## Yes, let’s vaccinate twice as many people against covid-19

I am very sympathetic to Robert Waldmann’s argument that we should give twice as many people one dose of the new Pfizer/Moderna vaccines, at least until supply constraints are eased, instead of following the FDA approved vaccination protocol and giving everyone two doses right from the beginning. What follows is a rough way of thinking about the logic and perhaps the magnitudes involved. Let me emphasize that this is just a finger exercise and I am not an epidemiologist, but with those important caveats I will share my work.

Here are my assumptions. The reproduction number of the virus is currently 1. This means that if behavior, transmissibility, and natural and vaccine acquired immunity are all unchanged, the number of people getting infected each day will remain the same. I assume that there are 300 million people in the United States, 40 million of whom are currently immune due to prior infection, and 260 of whom are susceptible. There are 400,000 new actual infections each day (two times the reported number of cases). These infections lead to 3,000 deaths per day (roughly the current number).

As the number of people with natural and acquired immunity increases, I assume that R decreases proportionately. Thus, with 400k new cases per day, in 100 days there will be 40 million more people with natural immunity, and R will drop from 1 today to 220/260 just due to individuals who recover from infections (without a vaccination campaign). I also assume that over the six months from January through June, 200 million doses will be distributed to either 100 million people (two doses each) or 200 million people (1 dose each), and that doses are administered at a constant rate over time. To keep the calculations simple, I assume that people with natural immunity are not vaccinated (hey wait, that includes me!). I assume that 95% of people who get two doses of the vaccine are immune (5% are vulnerable), and 85% of people who get one dose are immune. Finally, I assume that when a person becomes infected, they remain infected for one day, during which they pass the disease on to R other people and then either die or recover with natural immunity. (My guess is that this assumption is not harmless, it speeds up the adjustment times.)

So what happens in this simple model? First, the epidemic wanes rapidly in both cases. Almost all deaths occur in the first 60 days as natural and vaccine acquired immunity spreads rapidly in the population. This fast recovery could be an artifact of my timing assumptions, and it assumes no other behavioral or weather-related changes to R. In any event, the total deaths at 60 days are 65,000 with two doses person, and 53,000 with 1 dose per person, for a saving of 12,000 souls, plus many more severe illnesses averted. The absolute numbers seem somewhat optimistic (that is, low) to me (reflecting the fast waning of the epidemic in the model). The drop in total deaths seems plausible but presumably would be higher if the epidemic wanes more slowly than the model predicts, and especially if the epidemic explodes for a period in early 2021.

Because my model predicts the epidemic will wane quickly regardless of how doses are allocated, it does not suggest a large economic recovery benefit from giving 1 dose per person rather than 2. If (as seems reasonable) the epidemic drags on longer than my model suggests, doubling the number of people who are able to resume normal economic activity at each point in time could have large benefits for businesses, workers, and customers, and for public finances. We should also consider providing people with proof of vaccination and of prior infection (“immunity passports”) to make it easier for immune individuals to return to normal economic life.

I agree with Robert that it is unlikely that the federal government will lead the charge to double the number of individuals vaccinated. But the incoming Biden administration would do well to give this serious consideration (of course, this means doing more sophisticated analyses than I have done here). Yes, giving one dose per person will be controversial, but by April Biden will own the epidemic and it is far from clear Congress will step up with more economic relief. Doubling the number of people vaccinated might make the difference between a successful recovery and a presidency consumed with economic pain and political gridlock. This will be a clear test of Biden’s ability to act boldly rather than out of caution.