Vaccination makes a big difference in achieving herd immunity


On recent Skype call with my grandmother, I brought up the subject of the rapidly arriving Covid-19 vaccines.
Advanced age brings wisdom, but it also brings a high risk of serious illness from coronavirus infection, so I wanted to get him to get an FDA-approved vaccine as soon as possible.

But while touting the benefits of the vaccination, I noticed a puckered forehead, a frown, and a look of uncertainty on his face. It took me by surprise. Surely someone who gets their flu shot every year and has raised two doctors shouldn’t feel anxious about getting the Covid vaccine. But she clearly was.


This conversation left me worried not only for his safety, but also for the safety of our country. If my grandmother was hesitant, millions of other Americans probably feel the same way. A nagging question came to my mind: if vaccine mistrust is rampant in our country, when can we achieve collective immunity and move on to a new normal?

Collective immunity protects people with vulnerable immune systems. Here’s how.

Herd immunity occurs when a critical mass of people become immune to a pathogen like SARS-CoV-2, the virus that causes Covid-19. With enough people immune to the virus, the chain of transmission is interrupted, providing indirect protection to people who are not immune.


Inspired by Dr Jacob E. Jones, a family physician at my hospital who made predictions about the time it would take to achieve herd immunity depending on vaccine uptake, I set out to answer my question with a model that uses the following variables and definitions:

The base playback name R0 (pronounced R-nothing). This number represents the degree of infection of a pathogen. A R0 out of 2 means that one person infected with SARS-CoV-2 is likely to infect two other people. Currently, most estimates of R0 are between 2.5 and 4. For the sake of this thought experiment, I assumed an R0 out of 4.

Baseline prevalence. This is the percentage of people who are immune to the virus at any given time, either by acquired infection or by vaccination.

Monthly infection rate. This is the percentage of people who are infected and gain immunity to the virus each month.

Using only the basic reproduction number, it is possible to calculate the percentage of people needed to achieve collective immunity:

Si R0 is 4, then 75% of the population must acquire immunity to the virus in order to stop transmission.

At the end of September, a Stanford study estimated that 9.3% of Americans had antibodies against SARS-CoV-2. Granted, antibody tests may suffer from low positive predictive value when the prevalence of infection is low, but this is the best estimate we have so far. I’ll use this as the baseline prevalence.

If the baseline prevalence at the end of September – eight months from the start of the epidemic in the United States on January 21, 2020 – was 9.3%, the coronavirus has an infection rate of around 1 , 2% of the population per month. This background calculation is consistent with estimates in the medical literature, with one study estimating 52.9 million infections in the United States from February 27 to September 30, or an infection rate of 1.3% per month.

Using the herd immunity threshold, baseline prevalence and monthly infection rate, it is possible to calculate the number of months (m) to obtain collective immunity:

If the virus spreads at its current rate without a vaccine, it would take 55 months from October 2020 to gain herd immunity. This means May 2025. Even though I had assumed an R0 out of 3, it would take another 48 months to achieve collective immunity.

This white-fisted approach would consist of several years of misery, morbidity and mortality, not to mention persistent economic hardship.

Thanks to a miraculous feat of science, we have a shortcut to herd immunity: two vaccines with over 90% effectiveness, and maybe more along the way. Infectious disease expert Dr Anthony Fauci predicted that Covid-19 vaccines, one of which is being rolled out to frontline healthcare workers this week, should be widely available to the public by April 2021.

For the sake of simplicity, I’m going to skip the phased rollout and imagine that all Americans have a choice to get vaccinated in April. Since the two candidate vaccines are a series of two injections three to four weeks apart, it may take at least an additional month to achieve full immunity. At this point, in May 2021, the baseline prevalence of infection will be 17.7% (1.2% per month from October 2020, when the baseline prevalence was 9.3%).

We’re Almost There: Call Percent of Americans Who Get Vaccinated Pv and considering that 90% of people vaccinated will develop immunity, here is an equation for an estimate of herd immunity time from May 2021, using 39% as Pv – percentage of Americans who said they would receive a vaccine in an NBC News poll:

With just 39% of Americans receiving a government-approved vaccine, the collective immunity deadline is 19 months, or December 2022.

Nineteen months is not a walk in the park. While 17.7% of Americans are already immunized in May and 39% more would easily get a Covid-19 vaccine, that leaves around 43% of the population vulnerable to infection but skeptical about vaccination.

Convince roughly half of those skeptical Americans to take the hit, stimulating Pv to 60.7%, reduces the collective immunity period to two months, i.e. July 2021.

To convince a few more, to reach a critical mass of 63.7%, that would allow us to achieve collective immunity as soon as the second wave of vaccinations is over.

Scenario Collective immunity obtained
No vaccine May 2025
Low confidence in a vaccine (39% get vaccinated by May 2021) December 2022
Average confidence in a vaccine (61% get vaccinated by May 2021) July 2021
High confidence in a vaccine (64% get vaccinated by May 2021) May 2021

This model, like any model, makes assumptions. The first is that the coronavirus does not mutate. If it behaves like the flu and other coronaviruses and begins to accumulate minor mutations (a phenomenon called antigenic drift), then the virus might require annual immunizations to cover new strains, similar to influenza. This scenario would likely result in an endemic (baseline) infection level in the population.

Another hypothesis is that the anti-coronavirus antibodies last a long time. If the antibodies from natural infection or immunization only last six or 12 months, booster injections will be needed to maintain immunity.

Finally, these scenarios assume an ideal situation where all those vulnerable to the disease are identified and are offered the vaccine at the same time.

The purpose of this brainstorming experiment is to highlight the immense power of vaccines and the impetus to immunize. In the age of disinformation, it may not be enough to debunk myths and simply provide people with facts. Traditional methods of vaccine promotion can have paradoxical effects.

A large study looked at the effects of healthcare professionals trying to promote the measles, mumps, and rubella (MMR) vaccine in children among parents who are skeptical of the vaccination. Educational interventions, ranging from debunking myths (such as the link between MMR and autism), to teaching the dangers of measles, mumps and rubella have all made anti-vaccine parents. less likely immunize their children.

Meanwhile, after enacting stricter vaccine laws following a measles outbreak in 2014, MMR vaccine rates in California have rebounded to the critical threshold for herd immunity.

There is an arsenal of robust vaccine policies that can accelerate herd immunity: financial incentives, limits on personal or philosophical exemptions, and mandatory requirements for businesses and schools (once a children’s vaccine is approved).

My grandmother was less moved by my equations and statistics than by my constant concern for her health. After weeks of pushing her in the right direction, she’s now more open to shooting, but still hasn’t completely decided if she’ll get it when her turn comes.

Not all vaccine skeptics have a family doctor to guide them. Most do not personally know someone who works in a hospital who can describe the horror and devastation this virus has caused.

To beat this virus quickly, we need to embrace politics rather than persuasion.

Zach Nayer is a transitional resident physician at Riverside Regional Medical Center in Newport News, Va., And a new ophthalmology resident at the Harkness Eye Institute at Columbia University in New York.


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