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More on herd immunity and the “second wave”

The piece on herd immunity and the outbreak in India has been published on the CNN website More than half of Mumbai’s slum residents might have had Covid-19. Here’s why herd immunity could still be a long way off; this follows my article in The Conversation and the blog entry here.

In the meantime, new results have started to appear, adding to the confusion on whether we are nearing the herd immunity or not; see for example here. There are two strands to this research:

Medical strand

I am not an immunologist, but my understanding is that challenged by a virus, the organism responds in different ways, including antibodies, T-cells, B-cells, and the whole cornucopia of other elements. As we are now about 6 months after the outbreak started in serious outside China (Johns Hopkins data set starts on 22nd January 2020), data are now accumulating on the prevalence (how many people have it), variability (how people differ in their response), dose response (have asymptotic cases a lower immunological response), and dynamics (how long do these things stay in the organism). Unfortunately, my understanding is that the picture is mixed. Some experiments show a strong lasting response and some show a decline.

Is SARS-CoV-2 like the common cold viruses which – as far as I understand it – do not induce lasting immunity? After all, you can catch the common cold many times during the winter season and apparently this is not due to any mutations. Or, is COVID-19 like a flu, which infers immunity that lasts for months – if you catch a flu again in the same flu season, this is apparently due to a different strain and certainly each year the strains seem to be different. Or, is it like measles, which infers immunity for life?

Why is it important? If SARS-CoV-2 is like a common cold, we will simply have to learn to live with it for a long time and the whole concept of “herd immunity” is simply not applicable in a long term (in a modelling world, we will be using an SEIRS family of models). On the other hand, if SARS-CoV is like flu (or even better like measles), we can hope that it will at some point “burn out” (SEIR family of models). At the moment, we probably still do not really know (or at least, I do not know).

Modelling strand

The concept of “herd immunity” stems from an observation that for a virus to spread it needs to have a supply of susceptible individuals, the idea of a threshold is a modelling construct. Not surprisingly different models produce different estimates (for an explanation, see this blog entry); the estimates also depend on our understanding of how fast the virus spreads measured in terms of the reproductive rate, R.

But the situation is even more complicated, as the “herd immunity” levels depend on R which in turn is affected by, among other things, social distancing, mask-wearing, hand washing, home working, and other control measures we currently widely implemented. When quoting a number, the researchers usually mean the “herd-immunity-if-we-do-nothing-to-stop-the-virus”, i.e. under conditions of our return completely to the “normal” behaviour (whatever this means) – no lockdown, no masks.

As we believe that the “if-we-do-nothing-to-stop-it” value of R for coronavirus is about 3, the “classical” result (1-1/R) gives 67%, so we would need at least 70% of people to be immune to start seeing the reduction in the new case numbers. The total number of people infected will be much higher. This is also the smallest proportion of the total population who needs to be successfully vaccinated in order to reduce the epidemic and to prevent future outbreaks. If the vaccination success is about 80% (which is optimistic), we would need to inject nearly 90% of the population to get to this level. This is possible but would require very high levels of coercion, a long campaign, and huge investments; difficult to achieve before November elections.

Can this proportion be lower? There is an observation – which could be wishful thinking – that the infection stops spreading around the mark of 20% of people who have had an infection. This includes all people who have had an infection, not just the reported cases; if we believe that there are about 8 times more infections than reported cases, we are looking at a mark of 2-3% of reported cases – for the UK this would be about 2 million reported cases (as of the end of August we are at the 330,000 reported cases).

There are some theoretical results, including a very important and influential paper by my colleague from Strathclyde, Gabriela Gomes, which give some hope to these lower numbers. But, as of the end of August, we simply do not know.

I want to finish with a very sobering quote from The Atlantic:

The very concept of “herd immunity” – which, although it was not the official Sage-determined strategy, became part of a narrative that led British officialdom into a deadly swamp of complacency – implies the existence of one’s very own, very special herd. It is a correlative of genetic distinction, except that it is acquired rather than inherited. The people have absorbed the virus and their collective antibodies have melded into one triumphant, mystical body that is, like the island itself has always been, impregnable.

Why would any scientist fall for this nonsense? You didn’t have to be a specialist in infectious diseases to know that it was based on two entirely untested assumptions: that coronavirus would behave like flu and that it would confer long-term immunity on those who did not die from it. Scientists – let alone highly distinguished and respected ones – are not supposed to jump to such evidence-free conclusions. The only explanation for what happened is that, far from the government being “led by the science”, official scientific thinking was contaminated by its exposure to a political culture in which positive ­assumptions are compulsory, and British difference is taken as read.


This is a warning to us, scientists, as much as to politicians. Our ideas might look great on paper – or even on the computer screen – but implementation might have huge consequences.

Speaking about republishing the graphics, the article on the second wave in The Conversation (see also the accompanying piece on this blog) has widely been cited and the graphics used many times. A nice piece in the Polish edition of National Geographic appeared back in June (in Polish).

My article on the superspreaders has also been cited in a recent New Scientist article.

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