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Home >Science >Health >Opinion | Searching for herd immunity & why it matters

Many of you have probably experienced some version of what happened to me several years ago. It went something like this: this guy I didn’t know at all called and gushed, just a little too-friendly, about somebody else I barely knew. “Yeah, and Sanjiv’s been a great pal to me back in NYC." — Really? And you didn’t get his name “Sanjay" right?

“And he said all these great things about you!" — Really? A man I haven’t met in 20 years, and whom I didn’t really know then anyway? “So he suggested your name for this great business opportunity I’d like to tell you about."

Call me an idiot: I actually let the guy come and waste a couple of hours of my time, during which he drew endless meaningless diagrams and mouthed many empty platitudes—all in an effort to persuade me to join a famous pyramid scheme I shall not name, that was then seeking to erect new pyramids in India.

Call me an idiot: I didn’t bite. But let me paint you a picture of how such pyramids are erected. A given platitude-spouter has been persuaded of the scheme’s virtues. His task: go out into a wilderness where nobody has been so persuaded and try to recruit them. What can we say about people in the wilderness whom he wants to sign up? You can probably divide them into two groups. One, made up of those indifferent to his spiel, who forget about him the minute he has finished. The other, made up of folks receptive to his spiel, willing to sign up. In turn, new recruits themselves start recruiting, and likely face the same two kinds of people. On and on like that.

As time goes by, there is an ever-shrinking pool of receptive folks. Why? For one, many of them have already signed up. But it’s also possible that some who have signed up grow disillusioned about the scheme and spread the word, thus swelling the ranks of those unlikely to swallow the pyramid spiel. You can imagine a time when people in the pyramid have no success finding new recruits—because everyone out there is either already in the pyramid or is indifferent to its charms.

A time, you might say, when this particular population has grown immune to the spread of the pyramid. When it has developed a “herd immunity" to the pyramid. The only way the pyramid can now spread is to find uncontaminated populations. Which explains why someone might take an NYC-Mumbai flight, get on the phone and gush to strangers.

By now, you know the analogy I’m drawing here. We’ve all heard, forgive the pun, of herd immunity to the coronavirus. But how is it calculated, and what exactly does it mean anyway?

If a disease finds it increasingly hard to spread in a given population — not because of measures such as distancing or handwashing, but because a certain fraction of the population is immune to it—that’s herd immunity for you. Why does this work? When the disease first arrives, the people it infects, naturally, are those most vulnerable to it. Of the rest, some are resistant from the start. The ones who get the disease either die or recover, and those who recover are now immune to further attacks. (Though strictly, we are not sure yet whether being infected by covid-19 does give you such immunity, like with other diseases). In other words, as time goes by, an ever-larger fraction of the population becomes immune to the spread of the virus. It becomes ever-harder for an infected person to come into contact with others who are uninfected, thus susceptible, so that she can pass on the virus—purely because there are fewer and fewer such people around.

This does not necessarily mean the virus stops spreading. Instead, the spread slows until after a point, there are fewer people every day getting infected. Put another way, immunity in the population reaches a level high enough that the spread of the disease declines and eventually stops, even if measures, such as masks and distancing, are no longer in use. This is when the virus is defeated. A population becomes immune in this sense not because everyone in the population gets the disease. Instead, only a certain fraction needs to be infected. This is the meaning, and power, of herd immunity.

But what is that certain fraction? That’s the vital question, of course. Through this pandemic, we’ve seen the number 70% mentioned several times, meaning herd immunity comes about when 70% of the population is infected. Let’s start there and crunch some numbers.

Assume that covid-19 continues to spread till 70% of India has been infected. That would mean about one billion Indians have the disease. Right now, India’s case fatality ratio (CFR) is just under 2.5%. That is, of the 1 million who have already been infected, 2.5%, or 25,000, have died. If we assume the same CFR holds till we touch that 70% mark, the disease will have killed 25 million Indians.

Take a few seconds to comprehend that number. Spread out over a year, that’s one covid death nearly every second. That’s better than twice as many deaths as we see in India in a “normal" year. That’s the entire city of Mumbai, wiped off the map. Sure, we might then have herd immunity, but 25 million dead is a hell of a price—an unacceptable price—to pay for it. Clearly, just waiting to arrive at this 70% mark, with the resultant death toll, is not a good corona-fighting strategy.

Yet, to beat back this virus, to get the economy chugging again, we have to achieve that herd immunity. Which is why scientists are looking into the question of whether we need to touch that 70% mark at all. Can we have herd immunity with a much lower infection rate, thus a lower death toll?

One study was led by Tom Britton, professor of mathematical statistics at the University of Stockholm. The researchers noted that populations are heterogeneous, and this “can significantly impact disease-induced immunity". Why so? For one, perhaps susceptibility to the disease is related to age. So, if two people of different ages meet, the chance of passing on the virus depends on their ages. For another, people have “different activity levels" — in short, some of us go out more than others, meet more people than others, and that affects how the virus spreads.

Britton’s team found ways to represent these factors mathematically in their analysis. They also allowed for the use of preventive measures, such as masks and distancing, “implemented early and lifted late in an outbreak". They found that all this would significantly reduce the infection rate needed for herd immunity: instead of 70%, just 43% (“A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2", Tom Britton, Frank Ball and Pieter Trapman, Science, 23 June 2020).

Interestingly, age was less of a factor in this reduction to 43% than the differing activity levels of people. Britton speculated elsewhere that “if there is a large variability of susceptibility among humans, then herd immunity could be as low as 20%" (“A New Understanding of Herd Immunity", The Atlantic, 13 July 2020).

But because he doesn’t believe susceptibility varies very much, he concludes that herd immunity happens at an infection rate “between 35% and 45%".

But another professor of mathematics and statistics, Gabriela Gomes of the University of Strathclyde in Scotland, thinks susceptibility does vary enough, and any immunity analysis should take it into account. At the start of the virus outbreak, she suggests: “The highly susceptible people are more likely to get infected first." (same article in The Atlantic, above). The result is that the average susceptibility of the population drops right from the beginning. In effect, this is a “selective depletion" of more susceptible people, and this itself works to slow the spread of the virus. This is why her analyses “keep coming back" with a herd immunity … wait for it … “less than 20%".

Of course these are only mathematical exercises. Yet they are instructive in what they say about how the pandemic will play out, about the toll it will take of us all. So if we opt for optimism — and why not? — and Gomes’ 20% figure, when will India reach herd immunity? At our current daily growth rate of 3.5%, it will take us about 160 days to get there, or to the end of 2020. Herd immunity, and perhaps even a corona vaccine, by the new year? That would be something. Personally, I’d love to see something similar for pyramid schemes.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun

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