Thread by @Baylism

Here's my thoughts on the UK government's position. For clarity, I make the assumptions that covid19 has R0 = 2.5, 20% of cases need hospitalisation and 1% die
/1

If no-one was doing anything differently, the R0 of 2.5 implies that the number of cases will increase until 60% have had the disease and are immune. At this point, there is herd immunity [this is (R0-1/R0) - 1.5/2.5 = 0.6]
/2

The herd immunity happens because when 60% of an infected person's contacts are immune, the virus doesn't find enough susceptible people to persist [as only 40% of contacts can be infected and R0 = 2.5, one case is now, on average, only infecting 40% * 2.5 = 1 person]
/3

If we did absolutely nothing to stop this, the UK popn (66M) means 66M * 60% * 1% = 400,000 deaths [and 8M hospitalisations]
/4

An important detail: R0 is proportional to the number of susceptible contacts per day, and the probability of transmission to these contacts. Current measures reduce both of these - working remotely helps reduce the number of contacts; hand washing reduces P(transmit)
/5

Suppose the measures already in place have reduced R0 by 50%, so it is now 1.25. Herd immunity is now reached at 0.25/1.25 = 20% of the population immune. So reducing R0 by half has reduced the "critical proportion" for herd immunity by two-thirds
/6

It might seem counter-intuitive that we can have herd immunity when only 20% of the population is immune. But with R0 = 1.25, 100 cases only generate 125 new cases, and one fifth of contacts immune is enough.
/7

This is how flu is managed. Flu is a killer and there's a vaccine. Do we vaccinate everyone? No, the target is a seemingly low "75% of over 65s", and this is because R0 = 1.3; so herd immunity is reached when 23% of the population is immune.
/8

Back to the halved R0 and 20% immune for herd immunity - in the absence of a vaccine, this is only achieved when 20% of 66M people have had covid19: 13.2M cases, 132,000 deaths and 2.64M hospitalisations. This is still a huge number.
/9

Even if R0 is reduced to 1.01, the calcs lead to 6.5K deaths - surely too many for a plan? The only reduction that makes sense is R0 = 1 [or less]. Maybe this can be done: halving the number of contacts, & halving transmission to contacts, reduces R0 by 75% (60% needed)
/10

But there's a problem: we need to maintain the behavioural changes that reduce R0; if we go back to how we were a few week's ago, R0 increases; the threshold for herd immunity goes back up; and transmission restarts - unless the virus has been eradicated
/11

It is unlikely we can keep up a reduced R0 long-term without tanking the economy, destroying industries and ruining lives.
So, what are the choices?
/12

1. Behaviour changes reduce R0 but it still exceeds 1 = lots of deaths
2. As above, but we hunt down and isolate cases in an attempt to eradicate the virus
3. Behaviour changes reduce R0 below 1 - and we sit it out as virus transmission peters out by itself.
/13

The UK gov has decided against #2. This means we really need to see the evidence that current changes to behaviour (mostly hand washing) gets us to #3, and not #1. Where is this evidence?
/14

There are approaches where herd immunity might still be useful: keep the elderly safely isolated, while the rest of the population get disease and become immune - and the Gov seems to be thinking along these lines
/15

But this could be dangerous: the contacts of elderly people will often/mostly be other elderly people. If the elderly are not immune, there won't be herd immunity in their networks
/16

What all this amounts to is we need EVIDENCE that current behaviour changes are thought to reduce R0 to <1. Without extensive testing and continued contact tracing, this is the only way the virus will disappear by itself, and thereby protect the elderly.

sorry for the long thread!