The hard math of collective immunity to Covid-19 (2023)

While many things about the Covid-19 pandemic remain uncertain, we do know how it will likely end: when the spread of the virus begins to slow (and eventually stop altogether) because enough people have developed immunity to it. By then, people had developed "herd immunity," either from vaccines or people contracting the disease.

"Once the level of immunity crosses a certain threshold, the epidemic starts to die down because there are not enough new people to get infected," he said.Natalia DeanUniversity of Florida.

While determining the threshold for Covid-19 is crucial, there are many nuances involved in calculating exactly how much of the population must be immune for herd immunity to be effective and protect those who are not.

At first glance, it seems simple. The only thing you need to know is how many people each infected person infects on average. This value is called R0(pronounced "R nothing"). Once you have it, you can connect it to a simpleFormula for calculating herd immunity threshold: 1 - 1/R0.

just say R0The rate of infection with the COVID-19 virus is 2.5, which means that each infected person infects two and a half other people on average (usual estimate). In this case, the threshold of collective immunity to Covid-19 is 0.6 or 60%. This means that the virus will spread at an accelerated rate until an average of 60% of the population in different places is immune.

At this point, the virus will continue to spread, but at a slower rate until it stops completely. Just like a car doesn't stop when you let off the gas, the virus doesn't go away when you achieve herd immunity.

"You can imagine that when 60 percent of the population is infected, the number of infections will start to decrease. But when the disease starts to subside, it is likely that another 20 percent will be infected."Joel MillerLa Trobe University in Australia.

This 60% is also the threshold at which new virus inputs—for example, an infected passenger disembarking from a cruise ship at a healthy port with herd immunity—will soon disappear.

"That doesn't mean you can't start a fire at all, but the outbreak will subside," he said.Kate LongvigVirginia Tech and State University.

However, things can get complicated quickly. Herd immunity thresholds depend on how many people each infected person actually infects—and that number can vary by location. The average infected person in an apartment building can infect more people than the average infected person in a rural area. So, while r0A value of 2.5 for Covid-19 may be a reasonable figure for the whole world, but it will almost certainly vary widely locally, with the average much higher in some places, much higher in others, and much higher in some places further down. This means that the collective immunity threshold will also be higher than 60% in some places, and lower in others.

"I think the range of R0The data on Covid-19 is bigger than most people think," he saysMarek LipsitchThe Harvard professor advises health officials in Massachusetts and abroad. He cites data suggesting that in some urban areas that number could be more than double the overall US average.

just like r0It turns out that this is a variable, not a static number, and that people acquire immunity in different ways, which has important implications when calculating herd immunity thresholds.

Typically, researchers consider herd immunity only in the context of vaccination campaigns, many of which assume that every person has the same risk of infection and disease transmission. But this is not necessarily the case with naturally transmitted infections. Differences in social behavior make some people more susceptible to certain diseases than others. Biological differences also affect the likelihood of human infection.

"We are all born different, and as we go through different experiences, those differences add up," she saysGabriela GomezProfessor at the University of Strathclyde in Scotland. "It affects people's ability to fight the virus."

Epidemiologists call these differences "heterogeneity of susceptibility," meaning the differences that make certain individuals more or less susceptible to infection.

But it is too detailed for a vaccination campaign. "Vaccine distribution in the population often doesn't take into account the number of contacts between people or their vulnerability because we don't know that," she said.Virginia PitzerYale School of Public Health. Instead, health officials took a maximalist approach, essentially vaccinating everyone.

However, given the ongoing pandemic, there is no guarantee that a vaccine will be available anytime soon, and the heterogeneity of susceptibility has real implications for herd immunity thresholds for disease.

In some cases, it raises the bar even higher. The same may apply to places such as nursing homes, where the average person may be more susceptible to Covid-19 than the average person in the general population.

However, at a broader level, heterogeneity often lowers herd immunity thresholds. The virus first infects susceptible people and spreads rapidly. But in order for the virus to spread further, it must be transmitted to people who are less susceptible to infection. This makes it difficult for the virus to spread, so the outbreak develops more slowly than you would expect based on the initial growth rate.

"The first person is likely to infect the most susceptible in the beginning, while in the second half of the outbreak the less susceptible will be infected, which means that the infection can be caught sooner than you expect. Eliminate," Lipsitch said.

estimated heterogeneity

So how much lower is the threshold for herd immunity when we're talking about a virus circulating in the wild, such as the current pandemic?

According to standard models, approximately 60% of the US population would need to be vaccinated against or recover from Covid-19 to slow and eventually stop the spread of the disease. However, many experts I spoke to suspected that the herd immunity threshold for naturally acquired immunity was lower.

"I would guess it's probably somewhere between 40% and 50%," Pitzer said.

Lipsitch agrees: "If I had to guess, I'd probably say it's about 50 percent."

These are mostly knowledge-based estimates because it is difficult to quantify what makes one person more susceptible to disease than another. Many of the traits you think you want to attribute to someone—for example, the degree of social distancing—can change from week to week.

“The whole question of heterogeneity is only important if the source of the heterogeneity is a long-term characteristic of the person. If it's in a bar, that alone is not enough to be a permanent source of heterogeneity," explains Lipsitch.

Heterogeneity can be difficult to quantify, but is also an important factor in establishing herd immunity thresholds. Langwig believes the epidemiological community is not doing enough to correct its mistakes.

"We were a little messy thinking about herd immunity," she said. "This variability is important and we need a better understanding of herd immunity thresholds."

This has been attempted in some recent publications. June magazinescience PublishedOne study, which included moderate heterogeneity, estimated the threshold for herd immunity to Covid-19 in the general population to be 43%. But one of the study's co-authors,Toma BrittonaThe researchers from Stockholm University claim that their model does not yet take into account other sources of heterogeneity.

"In any case, I think the difference is larger, so in reality the level of herd immunity is probably a little lower than 43 percent," Britton said.

the restnew researchA different approach was used to assess differences in susceptibility to Covid-19 and establish a lower threshold for herd immunity. Ten authors of the paper, including Gomes and Langwig, estimate that the threshold for naturally acquired collective immunity to Covid-19 could be only 20% of the population. If so, the world's worst-hit region could be just around the corner.

"We concluded that herd immunity could emerge in the hardest-hit areas, such as Madrid," Gomez said. An earlier version of the article was published in May, and the authors are currently working on an updated version, which is expected to be published soon. I will post. This publication will include herd immunity estimates for Spain, Portugal, Belgium and England.

However, many experts consider the new research - not all of which is peer-reviewed - unreliable.

wtopic on TwitterIn May, Dean stressed that there was too much uncertainty in the fundamental aspects of the disease because of the different R values0Impact of relaxing social distancing in different locations - while maintaining accurate herd immunity thresholds. This threshold can be a single number as long as many people wear masks and avoid large gatherings, or a higher number if people give in.

Other epidemiologists are also skeptical of such a small number.Jeffrey SumanaAccording to a Columbia University professor, 20 percent herd immunity “is not compatible with other respiratory viruses. Not compatible with influenza. So why would one respiratory virus behave differently than another? I do not understand".

Miller added: "I believe the herd immunity threshold for [naturally acquired immunity] is below 60%, but I don't see clear evidence that anything [the site] comes close to."

Ultimately, the only viable way out of the Covid-19 pandemic is to achieve mass herd immunity everywhere, not just in the few places with the highest infection rates. And that will only be possible when the vaccine becomes widely available.

At the same time, in order to prevent the spread of the virus and reduce the risk of infection with R0Regardless of where you set the herd immunity threshold, social distancing, mask wearing, testing and contact tracing are routine around the world.

"If I had known that the herd immunity was where I think it was, which is 40-60%, I can't think of a decision I would have made differently now," Lipsitch said.

Shaman also argues that uncertainty about thresholds for naturally acquired herd immunity, along with the consequences of getting the threshold wrong, leaves only one way forward: to do everything we can to prevent new cases until we introduce a vaccine that will surely achieve herd immunity.

"The question is, can New York City withstand another outbreak?" - He said. - I don't know, but let's stop playing with fire.

This article was reproduced inA network of connectionsandSpectral grid.


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