The Integrity of Herd Immunity in the COVID Era
Sources:
https://www.sciencemag.org/news/2020/11/more-people-are-getting-covid-19-twice-suggesting-immunity-wanes-quickly-some
https://www.nature.com/articles/d41586-020-02948-4
https://intermountainhealthcare.org/blogs/topics/covid-19/2020/11/debunking-the-myth-of-non-vaccine-herd-immunity-in-covid-19/
Recently, we learned about two models for epidemics: the branching model and the SIR model. The branching model is an extremely simple representation, in which every node meets k other people and passes on the disease with p probability. The SIR model is a more nuanced for two reasons: one, it takes into account the fact that social circles tend to close in on themselves, and two, it also tracks the changing state of nodes within a network. These states are made up of: Susceptible (S), Infectious (I), and Removed (R). A node changes its state to removed when it receives the infection, recovers from it, and is therefore no longer susceptible. It therefore would theoretically support the notion of natural herd immunity – if enough of the population catch the disease and recover from it, the spread becomes more and more unlikely until the community becomes protected.
However, there is a crucial flaw with the SIR model, that flaw being temporary immunity – is it possible for a person who has once been infected to catch the disease again? While COVID-19 is still being documented, there have been enough cases of reinfections to prove that yes, it is possible to catch the disease more than once. As of now, Netherland has had 50 cases of reinfection, Brazil 95, Sweden 150, Mexico 285, and Qatar 243 – and these are just the cases that have been genetically proven. So as early cases begin to lose their immunity, the notion of herd immunity that persists on internet forums becomes increasingly weaker as well.
To analyze this, we should measure the likeliness of herd immunity via contagiousness of the virus, AKA the Basic Reproductive Number, R of 0. This is the product of k and p and represents the number of more expected cases per new case. The threshold for herd immunity is a percentage that is 1-1/R of zero, where 1-1/R of 0 % of the population must get the disease to achieve herd immunity. Estimates for COVID range from as low as 10% to 70% or higher. However, studies show that the percentages at the lower end of the spectrum are based on assumptions about social interactions that are not entirely true – for example, estimates of 10% assume that the first people to get the virus will be the “superspreaders” who have many contacts. The idea is that as the the superspreaders become immune, the people who are exposed to the virus will drop dramatically because the superspreaders are technically only involved in their own social circle. However, if this assumption does not hold water and anyone can be a superspreader, the threshold could shoot up to 70% or higher.
Either way, achieving natural herd immunity in the first place is extremely dangerous – an estimated 230 million cases would have to occur within the US, with 2.3 million deaths. Coupled with the fact that being in a Removed state is only temporary and does not guarantee immunity forever, natural herd immunity is a far-fetched, outdated concept. As this pandemic continues, we have to better understand how long immunity lasts for those who have caught COVID once before. Armed with this information, we can look forward to a more achievable solution, which includes herd immunity via vaccines that are administered for every time we become susceptible again.