You've heard a lot about "flattening the curve". @fernpizza, @jplotkin, Simon Levin, and I have a new preprint showing you the (provably!) most efficient way to do it! But as with many things that sound too good to be true, there's a catch

(THREAD) https://osf.io/rq5ct/ 

Why do we want to "flatten the curve"? We need to take pressure off the healthcare system by preventing a massive epidemic peak. Such a peak can overwhelm a healthcare system.

Before we have access to vaccines, antivirals, and good testing for an emerging new pathogen like SARS-CoV-2/ #COVID19, the key weapons in our curve-flattening arsenal are social interventions that reduce disease-causing contact, slowing down the epidemic/pandemic's rate of spread

The problem with these measures is that while they're worth it—they're lifesaving!—they are arduous and costly, as we're all finding out right now. So a policymaker would like to be as efficient as possible, and minimize the amount of time we need to intervene aggressively

We show that the optimal way to do this if you have a limited amount of time in which you can intervene is to "maintain and then suppress". First you intervene to maintain the epidemic at a constant level—keeping number of cases from growing, but also keeping it from shrinking

Why would you want to do that? An epidemic is like a fire, and susceptible individuals are its fuel. By letting it propagate slowly constant level—new individuals getting infected to exactly replace the ones who recover—you've made the curve *literally* flat.

But all the while you're getting rid of the fire's fuel—susceptible hosts—so when you eventually release your controls, the epidemic won't be able to explode to an enormous peak. Too little fuel.

But if a fire needs fuel, it also needs flames. And infectious hosts are the flames. As you continue your intervention, it is optimal to switch to a suppress strategy. Having gotten ride of enough fuel, you now put out the fire as best you can. Look at the dips in the green lines

This means that epidemic not only has little fuel, but has to start even lower to reach whatever peak it will reach after you stop intervening. So we maintain, then suppress. Or, as @fernpizza and I prefer to think of it:

STOP! Hammer time!

This intervention is extraordinarily efficient. As you can see in this figure, even an intervention of duration T = 2 weeks for a COVID-like disease dramatically flattens the curve. One of 4 weeks more than cuts the peak in half.

At this point, you might stop and ask "could anyone actually pull off an intervention like this?" And the answer is a resounding "no way!". It requires you to constantly adjust the degree of physical distancing during the maintenance phase to keep the curve literally flat

But it turns out that more realistic strategies—if their strictness and start time are well chosen—can mimic the optimal intervention surprisingly well. A figure will illustrate this...

Here we can see that intervening at a fixed level (blue curves) or just skipping the maintain phase and even going straight for suppress (no STOP!, just HAMMER TIME!) can reduce the peak pretty well. The optimzed fixed control is esp. cool: the blue curves *mimic* the green ones!

So things sound pretty good! We can't flatten the curve *optimally*, but a (more) realistic strategy, chosen well, can get pretty close to the optimum. Here we plot the reduced peak as a function of the length of time we get to intervene. Our non-optimal approaches do well!

But I warned you there was a catch. We must choose *when* to intervene. That requires knowing where we currently are in the epidemic curve. As we've seen with #COVID19 epidemiological data collection and modeling are hard. What happens if we mistime our optimized intervention?

What happens is, well, not good. If we're early, we get a resurgent second epidemic peak. But at least we have some extra time to prepare and increase health system capacity. If we're late... BOOM.

This lack of robustness to timing was one of the issues that led us to look into this question. https://twitter.com/dylanhmorris/status/1239080927155945472

Our investigations of this lack of robustness first led to a blog post, and now to this preprint https://dylanhmorris.com/post/mistimed-intervention/

As the title of that blog post indicates, the problem is that an epidemic of a novel pathogen to which there's little or no immunity in the human population initially grows (near) exponentially. And so when it comes time for us to intervene, the epidemic is growing very quickly

So a timing mistake of even a *week* produces a huge difference in the actual state of the world: far more or far fewer currently infectious cases than you expected. So optimized interventions are tantalizing—lots of bang for your buck—but they're dangerously easy to get wrong

So what can we do? Well, the fact that the steepness was the problem gives us some insight. What if we intervene immediately with weaker, more socially tolerable measures, and sustain this relaxed control. We won't flatten the curve as well as a perfect short intervention, but...

We're much more robust! And what's more, because we have a slower growing exponential, we can layer a short, more intensive intervention on top and it will be substantially more robust to mistiming.

Acting early, even in a limited way, dramatically increases the robustness of later, more aggressive measures.

There are lots more fun details in the preprint, and we'd be thrilled if you read it (look at this plot that kind of looks like a whale! Aren't you curious to know what it means? It's pretty cool, in fact...), but we have some key takeaways even from this simple model:

Principle 1: ACT EARLY. Being late is way worse than being early when it comes to epidemic mitigation. If you think you're too early, you're probably right on time. At worst, you're paying a cost to avoid the catastrophic risk of lateness

Principle 2: SLOW THINGS DOWN. Even weak interventions can buy you some breathing room to figure out a better, more robust strategy. Waiting to the last minute and trusting a perfectly optimized intervention to save you is courting disaster

Principle 3: WHEN ALL SEEMS LOST, BEAR DOWN. If you're late, the optimal intervention rapidly becomes the full suppression intervention. Get off that peak as fast as you can, and you'll save lives. If you're wrong and you're not late, the full suppression will still do some good.

Well, that was a lot of tweets! Thanks to anyone who made it this far. We're really excited about this research, and we hope you find it interesting and useful!