Special Reports:

COVID-19 vaccines

< Back to special reports

The first batch of COVID vaccines touched down in South Africa in February 2021. Health workers were the first to get a jab under the Sisonke study. But even before the country had bought any jabs, our reporters were writing about the logistics and the politics of the project. If you want to know how well the vaccines work, how the different jabs compare or what it takes to create a vaccine from research, to regulation, to rollout, you’re at the right place.

HomeArticlesEnding a pandemic: How to calculate how many people need to get...

Ending a pandemic: How to calculate how many people need to get vaccinated

  • Each COVID vaccine offers a different level of protection — this means that the number of people who need to be vaccinated in order to stop COVID from spreading in the country depends on which jab is used.
  • New variants that spread faster than the original coronavirus have emerged around the world. These more infectious versions of the virus influence the amount of protection needed within a population.
  • South Africa is currently aiming to vaccinate 67% of its population to achieve herd immunity — but here’s why the answer isn’t that simple.

South Africa’s national vaccine roll-out is underway — albeit on a considerably smaller scale than initially planned. We are just over a month into the Sisonke implementation trial which is immunising healthcare workers with the Johnson & Johnson vaccine and South Africa’s medicine regulatory body recently granted emergency approval for Pfizer’s jab.

But even as we ramp up vaccination efforts, the limited availability of stock means that the end of COVID is not yet in sight.

At the start of the year, the health department unveiled their plan to vaccinate 40-million South Africans as part of a three-phase roll-out. They said 67% of the population would need to be vaccinated in order to achieve herd immunity.

But what does that mean — and how did they get to that figure? We break down the key concepts and explain why the numbers aren’t as straightforward as they seem.

What is herd immunity?

Herd immunity means that enough people are protected from a disease, such as COVID-19, to the point where that illness can no longer spread within a population.

Let’s take a step back.

Before getting into population-level immunity, here’s what it means for a person to be protected from a disease.

When you get sick, your body tries to fight off whatever germ has infected you. It does this through something called an immune response.

There are two parts to this response.

The first involves B cells, which produce specialised proteins called antibodies. These antibodies are tailored towards a particular germ. In other words, this is not a one size fits all approach and the antibodies for each infectious agent, or pathogen, are different.

The second part of our bodies’ immune response involves T cells. There are helper T cells, also known as CD4 cells, which help the B cells make antibodies and also help our bodies to make killer cells. The killer cells destroy the cells in your body that have been infected.

Antibodies and T cells work to provide someone with immunity to a disease so that they can no longer fall ill with the disease. You can either achieve this protection naturally (so if you have been infected with the virus and recovered) or through vaccination (which will trigger an immune response without you having to get infected).

But this immunity applies to an individual; herd immunity operates at a wider level. Because not everyone in a country can achieve the same level of protection — either because not everyone will get exposed to the virus (to get natural immunity) or there are not enough vaccines available —  scientists can calculate what proportion of the population needs to have immunity in order to stop a virus from spreading and posing a risk to everyone.

This doesn’t mean that the virus disappears overnight — and the proportion of a population required to have immunity to achieve herd immunity is different for each disease.

“It’s not that as soon as you reach herd immunity in an ongoing epidemic, that then the pathogen goes away, or that it’s gone”, says Juliet Pulliam, director of the South African Centre for Epidemiological Modelling and Analysis (Sacema). ”It’s that the epidemic turns over and you still usually have about half the epidemic to get through before it goes away.”

So what proportion of South Africans need to be protected for the country to reach herd immunity for COVID-19?

The short answer: We don’t yet know the exact figure. But it is estimated that 60-70% of South Africa’s population would need to have immunity in order to reach the threshold (the point at which the virus is no longer spreading). Some scientists, however, believe the threshold needed is actually much higher.

For the long answer, let’s break down the maths behind the calculation.

Herd immunity is calculated based on something called the basic reproductive number of a virus, or R0. This number represents how many people get infected from one person who already has the virus.

The goal is to get the reproductive number below 1, meaning that each person infected is not likely to spread the disease to anyone else. This way the virus can be contained and will no longer be spreading within a population.

In the case of SARS-CoV-2 — the coronavirus which causes the disease COVID-19 — it is estimated that for every one person infected, they will spread the virus to between two to three others. According to a systematic review published in PLOS One in November 2020, “the average estimated reproductive number was 2.87; which is higher than the World Health Organisation’s estimate of 1.4 to 2.5”.

But using this reproductive number comes with a catch — transmission of the virus can vary widely depending on the environment in which a germ spreads and this basic number only applies to a population that has no immunity or protection. So, observing safety measures like wearing a mask, physical distancing and washing hands could reduce the risk of more people getting infected and lower the rate at which people get infected.

“If half of your population is immune, then you would expect on average that somebody’s going to create two infections, but if three-quarters of the population is immune, then on average you are going to expect them to create one infection,” explains Pulliam.

So an alternative number that could be used to calculate herd immunity is the effective reproductive number, or Rt. This number is thought to be more representative of how the virus is actually spreading within a community as it changes to take into account steps that could reduce people’s risk, such as if a portion of the population is vaccinated.

To work out the percentage of protection needed, you subtract one from the reproductive number and then divide that by the reproductive number.

So if we use the highest estimate, which is a reproductive number of three for COVID, then the calculation becomes two divided by three — which is how you reach a herd immunity level of 67%.

Here’s a step by step breakdown of how you work it out:

  • First, you take the reproductive number: That’s 3.
  • Then you take that reproductive number of 3 and subtract one. This leaves you with 2.
  • You then divide 2 by the reproductive number, 3.
  • That gives you a fraction of 2/3.
  • You then multiply this fraction by 100 to get 67%.
  • And voilà, your threshold for herd immunity is 67%.

But because viruses evolve over time and new variants then emerge as a result of that, their reproductive value doesn’t stay the same. In the case of COVID, new variants, such as the 501Y.V2 variant that was first identified in South Africa, and the B.1.1.7 variant first identified in the United Kingdom, are more infectious than the original form of the virus — so they spread faster.

A January preprint on medRxiv found that the B.1.1.7 variant could be spreading between 40% and 75% faster than the original virus. Preliminary modelling shared in a more recent preprint by the CCMID on 11 January, suggests a similar increased transmissibility of around 50% in the 501Y.V2 variant in South Africa.

This means that these new variants are likely to have a higher reproductive number therefore increasing the population-level or herd immunity needed.

Why don’t we just let people get infected with SARS-CoV-2 and wait until South Africa has achieved herd immunity in a natural way?

Well, partly because it would take a long time for enough people to get infected and would also mean many people would die as a result of the disease.

Another reason, which is particularly important when it comes to South Africa’s epidemic is the emergence of new variants.

The 501Y.V2 variant is now dominant in South Africa — meaning most new infections that occur are as a result of this variant. In addition to being more transmissible, this variant can also evade antibodies produced in response to the original version of the virus. So if someone has previously been infected with SARS-CoV-2, they can still be re-infected with the variant.

Earlier this year, the South African National Blood Service tested blood donations collected in January (following the country’s second wave). They wanted to see if there were SARS-CoV-2 antibodies present in the samples. This would tell them if someone had previously been infected with the virus. In a preprint study shared on 12 February, they shared data collected from 4 858 donors across four provinces — at the time the paper was published South Africa had reported 1 491 807 COVID cases.

Using this portion of samples, the researchers then calculated what proportion of the population in that particular province was likely to have been infected with the virus since the start of the epidemic. For example, their analysis of the 1 457 samples collected and tested from the Eastern Cape estimated that roughly 63% of people had already been infected — which is at least eight times greater than the number officially recorded at the time.

While this data is just an estimate, if we use that figure then the Eastern Cape would be quite close to achieving herd immunity. But these antibodies won’t be able to offer enough protection against the new variant — making vaccinations even more important to help stop the spread of the virus.

Choosing a vaccine — why is it not as simple as vaccinating 67% of the population?

Achieving herd immunity through vaccination isn’t as simple as just trying to reach two-thirds of the population. When you’re going for immunity through infection, then every case reported represents a person with immunity. So if 67% of a country’s population has been infected then the entire 67% will have immunity.

Vaccines, however, are a different story.

That’s because getting a jab doesn’t automatically secure protection from the virus. This is where the efficacy of a vaccine comes in. Vaccine efficacy provides an indication of what someone’s risk is of getting infected post-immunisation.

For example, Pfizer was one of the first COVID jabs to release its efficacy results of 95%. This doesn’t mean that 95% of people are protected in a population with the vaccine. Rather, this number shows how much the jab is able to reduce your risk of getting infected. So those that received the vaccine were 95% less likely to get COVID than those who didn’t get the shot.

But the efficacy of jabs differ — Pfizer offers one of the highest levels of protection. Because of this, the proportion of a population that needs to be vaccinated against COVID so that the disease no longer spreads (so that herd immunity is achieved) is different for each vaccine.

The Lancet published a paper in November 2020 estimating that even with a vaccine efficacy of 80%, you would still need to immunise between 75 to 90% of a population — and lower efficacies would require vaccinating the entire population.

This percentage is dependent on how the virus is spreading in a particular place, so it could be lower or higher depending on the country. Another catch to this estimate is that we don’t yet know how long protection provided by vaccines lasts — the Lancet’s calculation is based on the assumption that natural immunity wanes over one to two years.

As chair of the ministerial advisory committee on COVID vaccines Barry Schoub explains, if you have a vaccine efficacy of 80% and you’re aiming to reach 70% of the population then you need to multiply the two figures to get your immunity coverage.

In this case, 80% multiplied by 70% would get you to 56% immunity in a population, meaning there would still be a gap of around 11% needed to reach the herd immunity threshold.

How many people does South Africa need to vaccinate?

Let’s get into the specifics of how different vaccines would impact national roll-out plans.

South Africa has secured doses of the Johnson & Johnson vaccine along with the Pfizer jab, which recently received emergency use approval from the South African Health Products Regulatory Authority (Sahpra).

The Johnson & Johnson vaccine initially announced an efficacy of 57% in South Africa, where the majority of cases were as a result of the 501Y.V2 variant. A new analysis shared by the United States Food and Drug Administration on 26 February, shows that the jab actually has a higher efficacy of 64% in South Africa.

So with South Africa’s plan to immunise 67% of the population, the Johnson & Johnson vaccine would give you a population immunity level of 43%.

The Pfizer vaccine, which will also be used for South Africa’s roll-out, has a 95% efficacy, as previously mentioned. The Pfizer jab would therefore provide roughly 64% immunity with our current target of vaccinating two-thirds of the population — but we don’t yet have trial data on how the vaccine performs against the new variant identified in the country. Lab studies, however, indicate that the 501Y.V2 variant could lower the Pfizer jab’s efficacy (as was seen with Johnson & Johnson), which means the immunity provided on a population level is likely to be lower than 64% in South Africa.

Vaccination alone won’t guarantee the end of the pandemic but we have the ability to reduce the spread of the virus locally, explains Schoub.

“The answer then is human behaviour will also have to contribute,” he says. The use of safety measures like washing hands and physical distancing can reduce the spread of the virus and bring South Africa’s reproductive number low enough that we could reach herd immunity through vaccination.”

Aisha Abdool Karim was a senior health reporter at Bhekisisa from 2020 to 2022.