I'm exhausted from many late-night meetings, after kids in bed, so happy to see it out.
Where to start?
COVID-19 has one incredibly striking feature. Its severity varies strongly with age, hitting the elderly hard, but sparing most of the young.
We are talking ORDERS of MAGNITUDE. Estimates vary, but there is much agreement on this. 2/n
For example, Fergurson's numbers for mortality
0.1% 20-49
1% 50-64
6% 65+
You can find different and lower numbers, but the pattern is similar.
To us these are facts to grapple with, not to be ignored.
Before I continue, let me leave this here.
An online tool to visualize and experiment with possible responses to the epidemic within our model.
https://mr-sir.herokuapp.com/main
(Big shoutout to MIT's Rebekah Dix who created this!)
4/n
We take a standard SIR epidemic model and add multiple risk groups (MR-SIR for short). The typical SIR model you may see out there has just one group, but epidemiologists have such extensions.
What we add to this: we studying optimal lockdown policy in this framework.
5/n
In particular, we study policies that target different risk groups differently.
Our point: finer policy lever can help you save lives AND lower economic losses.
This diagram illustrates that.
Important disclaimer: even within the model there is a lot of uncertainty on parameters (we consider a range around a baseline). But it is a crucial weakness of any study of this kind.
However, we think the greater point that there are gains to targeted policies is robust. 7/n
Our MR-SIR model looks like this. Groups interact, and get sick, but have different mortality. 8/n
After parameterizing the model the best we could (comments welcome) we put this model through our Optimal Control of lockdown policies, both over time and across groups.
This is what we get for the frontier.
I like to emphasize the frontier rather than a particular point or policy.
Picking a point on the frontier requires picking a very tricky and controversial parameter: the Value of a Statistical Life (VSL). Different points on this frontier correspond to different VSL.
Some believe setting a VSL has ethical problems, but it is also just notoriously difficult to agree on this parameter!
How can you use our frontier or others like it then? 11/n
Say current policy, determined somehow by society or politics, is putting us on some point of the upper frontier. Then you can offer alternatives on the lower frontier that are better, saving more lives and reducing economic activity. 12/n
We find is that the most important distinction is separating the elderly (O for old) from the young (Y) and middle (M) aged. According to our parameters, targeting Y and M separately has marginal gains only.
Semi-targeting is almost as good as full targeting. 13/n
Just as an example, here is a point on the frontier and its policies. Comparing non-targeted with semi-targeted. 14/n
Note: we assume lockdowns are imperfect, only 75% effective, an important parameter in our model, also that mortality rises with hospital use. We can also feed in different private social distancing efforts, we are looking for evidence on how these translate into beta. 15/n
Next, we add in other policies to the mix.
Test-trace-and-isolate, but also what we call group-social distancing.
Our model includes a parameter for the fraction of infected that get isolated. Testing increases this fraction.
We find this is a very powerful tool, confirming many experts voicing this recommendation.
But targeting lockdown is still very helpful. 17/n
Combining targeting with testing should be especially useful in situations with scarce testing resources, which we are currently working on.
That figure is from the online GUI I mentioned earlier, the third tab here https://mr-sir.herokuapp.com/main 18/n
We also look at Group Distancing. People interact more with their own age groups and infections are predominantly from within age groups. As in this figure from here https://rivm.nl/en/novel-coronavirus-covid-19/children-and-covid-19
Policies to discourage against avoidable contacts across groups increase Group Distancing and we show this is very valuable.
Indeed, combined with testing, in our model it is a silver bullet of sorts. Again, a figure from the 3rd tab of the GUI:
Disclaimer again: we realize there is a huge distance to go from these ideas to actual policy. Many issues to consider. Not only parameter uncertainty as mentioned earlier, but features missing in our model.
To name one: if we attempt to isolate to old, how do we care for them?
Those are absolutely crucial questions and we plan to think about them more, with help from others. Again, comments and suggestions are very welcome.
If anyone has good reasons to run our model with other parameters, we'd be happy to. We also plan to put everything online soon.
To close, I wanted to advertise others' great work out there on this important topic. I've never been so impressed by our profession, the response to this crisis. Putting our heads together is powerful!
Highly recommended:
Gollier
@CGollier
: https://perso.math.univ-toulouse.fr/cattiaux/files/2020/04/gollier-22-04-2020slides.pdf
Rampini: https://nber.org/papers/w27063
Favero Ichino Rustichini: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3580626
All these studies have MR-SIR models and look at policies.
The main difference with our paper is we compute optimal policy.
