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Nitya Nigam Although there are many things we don’t know about COVID-19, there is one thing we do know: the pandemic will only end once enough people are immune to the virus, causing its spread to slow and eventually stop. At this point, whether immunity is obtained through people being infected or vaccinated, the population will have developed “herd immunity”. This threshold is an important figure to consider, since it informs decisions about how many vaccines need to be produced and when places can lift lockdowns and reopen. However, calculating this threshold is a complex process. To understand how we get to the herd immunity threshold, we need to derive an equation. If you’ve been reading about COVID-19, or know about the spread of disease, you should be familiar with the term R0, which refers to the average number of people infected by one infected person. R0 acts as a measure of how quickly a disease can spread. If R0 is 1, then the spread of infection follows a linear track - each infected person infects one more, who can only infect one other person, and so on. However, if R0 is larger than 1, the spread quickly becomes exponential. If R0 is 2, then the first patient can infect two other people, who can each infect two more causing 4 infections, then 8, then 16 and so forth. Therefore, our goal with herd immunity is to bring the number of people infected by a single patient down to 1, or even less. Say you are infected with COVID-19, and have a population of 10 people that you interact with. If we set R0 to be 2, then two of the 10 people get infected. This means that the chance of somebody getting infected is 20%. However, if five of your friends are vaccinated or have already had COVID-19, they would be immune to the disease. This means that there are only five remaining friends who could fall sick. The same probability of 20% applies to them, so only 0.2*5 = 1 of them will be infected. We can generalise this process for any value of R0. If we assume that each infected person comes into contact with N people in each time period (usually a day), then we can expect R0/N people to be infected on average. If there are immune people in the population (we can call this number I), then the number of new infections can be represented by the following expression: We want this to equal 1, so we have the equation: We want to solve this for I/N, which represents the proportion of the population that needs to be immune. Rearranging for this gives So our formula for the herd immunity threshold is just 1-(1/R0). However, finding an R0 value is more difficult than it may seem. R0 values can vary hugely by location - urban areas can have R0 values more than twice as high as country averages. There are also biological differences between people that can make them more likely to get infected. These biological variations, which are results of both genetic makeup and environmental factors, are referred to by epidemiologists as the “heterogeneity of susceptibility”. For example, R0 values would be much higher in places like nursing homes, where elderly people are far likelier to fall ill. On a broad scale though, heterogeneity tends to lower the herd immunity threshold. At first, the virus will spread to people who are more susceptible, but once most of these susceptible individuals are infected, the spread of the virus will slow.
There is disagreement in the scientific community regarding what the herd immunity threshold for COVID-19 really is. Standard models indicate that 60% of the US population would need to be vaccinated for herd immunity to be achieved, but some experts place the value between 40% and 50%. Another (non-peer-reviewed) study done in May suggests that the value could be as low as 20%. While the scientists debate, however, the best thing to do is prevent the spread of the virus and decrease the R0 value as far as possible. Social distancing, mask-wearing and widespread testing are our best bets to keep people safe and healthy until vaccines are widely available.
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