Covid: Endgame
The extreme infectiousness of Delta means that herd immunity is out of reach. How else, then, can pandemics end?
A legacy article originally published September 8, 2021
For a while there has been an increasing number of articles encouraging people to start living as though we are already in a post-pandemic world. Of course, we’ve heard this sentiment in conservative-leaning publications since May 2020. But it is now creeping into publications that have traditionally been more cautious encouraging masking, distancing, school closures, vaccination, etc.
In the New York Times September 7th David Leonhardt wrote, “For the vaccinated, Covid resembles. . .a mild [flu]. Society does not grind to a halt over the flu. In Britain, many people have become comfortable with the current Covid risks. The vaccines make serious illness rare in adults, and the risks to young children are so low that Britain may never recommend that most receive the vaccine. Letting the virus continue to dominate life, on the other hand, has large costs.”
It is likely that over the next couple of months, this sentiment will gain a strong foothold and will ultimately have the support of prominent figures including physicians.
Are they right? Should we have done so long ago? From the beginning even? What will be the consequences? Why is this now creeping into traditionally liberal publications that have held out in favor of more severe pandemic mitigation measures?
Pandemics have two kinds of ends: biological ones and sociological ones. Examples of biological ends include herd immunity, mutation of the virus into a less virulent one, and mutation of the host into a less susceptible one. The emergence of Covid19-delta has changed the endgame in that herd immunity is out of reach. And mutation of the host (us) will take many hundreds of generations. Mutation of the virus, of course, is happening but Covid has already made the epidemic-to-endemic transition. Covid is not likely to have a biological end in the near term.
So if Covid will not have a practical biological end, how will this pandemic end?
Pandemics also end when we cease as a species to act as if we are living during a pandemic.
As Nicholas Christakis writes in Apollo’s Arrow, “pandemics are also sociological phenomena, driven by human beliefs and actions, and there is a social end to pandemics, too, when the fear, anxiety, and socioeconomic disruptions have either declined or simply come to be accepted as an ordinary fact of life. . .In other words, plagues can end when everyone believes they are over or when everyone is simply willing to tolerate more risk and live in a new way.”
Leonhardt argues that for the vaccinated, those risks are already small. The daily risk of contracting Covid is only 1/5,000. Or maybe even 1/10,000. The vaccinated can relax, he says — the chance of getting Covid sometime in the next 3 months is barely 1%. This is misleading on many counts.
One problem is, for any pandemic, you can calculate a quantity called S(end) which is the fraction of the population who, after the pandemic is all over, never got infected with the pathogen at all. The fraction who got infected at some point during the pandemic is then 1-S(end).
To find S(end), the equation that needs to be solved is:
S(end) — 1/q * ln(S(end)) = I0 + S0–1/q * ln(S0)
Where I0 and S0 are population constants, 1/q is essentially the R0 of the pathogen (for delta it is about 8 or 9) and ln() is the natural log.
This equation has no closed-form, analytic solution and must be solved numerically. For a disease with an R0 of 8 or 9 like Covid-delta, S(end) is less than 5%, meaning 95% of the human population will eventually get Covid. So Leonhardt’s argument that the daily chance is only 1/5,000 per day is irrelevant. The pandemic will keep going on and on as long as it takes for 95% of people to become infected. If Leonhardt’s logic behind that 1/5,000 number were not flawed (it is), in this example the pandemic would continue for over a decade.
Then if it is inevitable that 95% of us are gonna get Covid before this is all over, should we just let go? If the pandemic ends when we say it ends, should we declare it over, consign it to the annals of history, and invite a new era of 20’s “Flapper Parties”?
Now is not the time. Too many people remain unvaccinated and vaccines protect very well against the most severe consequences of Covid. Also, there is hope that a third dose of the vaccine will provide even greater protection in the form of reducing q in the equation above, perhaps even to the point that S(end) could be closer to 20% than 5%. Finally, the endgame needs to be a coordinated strategy rather than a charging-of-the-field after a soccer match.
A March 2021 article in Nature examined the effect of staged lockdowns in a partially vaccinated population. The authors showed that the worst result is achieved when we try to achieve herd immunity by natural infection. A better result comes from herd immunity by vaccination. But an even better outcome can be achieved with vaccination plus staged lockdown.
This principle could be applied to the endgame we play now. Instead of declaring the pandemic over all at once, we might engage in cyclic lockdowns. For example, 2 months on, 4 months off, and so on, for as long as it takes. By doing so we may be able further reduce the total number of infections, avoid overwhelming our healthcare system, and allow more people including currently ineligible people to get vaccinated and protected from the most severe consequences of Covid infection. And if the “on” and “off” intervals are carefully chosen, we might even be able to enjoy some of our favorite holidays in relative normalcy.
We are almost ready to play our endgame. But make no mistake, it will be a long drawn out one with plenty of surprises from our opponent. The truth is, we probably won’t be living in a truly post-pandemic world before 2024. There won’t be any peace treaty or armistice to mark the moment. There won’t be any newspaper headlines declaring “PANDEMIC ENDS!” No. The end of Covid will be “fuzzy”, uncertain until viewed from many years on.
So, no. Now is not the right time to let up. Instead, we should be looking around for that sticking place to which we can screw our resolve for the long winter ahead.