Happy New Year! How effective does a vaccine have to be to eliminate SARS-Cov2 from the planet?
The Moderna, Pfizer and Astrazeneca vaccines are out! What an exciting way to start 2021. Everyone wants them, but the question I have been pondering the first few days of this New Year is: Can we eliminate SARS-Cov2 from the planet? Can we physically drive this virus to extinction? We know, at least in theory, that vaccines can do that. A famous example is smallpox, which was declared eradicated in 1980 by the World Health Organization.
In this notebook, I explore three Susceptible-Infected-Recovered (SIR) models of increasing complexity: constant population without births or deaths, constant population with new births and deaths, and constant population with births, deaths and a vaccine. I work through some basic aspects of these models, including conditions for disease eradication and arrive at the following conclusion:
To drive SARS-Cov2 to extinction, the total fraction of the population protected by the vaccine must exceed 1 - 1 / R_0, where R_0 is the infectivity of the virus in the absence of all social distancing conditions and at the beginning of the pandemic. For SARS-Cov2, I think it’s not unreasonable to expect R_0 ~ 7 - 12 (though please note that these are my estimates; there are a number of papers out there estimating R_0 for SARS-Cov2 and initial estimates ranged from 2 - 5).
Fortunately, both the Pfizer and Moderna, though not the Astrazeneca, vaccines both have an efficacy exceeding 90%, suggesting that it may indeed be possible to wipe out SARS-Cov2 from the planet if we socially distance AND vaccinate.
So go get those vaccines!