COVID-19: The Early Phases

We're in the early phases of the COVID-19 pandemic. I've been working from home and minimizing time in public since early March. There's not much to do but read the Internet and speculate on the pandemic.

I figure now is a good time to make those speculations public. If nothing else, it will make for interesting reading years down the road, to see how much I did or didn't know at this point in time.

On "Flattening the Curve"

The week of March 9, 2020 is when the general public in the US started to take the crisis seriously. By the end of that week, the US had declared a state of emergency and the WHO had declared a pandemic.

The phrase "flatten the curve" became widespread over the course of that week. You can find representative samples of the argument here in the NY Times and at greater length in StatNews.

These arguments are usually accompanied by graphs like this one from the CDC:

Flatten the curve in chart form

Some skeptical commentators have pointed out that axes on this graph are not labeled. They go on to explore what happens when we do put real numbers on those graphs. Let's follow that path.

I put together a simple SIR compartmental model to run the numbers. You can read the whole thing on Kaggle, but the most important graph is here:

SIR model with R_0 = 1.4 in the US

This is an "optimistic" scenario for curve-flattening in the US. It predicts that, on the way to herd immunity, we will see ~170M people infected with COVID-19 and peak at ~20M simultaneous infections roughly one year from now.

Given that we see headlines about hospitals are already showing signs of stress now, when the hardest hit cities have only a few thousand cases and we have only 20K confirmed cases nationwide, it's hard to imagine what 20M simultaneous cases would look like. I don't know exactly how far hospital capacity could be stretched in a pinch, but this scenario does seem to be several orders of magnitude beyond it.

Even if we set aside common sense and assume we have perfect control over the rates of infection, the outlook is grim. Let’s say the goal is to expose 70% of 300M US residents to COVID-19 to reach herd immunity. Assume each infection lasts two weeks. That translates to ~3 billion infection-days. We can have 8M people sick for 1 year, or 4M people sick for two years, or 16M people sick for 6 months. None of these options seem very appealing.

No curve is flat enough to prevent a public health catastrophe.

Suppression vs Mitigation

I'm neither the first nor the most qualified person to make this point.

The Imperial College COVID-19 Response Team published a study with more detailed models that arrive at a similar point. They define two strategies: suppression and mitigation.

In the suppression case, we aim to keep R0 below 1 and reduce community transmission to 0. We try to curb the spread of the virus until a vaccine arrives, which could take 12-18 months or longer.

In the mitigation case, we aim is to keep R0 low but not necessarily below 1. We will see exponential growth in the number of infections before the effects of herd immunity start to kick in. If R0 is relatively low, the peak number of infections and total number of infections will be lower and arrive later, ie. the curve will be "flattened".

However, as we've seen in the earlier section, the peak is never low enough to prevent a public health catastrophe. Here are the estimates from their more detailed model:

Imperial College esimates of curve flattening

They also study the possibility of toggling suppression strategies off and on to keep society functioning 1/3 of the time while staying just short of overwhelming ICU capacity.

graph of periodic suppression in GB

This is technically reasonable, but to me it doesn't seem feasible politically, socially, or economically. Would businesses be viable in a scenario where they're not sure exactly when the next shutdown or reopening will happen? Would the general public appreciate politicians flip-flopping on suppression policies every few weeks? I'm doubtful that any countries will intentionally implement such a strategy, though I suspect the pattern could develop by accident.

The Future of Long Term Suppression

My prediction is that we're going to be implementing suppression measures for a long time.

I believe the public will demand that measures be taken to suppress the epidemic long before we get far down the road to herd immunity. China's experience shows that it is possible to stop an epidemic after it's started, at high cost. I expect the public will demand and responsible politicians will implement measures sufficient to stop the epidemic as soon as the hospitals start to become overwhelmed. For example, see Italy's shutdown, or the blow-back to the UK's (perceived) plan to aim for herd immunity.

If we are aiming for suppression, the best case scenario looks something like South Korea. Strong measures are used to curb the initial surge in cases. Widespread testing and contact tracing helps to identify and quarantine new and suspected cases quickly, and prevent further outbreaks. Otherwise business carries on mostly as usual. However, it's an open question whether or not this will work in the long term, or if it's only a matter of time until a enough cases slip through the cracks and start another serious outbreak.

I've done some simple data analysis to try to track how well the suppression efforts are doing. It will be interesting to see which countries can avoid exponential increases in the number of infections for long periods of time, and what kinds of measures they take to achieve it.

It's still too early to draw any conclusions from those numbers, but I'm going to make a few predictions anyway:

  • I predict that we will see intermittent school closures (ie. failure to stay open for >= 2 months) in the urban center where I live for the rest of 2020. (80% confidence)
  • I predict that the rate of international air travel won't return to pre-crisis peaks for 1 year (80% confidence) or even 2 years. (70% confidence)
  • I predict that I, personally, won't be working in an office for more than 1 consecutive month in the remainder of 2020. (70% confidence)

I hope I'm wrong.

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