affect the stable operation of the system. It is sinking in for people how limited the actual testing throughput is, especially if quick turnaround is important. We've got to focus that testing capacity in a place where it informs more than curiosity or treatment of a single individual, especially since by and large the treatment doesn't depend on the result of the test, and the precautions have to be taken whether the person tests positive or not.

As has been widely reported, researchers at the Imperial College of London have published an analysis of detailed simulations of COVID-19 propagation under various assumptions about public policy. The researchers' own press release at https://www.imperial.ac.uk/news/196234/covid19-imperial-researchers-model-likely-impact/ emphasizes the insufficiency of policies aimed at "mitigating" rather than "suppressing" the virus's spread. But there's potentially very good news in their report that doesn't seem to be widely understood.

Look at Figure 4 of the paper itself, at https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf. Take away the caption and the axis labels, and you're looking at something every engineer should recognize: the temperature chart for a normally operating on/off thermostat, fifteen feet away from the adequately sized air conditioner that it controls, on a hot summer afternoon.

When the temperature climbs above the set point (plus a degree or so of comfort range), the thermostat triggers and the A/C kicks in. The measured temperature overshoots significantly past the set point, because the coolant itself takes a while to chill and the vent isn't right next to the thermostat. But once it has peaked, it drops almost as quickly as it rose. That's a sign that the mechanism (compressor) that's connected to the on/off control variable is more or less adequate to bring the output variable (temperature) under control.

(Even when the mechanism is big enough, if the system hasn't been operating under control previously, that first overshoot is kind of brutal. The second and subsequent peaks are lower, for reasons that needn't be explained in detail—Google "phase margin" and "gain margin"—but are a completely expected feature of a wide class of model systems. Real-world systems usually, but not always, behave similarly, if they're at all control-stable to begin with.)

There's a limit to how cold the A/C can make the room, but the system doesn't attempt to drive the temperature down as far as possible. It kicks out at the set point (minus another degree or so of control hysteresis). The measured temperature keeps getting colder briefly, as chilled air goes on circulating. But the main reason why there's a pause before the thermostat triggers again is that there's a "deadband"—an intentional gap between the lower "off" threshold and the higher "on" threshold.

Ideally, you might like it to be colder in the room. But running the compressor for too long at a stretch is a recipe for system failure, followed by an uncontrolled temperature spike. You go into a heat wave with the compressor you have. A STABLE CONTROL SYSTEM TRUMPS IDEAL COMFORT. Read that twice, because it's going to be a very, very hard principle to stick to once it's translated into a health care policy setting. Trolley problems don't begin to compare.

Now let's put those axis labels back in place. This chart isn't for a thermostat; it's for a COVID-positive-ICU-admission-rate-stat. And when you read the text of the paper, you find that the on/off control is for "social distancing" and "school/university closure" policies that involve "plausible and largely conservative (i.e. pessimistic) assumptions" about individual (and even institutional) compliance. The chart is drawn from an individual simulation, but the explanatory text and tabular data (Tables 4 and 5) make a convincing case that its qualitative shape is robust against variation in multiple numerical parameters. And that's really, really good news.

The Imperial College researchers' model is doubtless wrong in detail, but that doesn't matter. What matters is that the COVID-positive ICU admission rate is a practical thing to measure with finite resources, and the absolute accuracy of the measurement doesn't even have to be particularly good as long as its biases are consistent from week to week. And like a thermostat fifteen feet away from the A/C vent, it's got about the right amount of phase lag relative to the control mechanism to permit some degree of tuning for cycle time. (Figure 4 appears tuned for about 8 weeks on, 4 weeks off, once the initial crisis is past; the text suggests that this is largely sensitive to the ratio of "policy on" to "policy off" thresholds.)

Simply put, if we can arrest the first wave of ICU admissions before it overwhelms our hospitals and their staff, we can cycle in and out of social-distancing mode every few months for as long as we have to. But it's only going to work if it's an honest-to-goodness feedback control system. It's not a calendar thing, any more than your heartbeat is a stopwatch thing. Not my area of expertise, but it's probably worth asking a cardiologist to explain the mechanism behind a premature atrial contraction, and why you don't really want your ventricles driven by a fixed-rate pacemaker while your atria are doing that.

It's easy enough to guess at the control thresholds by eyeballing Figure 4. Whatever your bursting-at-the-seams ICU intake rate is, turn on social distancing when COVID-positive admissions reach 8% of that (averaged over the last week or so), corrected as best as you can for local conditions and limited testing accuracy. And whatever threshold you set, turn social distancing back OFF at half that threshold.

Don't take my word for it, and definitely don't set those thresholds without expert advice if you can get it. Talk to Neil Ferguson, or (since he's now COVID-positive himself) any of his co-authors (preferably one with an engineering background). But do, please, start figuring out how to get as clearly defined a measure of COVID-positive ICU admissions as you can, and how to keep that measurement system reliable and consistent over many months, come hell or high water. That's the weakest point in most control systems. And when it comes time to justify closing the schools two weeks earlier than expected on the fourth go-round, maybe because somebody appears to have "left a window open upstairs" - you're going to need data that everybody around you can trust.