It’s not about the destination, it’s about the journey. Whether you believe this applies to life or not, this statement certainly applies to the topic of herd immunity. Herd immunity has been in the news quite a bit lately. There were reports that the president’s new favorite scientist, Dr. Scott Atlas, favored herd immunity as a national strategy, a claim that Atlas later denied. Meanwhile it has become commonplace to hear people say “we are all going to get COVID anyway, so why not get it over with?” which is essentially an embrace of the inevitability of herd immunity. In light of this, I thought it would be worth revisiting what herd immunity is, how we get there, and what it means for the future.
Back in May, I talked about herd immunity and explored whether it was the solution to the pandemic. Feel free to skip the bullets if you remember this, but here is a brief overview for the rest of you:
1. Herd immunity means that a population is no longer vulnerable to large scale outbreaks. It occurs when the number of people that are susceptible to the virus becomes small enough that recoveries begin to outnumber new infections causing the outbreak to slowly recede.
2. The rate at which new infections occur is described by the reproduction rate (Rt), which measures the average number of new infections caused by each infected person. If this drops below one, then recoveries outnumber new infections. This quantity changes over time and varies from place to place. There is a handy website for estimating Rt within each state called rt.live. It suggests that Rt is currently between 0.8 and 1.3 in the US.
3. As people change their behavior, Rt goes up and down, so the best way to determine when lasting herd immunity will be achieved is to look at the initial reproduction rate R0 (also called the basic reproduction ratio) since this tells us how fast the virus was spreading under normal circumstances. In standard models like the SIR model, which is the basis for the results in this post, the herd immunity threshold can easily be expressed in terms of R0. It is reached when the fraction of the population that is susceptible drops below 1/R0 or equivalently when the number of people that are immune exceeds 1-1/R0.
4. For COVID, most estimates that I have seen place R0 between 2.2 and 3.6. So, the best-case scenario (R0=2.2) is that herd immunity will be reached once more than 55% of the population is immune. The worst-case scenario (R0=3.6) is that herd immunity will be reached once more than 73% of the population is immune. Unfortunately, recent estimates seem to favor the latter scenario.
5. One of the reasons why social distancing is an effective mitigation strategy is that it temporarily lowers the bar for herd immunity. For example, if social distancing cuts the probability of infection in half, then that is like decreasing R0 to somewhere between 1.1 and 1.8. This would cause the herd immunity threshold to end up somewhere between 9% and 44%. If the probability is reduced further, then that threshold can even drop to 0%. That is the reason why we saw the outbreaks abate back in May before roaring back once things started to reopen.
If long lasting immunity to COVID is achievable (something that has not been established conclusively), then it is essentially inevitable that we will achieve herd immunity in the long run. The question is, how will we get there?
One possibility is to just let the outbreak happen uncontrolled. We have already caught glimpses of what that looks like back in March on the streets of Italy and NYC. Unchecked, this would cause herd immunity to be reached very quickly, but along the way hospitals would be often overwhelmed. Another possibility is to try to manage the epidemic through mitigation measures like mask wearing and social distancing. In this case, it takes much longer to reach herd immunity (spreading the disruptions out over a longer window of time), but the peak is more manageable. In both of these cases, most of the population must get infected in order to achieve herd immunity along the way.
Both of these outcomes are problematic because they would produce a staggering number of hospitalizations and deaths. For example, if the mortality rate is 0.5% (on the low end of most estimates) and the herd immunity threshold is 55% (the more optimistic scenario), that would result in a total of over 900,000 deaths in the US, and if the mortality rate is higher or the threshold is higher, well…you get the picture. For this reason, most of the world is hoping and praying for a vaccine so that immunity can be obtained without all those infections along the way.
There are some promising vaccines undergoing clinical trials, but it will take a while before they are approved and ready for mass distribution. This means it may be many months before a vaccine is widely available. What should we do in the meantime?
There are a couple of things that we should know:
1. First off, we need to keep in mind that new infections don’t stop immediately when herd immunity is reached. Instead, new infections slow down gradually. In other words, herd immunity is less like a light switch and more like the brakes of a car. When you try to stop a car, the amount of time it takes to stop depends on how fast you are going. The same is true of herd immunity. The more people that are infected when herd immunity is reached, the longer it will take for the pandemic to end and the more people that will get sick along the way. For example, the graph below shows the fraction of the population that gets sick AFTER reaching herd immunity (vertical axis) is reached as you vary the fraction of the population that is sick at the time that herd immunity is reached (horizontal axis). Note: This assumes an intermediate scenario with R0=2.5.
In this scenario, we need 60% of the population to be immune to reach herd immunity. If all of those people are still sick at that point in time, which corresponds to the top right corner of the plot, then most of the remaining 40% of the population will still get sick before the pandemic burns out. The good news is that this is not actually a plausible scenario, but I include for the sake of comparison. On the other hand, if almost nobody is sick when herd immunity is reached (bottom left corner), then almost nobody will get sick after the fact. The thing to note here is how steep the curve is near 0. This means that small increases in the number of sick people at the time we achieve herd immunity, can have a big effect on the number of people that get sick afterwards.
So, whether herd immunity is reached through vaccination or though infection, it is important the outbreak be under control at that point with a relatively small number of infections if we want to avoid unnecessary deaths afterwards.
2. The second thing to remember is that getting immunity through vaccination is much safer than getting it through infection. So, if we need 60% of the population to be immune, we would like as much of that 60% to come from vaccination as possible. Slowing the spread of the virus down now buys us more time to get that vaccine ready. Below I have plotted a rough estimate of the total number of deaths (color) assuming a fixed 0.5% mortality rate as you vary both the number of people are sick when we reach herd immunity (horizontal axis) and the number of people who are vaccinated at that time (vertical axis).
We want to be close to the upper left corner where lots of people become immune through vaccination and very few people are sick when herd immunity is reached. This keeps the death toll low. We want to avoid the bottom right where few people are vaccinated, and many people are sick when herd immunity is reached because this would lead to many more deaths.
Unfortunately, time is not on our side. Currently we are seeing around 40,000 new cases and 1000 deaths per day. This means that each day we are moving further down the plot as more people get immunity the hard way. These totals are down from a peak of almost 70,000 cases per day (in late July) and 2200 deaths per day in mid April, but they are still much higher than what most countries are seeing and much higher than the lows we saw in late May/early June. It remains to be seen how this will change as schools restart and our activities move indoors for the winter. If we allow the virus to spread quickly now, then if and when a vaccine becomes available, we will be much further to the right within this plot.
So, the takeaway messages are that:
1. The claim that “we are all going to get the virus eventually” only makes sense if you assume a vaccine is NOT coming. If a vaccine is not on the horizon, then it makes sense to get through this as quickly as possible WITHOUT (and this part is important) overwhelming our capacity to treat and care for those who are sick. However, if a vaccine does become available, then this sort of nihilistic thinking and the reckless behavior it inspires will lead to countless needless infections and deaths.
2. If a vaccine does become available, then our efforts to slow the spread of the virus now will pay significant dividends in terms of lives saved.
So, yes, we want herd immunity, but it is much better to get that through vaccination than through infection. Given that there are already a handful of vaccines that are in stage 3 clinical trials. I am holding out hope that we will reach herd immunity the easy way.
PS. The plots and thresholds used in this post were calculated using the SIR model. This is a simple model intended to provide a qualitative description of the pandemic rather than precise predictions. So, you should put more stock in the trends displayed here than the specific estimates for infections and deaths.
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