If you have been following the news, you have no doubt heard about herd immunity as a possible solution to the coronavirus problem. The thought is that once enough people have contracted COVID-19, we will have herd immunity and therefore we will not need to worry about a repeat of the current pandemic.
In this post, I would like to explain what herd immunity is and what it does and does not mean for the fight against COVID-19.
So what is herd immunity? It is the notion that once enough people within a population are immune to a disease then the population as a whole is no longer susceptible to a large outbreak. To illustrate why this is the case, let’s take a look at the math (don’t worry this won’t involve anything beyond understanding proportionality). In the SIR model (the starting point for most epidemiological models), the number of people who get infected is described by the equation
This equation says that the rate of change for the number of infected people (the left hand side of the equation) is proportional to the number of people that are already infected and a growth factor (the thing multiplied by I in the equation) that is related to the number of people who are susceptible (S), the size of the population (N), and the basic reproduction ratio (R0, which accounts for the recovery rate, the transmission probability and the contact rate between individuals). If this growth factor is positive, then the number of people who are sick will grow over time, but if it is negative, then it will shrink.
In the early stages of an epidemic caused by a novel virus, the entire population is susceptible (S=N), so this quantity is positive whenever the basic reproduction ratio is greater than 1. However, as the infection spreads, the susceptible population is depleted, and this quantity gets smaller and smaller. If the outbreak is allowed to run its course, then the number of susceptible people will eventually become small enough that the growth factor becomes negative. At that point, the number of infected people will begin to decrease. Herd immunity is acquired when this quantity switches from positive to negative.
So what does that mean for COVID-19? Here are few things you should know:
1. Depending on the true infectiousness of the virus, we will need somewhere between 50% and 70% of the population to have immunity (assuming R0 is somewhere between 2 and 3.3). You can calculate this by noting that the expression in parenthesis is positive as long as S>N/R0.
2. Herd immunity does not mean that you no longer have to worry about getting sick. People will continue to get sick as long as there are still infected and susceptible people interacting. However, it does mean that the number of people who are getting better will exceed the number who are getting sick.
3. Herd immunity does not mean that the epidemic is over. During severe outbreaks, a substantial number of people are infected AFTER the herd immunity point is reached.
4. Herd immunity does mean that once the outbreak is over, you don’t have to worry about large outbreaks (with the same strain) happening again. The exponential growth that occurs during the early stages of an epidemic is not possible with herd immunity.
5. Herd immunity does not last forever. Unless people inherit immunity from their parents, over a couple of generations the susceptible population may become large enough to make populations vulnerable again.
6. Mitigation and suppression measures are effective because they effectively lower the threshold for (temporary) herd immunity. They can therefore prevent new outbreaks from occurring and quickly bring ongoing outbreaks to a halt. However, once those measures are lifted, that artificially lower threshold returns to normal and the population may become vulnerable again.
Here are some simulations to show how this works. I again looked at an outbreak in a population of 50000. I generated random values for R0 that are centered at 2.28 with standard deviation 0.12 and then simulated an outbreak 100 times for each case and plotted the average outcome (with error bands). I did not try to account for any mitigation measures here so the assumption is that people carry on with their lives as normal for the duration of the simulation.
The only difference between the 4 curves is the initial state of the system. For the red curve there are 10 people infected initially and everybody else is susceptible. For the magenta curve, there are still 10 people infected initially, but 60% of the population is immune from the get go, so the population has herd immunity. Notice the huge difference! The red curve has a dramatic spike in infections and most of the population gets sick. For the magenta curve, nothing happens. The outbreak quickly fizzles out and very few people ever get sick.
The blue and green curve are similar to the red and magenta except that both start with 10000 infected people instead of 10. This is closer to what happens when herd immunity levels are reached in the middle of an outbreak. Here you see that in the case without herd immunity (blue), there is a huge spike and like the red curve, most of the population is ultimately infected. With herd immunity (green), the number new infected people declines from the start and the outbreak slows to a halt. There are still quite a few people (4000-5000) who get infected even with herd immunity, but it does not come close to the number of cases without immunity.
There are a number of prominent voices arguing that we let people get infected so that we reach herd immunity sooner. The country of Sweden has actually adopted this as official policy by trying to protect vulnerable populations and allowing low risk individuals to continue going about their daily lives in the hopes that they will acquire immunity.
Depending on who you are, this may either sound like a brilliant or terrible idea. However, it is actually quite difficult to say whether this would be wise.
Everyone agrees that allowing the virus to spread will increase the total number of cases in the long run (potentially by a factor of 10 or more). However, that does not necessarily mean that we will be worse off. There are many factors to consider:
1. More cases will (likely) mean more hospitalizations. If the healthcare system is not prepared to handle those additional cases, then this could lead to higher death rates among all patients, even those who do not have COVID-19.
2. When predicting mortality, who gets sick makes a huge difference. If you can protect high risk individuals (who have mortality rates >10%) while allowing low risk individuals (who have mortality rates closer to 0.1%) to acquire immunity, then the number of deaths could actually be lower even with a dramatically higher number of cases. However, if the demographic breakdown of new cases is similar to what we have seen thus far, then a tenfold increase in the number of cases would lead to approximately a tenfold increase in the number of deaths.
3. How you achieve to herd immunity matters. If you can use vaccination, then the number of people who have to die to achieve herd immunity will be quite small. However, if 60% of the population has to get sick to achieve herd immunity, then that will lead to a huge number of deaths even if the death rate is low (an 0.1% mortality rate would mean 200 thousand deaths and a 1% mortality rate would mean 2 million deaths).
4. Similarly, the number of people who are sick at the time herd immunity is reached has a significant effect on how many get sick afterwards. If there are a lot of people who are sick when herd immunity is reached, it could still take quite a while for the infection to die out and during that time many additional people will be infected. However, if the herd immunity threshold is crossed when there are few infections, then this tail end of the epidemic will be less severe.
So all this is to say that the issue of herd immunity is more complex than some portray it to be. It is far from obvious whether that is a good strategy or not. Sweden will be an interesting test case for the rest of the world, and I hope their method works! However, at this point I do not think that implementing such a strategy in the US would be wise at least until we get a clearer sense of the mortality rate and the prevalence of asymptomatic cases and until we are able to better identify and track new cases through testing and contact tracing.
And if you are thinking about exposing yourself to the virus so that you can do your part to help achieve herd immunity. Let me implore you to think twice because:
1. It is still not clear to what extent people who recover are immune and how long that immunity might last.
2. There are reports of significant long-term complications from the unfortunate few who end up with a severe infection.
3. You could spread the virus to someone else who is high risk even if you have no symptoms.
4. If you succeed in infecting yourself, there is a decent chance that you could need medical attention and that would me exposing doctors and nurses to the virus as well.
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