The question (is it too early to impose restrictions) is, in econ-speak, about the *marginal utility of inaction.*

So we’ll analyse this with a couple of hypothetical case studies, one a bit like the situation in March, and one a bit like now, in the UK. This is all very qualitative back of the envelope stuff, but I think it keeps the maths simple, which is how we like it.

Back in March, R ~ 3 prior to lockdown. Epidemic doubling every 3–4 days.

Delaying lockdown by a week buys you… one week out of lockdown. It also quadruples the number of cases you have and perhaps quadruples the deaths as well. [This is debatable because it depends on who got sick, and also to what extent the death rate is high due to the healthcare system being overwhelmed.]

We now know that lockdown in UK terms is R ~ 0.7 and 3 x 0.7³ ~ 1, i.e. you need appx 3 weeks in lockdown for 1 week outside, just to bring the epidemic back down to where it was before.

So, if you advocated for a week’s delay in March, you bought 1 week of no restrictions. Your price was quadrupled number of sick people and three extra weeks in lockdown at the end. Bad, bad deal.

Today, with no extra measures, R ~ 1.4. This corresponds to doubling cases every week — maybe slightly longer.

If we imagine a new national lockdown is possible, 0.7 * 1.4 ~ 1, so 1 week of lockdown cancels out 1 week of the current growth rate.

The policy aim is no new national lockdown, so restrictions will try and keep R~1, until perhaps as late as March 2021. This means that we aim to maintain our infection rate when the restrictions are imposed. It’s currently running at ~5,000 cases a day

Extrapolated until March, assuming this intervention takes R ~ 1, then we have ~ 1m cases, which would be ~5,000–10,000+ deaths [debatable, this is all back-of-envelope as I’m sure people would appreciate].

So what’s the marginal utility of delay now?

If we delayed restrictions for 1 week, the current cases might approximately double. Then if we took R~1, we’d be looking at 10–20,000 deaths. If we delay restrictions for 2 weeks, 20,000–40,000.

Seems a steep price to pay for just 1–2 weeks with no additional restrictions.

Because R is “only” 1.4, the trade-off is not as bad. That’s thanks to all of our efforts, btw — distancing, masks, wfh, test and trace, all of it means R=1.4. Given only 10%-ish of us are immune, it might be around 2.5–2.7 “naturally” if we all behaved as we did in March.

1 week of no restrictions can approximately be cancelled by 1 week of lockdown now, not 3. That’s good. And medical interventions, shielding etc. should mean that the death rate is lower. Also better than March.

But frankly I think we should impose restrictions we expect will take R < 1 and then loosen them, rather than hoping this piecemeal attempt makes a difference. I am suspicious it will not help and then we’ll be in a position of delaying action for not much benefit.

Basically: if you are going to act anyway, then delaying action has very little marginal utility. You get a few weeks now and pay a hefty price later. If you are planning on inaction, or just some shielding the vulnerable approach, that’s a different ballgame. Just delay — rather than switching to some different strategy — doesn’t help much.

Naturally there are lessons here for climate change also but I’ve made my point. If you disagree with my (very loose, non epidemiologically informed rambling) I’d love to hear it.

Finally, I read a viral post earlier which expressed a lot of extremely relatable sentiments about how we’re all sick to death of restrictions and lockdowns and we have no idea what the endgame is here — are we just waiting for a vaccine which might never arrive, or could take years to come? What is the endgame? Why put up with this when there was no end in sight?

There was always an option, which was to try and use the initial lockdown as a means of getting the rate of COVID down to the point where we could successfully test, trace, and isolate every case. Not some of the cases. Not some of the time. Every case. I.e. the goal would have been Zero COVID.

Clearly for the UK, which we now know had millions of people infected in March, this would have been extremely difficult; maybe not even possible. But it would have been an option that we could have, at the very least, discussed.

But instead of going for that — instead of waiting to relax restrictions until we were certain we could trace every contact of every sick person — we, um, just sort of let everything go on the 4th July. And then we encouraged everyone to go back to the office and to go and eat out in restaurants and pubs while we were still unable to trace contacts.

So if you have ire, which is understandable, then it should probably be directed at the people who made those decisions, rather than anyone who is trying to get people to seriously consider the tradeoffs of what happens when you have an expanding epidemic.