Herd all about it

Here are a few numbers that I’ve been bouncing around my head. The govt’s strategy is clear: they want the disease to spread widely, in order that we as a population may achieve “Herd Imunity”. A simple relationship that has some importance to this blogpost: if the basic reproductive rate is R0, then herd immunity requires a critical proportion pc = 1-1/R0 of the population to achieve immunity (as this reduces the effective R0 in the population to 1, meaning infections do not spread). In the absence of a vaccine, the only way of achieving immunity is for this proportion to actually catch the disease. R0 for coronavirus is uncertain but probably around 3, meaning we need 2/3rds to be infected and subsequently immune, say 40 million people in round numbers.

In order to achieve this over the spring/summer, we have about 20 weeks. 2 million cases per week on average, let’s say 4 million per week around the peak (it won’t be a completely flat infection rate). That’s more than half a million per day.

The Govt’s estimate of the death rate is no more than 1% (and they claim to be confident about this), but that is still 5000 deaths per day. On average, there are currently about 1700 deaths per day from all causes in the UK — that’s just demographics and average mortality.

Incidentally, at the time of writing, about 10% of Italy’s daily deaths are now due to the coronavirus, despite the total number of recorded cases being less than 0.03% of their population.

So, getting back to the UK, the govt’s explicitly stated plan is for the death rate to increase by a factor of about 4 for a sustained period, with ¾ of these due to COVID-19. Along with the deaths, we may reasonably expect a rather larger number to require hospital treatment. 5% would be 25,000 new hospital admissions per day. Every day. For a sustained period. It doesn’t take a genius to work out that this will not happen, people will not be treated and in reality this is likely to push the death rate higher. I find it hard to believe that a 1% mortality rate will stick when people who need urgent critical care are left to fend for themselves.

I find this “plan” to be abhorrent and sociopathic. Unless there is quite literally no better alternative. However, the Govt has made no attempt to argue the case.

What I feel we should be doing is taking steps to reduce the spread, while also aiming to limit the economic damage. The Chinese approach of a full lockdown is clearly not sustainable in the long term, but South Korea, Japan and Singapore all seem to have achieved markedly better control with weaker restrictions and might all provide useful lessons.

We don’t need to stop all transmission to win! We only need to reduce transmission by a factor of about R0 to stop the epidemic in its tracks. If infected people generate fewer than one new case on average, it will die out. Someone estimated that China achieved a 10-fold reduction, getting the effective R0 down to 0.3 in their full lockdown. Something in between “nothing” and “stay in your room” could surely balance our socioeconomic needs with the health of the nation.

Even if we simply cannot get the effective reproductive rate down below 1 on any plausible basis, it is still surely worth lowering it from the current level. Let’s say we halve transmission by (eg) getting as many people as possible to work from home, reducing social mixing events substantially. I’m only talking about halving our daily interactions, not becoming hermits! If the effective R0 is halved from 3 to 1.5 then the growth rate over time is reduced by a factor of almost 3. And the total number of cases to achieve herd immunity is reduced from 2/3 to 1/3. Half as many cases over 3 times the time interval is a factor of 6 in the stress on the system. Getting R0 to 1.2 would have dramatic effects, with a growth rate 5 times slower and a total penetration of 1/6th of the population. That’s a factor of 20 compared to my original calculation.

if the govt thinks this is unachievable or too costly, I’d like to see their working. Currently, they don’t show any indication that they are even trying.

3 thoughts on “Herd all about it

  1. The thing I don’t get (which may be what you’re getting at too) is that worldwide the total number of cases is in the 150000 range. So, the UK plan would seem to imply a rate (and magnitude) that far exceeds anything we’ve seen to date. Just seems bizarre (assuming that what’s being reported is actually the plan).

  2. More recent tweet thread from Adam Kucharski suggests there’s been a bit of (very) poor messaging and that they don’t really want to aim at herd coverage quickly…rather, they see it as a likely/inevitable end-point.

    But the time scale is everything here and Vallance definitely said he wanted it done before next winter peak.



    “If you suppress something very, very hard, when you release those measures it bounces back and it bounces back at the wrong time,” he said. The government is concerned that if not enough people catch the virus now, it will re-emerge in the winter, when the NHS is already overstretched.

    Something is messed up.

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