Visualizing when to Intervene in an Epidemic

A lot of great visuals have been created to communicate the idea of “flattening the curve” so that the healthcare system doesn’t get overwhelmed from Coronavirus COVID-19 cases. I haven’t seen much to help visualize the importance of intervening early with precautionary measures in an epidemic. I hope this post helps to convey some of the ideas.

Let’s consider the ‘cost of the epidemic’. Naturally, this is a vague concept, but you can imagine it as combining lives lost, long-term health impact, economic impact, etc. Suppose it looks like the following graph, depending on how early we intervene with precautionary measures (the x-axis):

Example: cost of an epidemic as a function of intervention time

Now at first glance, it seems like the optimal time to intervene is the minimum in the graph (see below). This represents the best trade-off between the costs of the intervention and the damages the intervention prevents. If the intervention is later than this, it is more costly and complicated and less effective at preventing damage.

The ‘optimal’ time to intervene supposing the cost function is correct.

But now remember that the vague concept of ‘cost of the epidemic’ is indeed vague and we have a lot of uncertainty about what the costs actually look like. For instance, any of the following curves could be defensible versions of the cost:

Uncertainty about the cost: any of these curves could be right.

Then by targeting what we think is the minimum cost, there is a significant chance that we get it very wrong and see costs blow-up despite the intervention:

The optimal cost in one estimate could be very far from the optimal in another estimate.

This leads to the following observations. (1) We’re better off targeting intervention earlier than what we think is optimal. (2) The more risk averse we think society should be in these situations, the earlier we should take precautionary measures. This is so that we’re more sure that we don’t pick a point after the blow-up. (3) Estimating how much we could be wrong is extremely sensitive to the worst case scenario that we construct. So it’s hard to optimize with respect to that either, because it could be very wrong.

The point is that, in these complex systems, our estimates of risk are extremely sensitive to how we estimate them. Equally defensible ways to measure risk could give very different results. And so if we’re thinking about a cost-benefit optimization in these settings, we’re likely to get it very wrong. Instead, we should aim to be very conservative compared to what our risk measures tell us to do, which is why it’s very important to act early in limiting an epidemic in case the worst cases materialize (while of course hoping for the best).

Clearly this is a simplified description, it’s only meant to convey some general ideas. I encourage you to read more. A good place to start is here.



PhD student @ Cornell University, Twitter: @aklamun

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