The global coronavirus pandemic has raised questions about a phenomenon known as “herd immunity” and spurred hopes that it can help slow or end the outbreak. Herd immunity occurs when a large portion of a community – the herd – develops some degree of immunity to a virus, making the spread of a disease from person to person less likely. As a result, the whole community gains protection, not just those who are immune.

Evidence gathered so far by epidemiologists suggests that a person infected with COVID-19 passes the virus on to between two and three others, on average. Here’s what that looks like across seven generations of infection, and how immunity can disrupt the chain.

There are two pathways to herd immunity – natural infections or vaccines. It is still not clear whether natural infections alone will lead to widespread immunity; while most people who have had COVID-19 did develop antibodies, it is too early to know how much protection they offer and for how long. A vaccine can provide widespread immunity faster and more reliably.

The simulations below use a mathematical model to illustrate how the virus could spread at different rates through the same community, depending on levels of vaccination. The Reuters model reflects projections by experts that the COVID-19 vaccines currently in development will be around 70% effective, meaning they will protect 70% of vaccinated people from infection by the virus or from severe illness if they do become infected.

Each simulation comprises a community of 9,000 people, with individuals represented by squares. Each community has a different number of vaccinated individuals, before the same number of infected individuals is introduced.

The simulations employ key epidemiological parameters, such as the period of time a person is infectious, to demonstrate how the virus could spread. In each scenario, infected people have “contact” with other squares, who may or may not become infected. Each frame of the animation comprises a day.

There are some limitations in modelling real-life interactions. For instance, the model assumes each person will have the same number of contacts but in reality, some people are more social than others, which would affect how likely they are to spread the disease. There is also much that is still unknown about some of the epidemiological parameters of COVID-19, but the simulations encompass current knowledge and establish a fair comparison across the various vaccination scenarios.

Experts believe that if no other measures are taken, herd immunity could kick in when between 50% and 70% of a population gains immunity via vaccination.

“It depends on whether the vaccine has 100% efficacy, but the number most people are looking at (for herd immunity) is about 60-65%,” said Catherine Bennett, Epidemiology Chair in the Faculty of Health of Melbourne’s Deakin University.

To get a robust indication of when the herd immunity threshold is reached, Reuters ran 1,000 random simulations across each vaccination scenario. Here’s what that series of simulations shows.

Infections drop

dramatically

around here

Results of

thousands of

simulations

Infections drop

dramatically

around here

Results of thousands

of simulations

Infections drop

dramatically

around here

Results of

thousands of

simulations

### Balancing vaccine distribution

The way a vaccine is distributed has implications for its effectiveness. If it is shared unevenly within a community, for example if people in wealthy areas have greater access than those in poorer locations, that creates safe clusters but leaves large areas of susceptible people.

“We need to be sure that we spread the vaccine equitably through the population,” said Joel Miller, a senior lecturer in applied mathematics at La Trobe University in Melbourne, who uses mathematical models to help create government and non-profit organization policies for the control of infectious disease.

In the early stages of distributing a new vaccine, higher priority may be given to healthcare workers and other people on the front lines, or those considered most vulnerable, a process known as “targeted vaccination.” Miller said it is crucial that people who might be considered super spreaders, such as public transport workers, also receive the vaccine quickly.

“An ideal vaccination campaign will ensure that the vaccine goes to groups that are at highest risk but also those that are most responsible for spreading infection,” said Miller.

### Movement restrictions

The movement of people also has implications for the spread of a virus. The base Reuters model works on the assumption that a small percentage of people travel to communities outside their immediate surroundings.

In the chart below, we compare two populations: the first group has people who mix and travel widely and the second group has relatively static citizens. The difference in the speed of the spread of a virus is clear.

At lower vaccination levels, the number of people who end up infected is similar in both groups, but the spread is much slower in the static population, which keeps the number of cases at a manageable level for hospitals and healthcare providers. That scenario is reflected in the lockdown measures and travel restrictions imposed by many countries during the coronavirus pandemic to try to “flatten the curve.”

###### If one in four people travel

0 days

Even when a high percentage of the population is vaccinated, the number of infected people can be reduced further when people don’t travel around.

###### If one in four people travel

0% infected

###### If no one travels

0% infected

### Vaccination vs natural infection

Herd immunity can also be attained when a large number of people have had a disease and recover. However, the jury is still out on what kind of protection a natural infection with this new coronavirus provides, and certainly more people would die while waiting for the herd effect than if a vaccine was produced.

“The risk is not acceptable,” said Bennett. “We can’t afford to have people infected to reach herd immunity when we know so little about the longer term effects.”

### While we wait

There is currently no vaccine for COVID-19, although there are trials underway at different stages around the world. It usually takes several years for a vaccine to be identified, tested, produced, and finally reach the consumer market. Vaccine makers hope to dramatically compress that timeline for COVID-19 through faster trials and by manufacturing at scale even before the products have proved successful.

In the meantime, social distancing, wearing masks, hand hygiene and other interventions can reduce transmissions and contribute to creating the herd effect. The new coronavirus is spread primarily via droplets expelled when a person coughs or sneezes, and aerosol particles expelled when we talk.

The World Health Organization (WHO) says masks can be used as part of a comprehensive package of prevention and control measures that limit the spread of respiratory viral diseases. A study commissioned by the WHO and published in the Lancet in June said that wearing a mask can “result in a large reduction in risk of infection” from COVID-19.

If we apply the use of masks and/or social distancing to our earlier model, with no immunity, a slower spread can be seen. The point at which herd immunity kicks in can also be lowered.

###### With masks

###### Distancing between

some contacts

Same population size, more spread out

###### Masks and distancing

Same population size but more spread out

The overall goal is to reduce the effective reproduction rate of the virus to less than 1, at which point an outbreak would be subsiding as infected people transmit the virus to fewer than one other person on average.

Epidemiologists largely agree that a combination of vaccination and continued social responsibility measures like physical distancing will provide the strongest chance of achieving that goal. The combined approach is critical given early vaccines brought to the market will likely not have 100% efficacy.

“It’s about adding layers,” Bennett said. “It gives us extra protection from community spread. The situation is very much better in places where a combination of measures is being used.”

#### The model

Use the sliders to input your own parameters to the Reuters model and see a simulation of the spread.

#### Methodology

The simulations start by creating a predefined number of squares. Each square represents a person. It initializes the population with 5 infected individuals and a percentage of vaccinated individuals. Both the infected and vaccinated were chosen randomly. A percentage of the vaccinated individuals (100% - vaccine effectiveness) are randomly selected and marked susceptible. To explain: If the vaccine effectiveness is 70%, 30% of the vaccinated squares will be marked susceptible.

For the purpose of this illustrative simulation, every infected cell has “contact” with 8 immediate neighbours. A fraction of randomly selected cells also have an extra “long distance neighbour”. Such a consistent number of contacts may be unrealistic, but this ensures a fair comparison across various vaccination scenarios.

These neighbours can be infected, vaccinated, or susceptible.

The simulation runs for many “frames”. Each frame represents one day.

Initial parameters used are: R0 = 2.5, days of infectiousness = 7, transmissibility calculated using SIR formula.

The average rate of contact used in the formula is 8 because each infected cell has 8 neighbours.

Each day, the simulation runs for every infected cell. The infected cell is made to contact each of its 8 neighbours with the following conditions:

- if the neighbour is vaccinated or already infected, move on
- if the neighbour is infected, move on
- if the neighbour is susceptible, generate a random probability and check if it falls within transmissibility. If it does, then infect the neighbour. The “generation” of this neighbour is = generation of source + 1

A cell remains infected for the “Days of infectiousness” parameter above = 7 days, or 7 “frames” of the simulation. After 7 days, the cell is moved to the “removed” category.

#### Notes

The graphic which simulates the impact of wearing masks uses a risk reduction figure of 44% as stated in a study commissioned by the WHO and published in the Lancet in June.

### Sources

Reuters calculations; Dr Joel Miller, La Trobe University, Melbourne

By Manas Sharma and Simon Scarr

Writing by Jane Wardell

Additional reporting by Christine Soares

Editing by Tiffany Wu