By Charles Nicolson

My previous article was a qualitative description of infections due to coronaviruses and described one of the methods used for creating herd immunity.

The method I discussed was simply to let the coronavirus run its course and allow people to return to their normal daily living while implementing precautions to protect those at higher risk levels. Specialist epidemiologists no longer even consider this type of approach because it has led to unacceptably high loss of life without speeding up the return of society to normal.

Another document described in a recent ‘Getting Technical’ article was the Great Barrington Declaration which recommends that people at lower risk of severe Covid-19 return to normal life thereby allowing SARS-CoV-2 to spread to a sufficient level to give Herd Immunity.

People at high risk, such as elderly people, it says, could be protected through measures that are largely unspecified. The writers of the declaration received an audience in the White House and sparked a counter memorandum from another group of scientists in The Lancet, which called the herd immunity approach a “dangerous fallacy unsupported by scientific evidence.”

Public-health experts do not support herd immunity being used when vaccines are not available. Marcel Salathé, an epidemiologist at the Swiss Federal Institute of Technology in Lausanne says, “I’m a bit puzzled that it’s now used to mean how many people need to get infected before this thing stops.”

Epidemiologists can calculate the approximate percentage of a population required for herd immunity to arise. This percentage depends on a reproduction number designated as R0, which is the number of cases likely to result from one infected individual in a normal, well-mixed population, according to Kin On Kwok, an infectious-disease epidemiologist and mathematical modeller at the University of Hong Kong.

The herd-immunity threshold is 1–1/R, therefore, as more people become infected by each individual who has the virus, the higher the percentage of the population needs to be immune to achieve herd immunity.

Looking at an example of a more commonly known disease, measles, which is highly infectious to normal well-mixed populations, the R0 is between 12 and 18 which calculates to a herd-immunity threshold of over 90% of the population.

The R0 assumes that everyone is susceptible to the virus. However, a variation of R0 called the R effective (abbreviated Rt or Re) is more commonly used in calculations because it allows for changes in susceptibility within the population being considered.

The formula 1–1/R0 produces a theoretical number for herd immunity but this is not a specifically defined point but rather a factor similar to a gradient, according to Gypsyamber D’Souza, an epidemiologist at Johns Hopkins University in Baltimore, Maryland, and, because variables can change (including R) as well as the number of people susceptible to a virus; herd immunity is not a steady state.

When herd immunity has been attained across a population it is still possible to have large outbreaks particularly in areas where vaccination rates are low. “We’ve seen that play out in certain countries where misinformation about vaccine safety has spread,” the epidemiologist Salathé says. “In local pockets, you start to see a drop-in vaccination, and then you can have local outbreaks which can be very large, even though technically the level for herd immunity had been reached according to the calculations.” The practical goal is to prevent people from becoming unwell rather than to attain a theoretical number in a model.

The other related question is “How high is the threshold for SARS-CoV-2?”

Reaching herd immunity depends to a greater or lesser extent on what is actually happening in the population. Kwok and his team have estimated the Rt in more than 30 countries, using data on the daily number of new Covid-19 cases as from March 2020. They then used these values to calculate a threshold for herd immunity in the population of each country.

The numbers ranged from as high as 85% in Bahrain, where the Rt had been determined at 6.64, to as low as 5.66% in Kuwait, where the Rt was measured at 1.06. Kuwait’s low numbers showed how it was putting in place effective measures to control the virus, such as establishing local curfews and banning commercial flights from many countries. If the country stopped those measures, Kwok says, the herd-immunity threshold would go way up.

Herd-immunity calculations such as the ones in Kwok’s example are built on assumptions that might not reflect real life according to Samuel Scarpino, a network scientist studying infectious disease at North-eastern University in Boston, Massachusetts. “Most of the herd-immunity calculations do not have anything at all to say about behaviour. They assume there are no interventions or changes in behaviour or anything like that,” he says. This means that if a change in people’s behaviour (such as physical distancing) drives the Rt down, then “as soon as that behaviour goes back to normal, the herd-immunity threshold will follow that change”.

Estimates of the threshold for SARS-CoV-2 range from 10% to 70%, or even more but models that calculate numbers at the lower end of that range rely on assumptions about how people interact in social networks that might not hold true, According to Scarpino. low-end estimates assume that people with many contacts will get infected first, and because they have a large number of contacts, they will spread the virus to more people.

Scarpino refers to these people as ‘super spreaders’. He goes on to say that as more people gain immunity to the virus, the transmission chains among those who are still susceptible are greatly reduced and therefore “as a result of that, you very quickly get to the herd-immunity threshold”. However, these types of situations are seldom simple and straightforward. If it turns out that anybody could become a super spreader, then “those assumptions that people are relying on to get the estimates down to around 20% or 30% are just not accurate,” Scarpino explains.

The result is that the herd-immunity threshold will be closer to 60–70%, which is closer to what has generally been found to occur.