George Rebane: The big decision and the second wave
It’s obvious that we cannot keep the economy locked down until the last vestiges of the COVID-19 pandemic disappear. That would destroy America’s and the world’s economies and result in much greater morbidity and mortality than caused by the virus exhausting itself.
Starting with President Trump and our states’ governors, all the world’s political leaders have now decided to open up commerce sooner than later, the Big Decision for each is when, where, and how. The major factor impacting that decision concerns the size and virulence of the inevitable second wave of infections. And that is determined primarily by the level of herd immunity a given population had achieved at the end of the first wave.
Herd immunity is achieved by that part of a target population that has survived the disease and developed antibodies which make them immune to further exposures to the virus. Since the virus is relatively short-lived in any one person — in a matter of 2-4 weeks they either survive it or die — the cohort of people is relatively small who at any time can infect the remaining uninfected and vulnerable. And if these uninfected make up a relatively small fraction of people who are out and about, then the rate of infection (the “reproduction” rate) goes down since the chances of running into another vulnerable person while contagious is appropriately reduced. And that is called herd immunity, which then increases as more survivors make up a greater share of those who are out and about. That is how less virulent epidemics like COVID-19 die out.
Populations that are mostly isolated from each other, like we currently have during the nation’s lockdown, develop different levels of herd immunity depending on a number of factors such as population density, quarantine practices, and demographics. We see this in the lower impact the virus has had on California relative to the greater New York/New Jersey area. Many disease experts now think that California, as a major gateway to Asia, also had a head start developing its herd immunity beginning last fall. To that we can add the size of the state and how well, in the aggregate, Californians have practiced self-quarantining and social distancing.
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To illustrate how herd immunity will impact the second wave using California’s 40 million as the target population, please examine the nearby graphic which plots various infected population curves that depend on the percent of people already having become immune. We can see the steady reduction of intensity or curve flattening for the higher levels of initial herd immunity. The progress of epidemics is a complex (non-linear) process which becomes very apparent when the herd immunity rates get above 30%. It is then that the second wave, already reduced, starts to really become delayed, flatten out, and also takes longer to extinguish.
These curves and the related data table were generated with Epidyne, an epidemic spread model, using a set of currently accepted values for such input parameters as maximum reproduction and mortality rates.
What the information shown here also underlines is the role of randomized immunity testing to determine the level of a target population’s herd immunity. COVID-19 testing comes in two varieties — infection and immunity tests. Widespread, rapid turnaround infection testing gives policy makers a snapshot of what fraction is infected today, a fraction that most likely will change tomorrow. Immunity (e.g. antibody) testing yields a longer lasting result that is also a conservative minimum, since a greater share of the target population gains immunity with passing days.
With all this under our belts, we can now understand why there is a growing body of epidemiologists who are beginning to tell us that comprehensive quarantining may have been overdone, or even a mistake. This for the simple reason that COVID-19 affects minimally many (most?) of the people it infects. A big and yet unknown fraction of the infected remain asymptomatic who are contagious for a short while and then become immune, contributing to herd immunity build-up. These experts are basically saying too widespread quarantining will inhibit the build-up of herd immunity, and therefore will make the second wave more intense and deadly — in short the virus says, “pay me now or pay me later.”
There is much more to the analysis of both the spread of the pandemic and the effectiveness of testing (since they are all to an extent unreliable). For readers interested in the details, I invite them to visit Rebane’s Ruminations.
George Rebane is a retired systems scientist in Nevada County.
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