Can we get R<1?

Submitted by martin on 17 April, 2020 - 9:33 Author: Martin Thomas
Logistic function

Austria, the Czech Republic, Denmark, Norway, Italy, Spain, and France have all announced measures to ease their pandemic lockdowns.

Several other countries in Europe look as if they are at or past a pandemic peak. The UK may be around a peak.

As of yet, no-one - not the scientists, not the governments, and not us either - has even a halfway clear picture of how these easings (over-hopefully called "exit strategies") can best be designed to avoid new peaks. Only slow, piecemeal, feeling-our-way approaches are possible. The UK looks not yet ready even for that. The wild "exit now" talk of Bolsonaro in Brazil and Trump in the USA, fortunately resisted by state governors, makes no sense.

The measures of social equality and care for the worst-off which we’ve been campaigning for through the pandemic will still be vital, or even more vital, to make easing work.

Richard Horton, editor of The Lancet and the most strident medical critic of British government policy, has said "to exit lockdown, we need to maximise economic productivity under an R<1 constraint".

What does that mean? And is it possible?

R is the reproduction number of an epidemic: the average number of new infections each sufferer generates. R0 is the “basic” R, in a population with no immunity. If R<1, the disease dies out. If R>1, the disease grows, but more people become immune from having had the disease. As the proportion without immunity decreases towards 1/R0, R decreases towards 1. Eventually the average sufferer comes to generates less than one new infection because so many of the people they meet are immune.

Without intervention, the epidemic grows until 1-1/R0 of the population - half if R0=2, two-thirds if R0=3, etc. - have gone through the disease. Covid-19, sadly, seems to have a fairly high R0 in ordinary conditions.




The graph of epidemics: green line for cumulative total of cases, red line for new cases, over time

At 1-1/R0 the curve goes flat and we have what's called "herd immunity". Not everyone is immune, but enough are immune that the population as a whole resists growth of the disease.

Sometimes "herd immunity" is referred to as a bad strategy to which there are alternatives. Short of a treatment where everyone can be cured just by taking a pill - and no-one predicts that - or the virus mutating to be fairly harmless, every strategy has to be a "herd immunity" strategy.

A vaccine allows a much lower threshhold for "herd immunity". A 90% effective vaccine, taken by 90% of the population, would get there with just 10% having immunity from previous infection as long as R0<5.8. (No vaccine is 100%. The MMR vaccine, a very good one, is 97% effective against measles and 88% against mumps. No vaccination program is 100%. Double-dose MMR is running at about 86% in Britain).

We may not have a good vaccine for a long time yet. What then?

Then we have to find ways to push down R0 (and hence both R over time, and the "herd immunity" threshhold at which R<=1).

That is the aim of the lockdowns and social distancing. The MRC Centre at Imperial College does daily-updated estimates of R for European countries. Their best guess is that the lockdown in the UK has reduced R from between 3 and 4 to about 0.7.

With R at 0.7 for the time being, any population has "herd immunity" for the time being, and new infections will decline whatever the proportion who have already gone through the disease. Until the lockdown eases.

There is much uncertainty about the calculation. The MRC team have estimates for different R0 for different European countries (depending on levels of crowding and so on), which vary between 2.8 for Sweden and 7 for Belgium, but only estimates.

To continue without schools, travel, social gatherings, etc. for some months may be good, but hardly for years. The issue will become one of finding a policy which allows social and economic life while keeping R below or close to 1, either by having a large enough immune population, or by adjusting social life to push down R0.

It won’t be easy. Sweden’s non-lockdown “social distancing” policy, in favourable social conditions, is estimated by the MRC team to have reduced R only to 1.8.

A lot more people have had the disease than the 0.16% certified cases in the UK or in Germany. Test figures do not tell us how many more, because even in Germany (the highest-testing large country) only 2% of the population have been tested, plus, no-one knows how many of that 2% who tested negative a while back have got the disease since.

The MRC team estimates 11% have had it in Sweden, 4% in the UK, but as few as 0.5% in Norway.

Even the Swedish 11% requires social measures producing R0<1.12 to get “herd immunity”. But then Sweden's former Public Health Epidemiologist, Johan Giesecke, reckons that the real figure for Sweden is not 11%, but about 50%.

China seems to have exited lockdown, and South Korea to have avoided it. That is hopeful. But that has been done by measures of state control and surveillance which European states could not equal. Even France, which many more police per head of population than the UK, and has imposed 100 times more fines for breaches of lockdown, couldn't come near it.

South Korea managed to "contain" an outbreak originating from a religious gathering. It did a lot of tests, but not nearly as many as Germany, and charging people $150 for them. The difference is that the government tracked everyone's movements through their mobile phones, credit-card use, and CCTV, and then notified all the contacts of people who'd tested positive. The population was already epidemic-conscious because of SARS and MERS, and complied.

Taiwan, New Zealand, and South Korea, with heavily-policed borders, may be able to "contain" the virus in the medium-term.

In Europe it is more difficult, but voluntary tracking-and-tracing programs may have enough take-up to work, even after the virus has spread widely. On the calculations of their advocates, those will require testing on a scale over a hundred times bigger even than that of the highest-testing big country at present, Germany, or several hundred times the UK's current rate.

Another possibility is age-segmented easing of lockdowns. If the people most at risk are "locked down" while younger people circulate, that can work out better for those most at risk, because when they re-emerge they will be "protected" from chains of infection by higher immunity in the population around them.

Some lockdown-easings include school reopenings. That may work if lockdown-easing works at all.

Most children and teenagers who get Covid-19 have no or few symptoms.

Cases that will develop symptoms are probably infectious even before they develop those symptoms, but according to the World Health Organisation (2 April) probably those who never develop significant symptoms are much less infectious. So the chance of catching Covid-19 from children or teenagers looks small.

New York City has statistics for teachers who have died from the virus: 21 of them, or 0.2% of the deaths, while they are are 0.9% of the population. 72% of Covid-19 deaths in NYC are over 65. The death rates for teachers are lower than from the under-65 general population, although before 16 March they were in closer contact with swarms of school students than workers generally are with their workmates. That suggests school students with the virus are less likely to pass it on.

The governments, however, have said that large public gatherings (demonstrations, pickets, etc.) will be among the last activities to be reinstated. Bias must be suspected there. It is easier to do a big demonstration with "social distancing", and only slight contact between individuals, than it is to run a school or workplace that way.

None of the statistics is solid. We do know, fairly certainly, that measures of social equality will minimise the risk in the "easings-off", as in the lockdown.

PPE, and PPE training, for all, especially including care workers who currently lack it. "Requisition" the care sector and integrate it into the NHS, under NHS workers' conditions. Full isolation pay for all. Vastly increased testing. Good housing for all, especially the currently-overcrowded. Close the detention centres. Empty the jails of all prisoners other than those who indicate a real risk to life and safety.

Add new comment

This website uses cookies, you can find out more and set your preferences here.
By continuing to use this website, you agree to our Privacy Policy and Terms & Conditions.