The Tricky Math of Herd Immunity for Covid-19

“It doesn’t mean you won’t be able to start a fire at all, but that outbreak is going to die,” said Kate Langwig of Virginia Polytechnic Institute and State University.

However, things quickly get complicated. The herd immunity threshold depends on how many people each infected person actually infects—a number that can vary by location. The average infected person in an apartment building may infect many more people than the average infected person in a rural setting. So while an R0 of 2.5 for Covid-19 may be a reasonable number for the whole world, it will almost certainly vary considerably on a more local level, averaging much higher in some places and lower in others. This means that the herd immunity threshold will also be higher than 60 percent in some places and lower in others.

“I think the range of R0 consistent with data for Covid-19 is larger than most people give credit to,” said Marc Lipsitch of Harvard University, who has been advising health officials in Massachusetts and abroad. He cited data indicating it could be more than twice as high in some urban settings as the overall US average.

And just as R0 turns out to be a variable, and not a static number, the way people acquire their immunity also varies, with important implications for calculating that herd immunity threshold.

Usually, researchers only think about herd immunity in the context of vaccine campaigns, many of which assume that everyone is equally likely to contract and spread a disease. But in a naturally spreading infection, that’s not necessarily the case. Differences in social behaviors lead some people to have more exposure to a disease than others. Biological differences also play a role in how likely people are to get infected.

Gabriela Gomes of the University of Strathclyde in Scotland studies how biological and behavioral differences can affect the spread of a virus. She concludes some parts of the world may already be close to reaching herd immunity.Courtesy of Gabriela Gomes
“We are born different, and then these differences accumulate as we live different experiences,” said Gabriela Gomes of the University of Strathclyde in Scotland. “This affects how able people are to fight a virus.”

Epidemiologists refer to these variations as the “heterogeneity of susceptibility,” meaning the differences that cause some people to be more or less likely to get infected.

But this is too much nuance for vaccination campaigns. “Vaccines are generally not distributed in a population with respect to how many contacts people have or how susceptible they are, because we don’t know that,” said Virginia Pitzer of the Yale School of Public Health. Instead, health officials take a maximalist approach and, in essence, vaccinate everyone.

However, in an ongoing pandemic with no guarantee that a vaccine will be available anytime soon, the heterogeneity of susceptibility has real implications for the disease’s herd immunity threshold.

In some cases it will make the threshold higher. This could be true in places like nursing homes, where the average person might be more susceptible to Covid-19 than the average person in the broader population.

But on a larger scale, heterogeneity typically lowers the herd immunity threshold. At first the virus infects people who are more susceptible and spreads quickly. But to keep spreading, the virus has to move on to people who are less susceptible. This makes it harder for the virus to spread, so the epidemic grows more slowly than you might have anticipated based on its initial rate of growth.

“The first person is going to be likely to infect the people who are most susceptible to begin with, leaving the people who are less susceptible toward the latter half of the epidemic, meaning the infection could be eliminated sooner than you’d expect,” Lipsitch said.Estimating Heterogeneity

So how much lower is the herd immunity threshold when you’re talking about a virus spreading in the wild, like the current pandemic?