Post #681: How long until 70% are immune?

Posted on May 4, 2020

Source:  Virginia Department of Health.

Given the ongoing growth in new cases in Virginia, I think I have to start asking this question:  If the current situation holds, how long will it be before 70% of the … let’s say working-age adult population — has had coronavirus?  That’s the point at which most experts expect this pandemic to die off naturally, due to “herd immunity”.

And, secondarily, is that 70% point likely to be passed before or after the date at which we can reasonably expect to have a vaccine?  At which point, it’s moot:  We’ll get immunity from the vaccine.

This is motivated by a couple of graphs, from the Virginia Department of Health, above.  Realizing that death is not the sole outcome, and that death is a somewhat lagging indicator, that said, this disease:

  1. Does not appear particularly dangerous for those age 20 and under.  Zero deaths to date in Virginia.
  2. Does not appear particularly dangerous for those age 21 – 40.  So far, six deaths, for a case rate of about about 1 death per 1000 cases.  (Case rate is per officially diagnosed cases).  Arguable, given the large number of persons infected but not officially diagnosed (now being revealed by studies of the presence of antibodies), that’s probably close to 1 death in 5000 persons actually infected with coronavirus, in that age group.   We have no way of knowing whether or not those individuals had known risk factors.
  3. Becomes increasingly dangerous for populations older than that, with a peak in the 80+ population largely owing to the very large number of deaths in the nursing home population.

Given this, stay-at-home orders that are uniform for all age groups are probably inefficient.  I think there’s a case for letting the younger generation get on with their lives as they see fit.  And, maybe, for using this as an opportunity for the older generations to get out of the way and hand off economic tasks to younger generations.

How long would it take to reach herd immunity?

At some level, this is just arithmetic.  I’ll do three scenarios.

A static scenario asks:  At the current daily rate at which newly-diagnosed cases are appearing in Virginia, how long will it take is to reach 70% of the adult population?  The answer this is, about two years.  That’s well past the point where we have a vaccine under any plausible scenario.

A fixed-growth scenario asks:  At the current rate at which those new case counts are growing (about 5% per day), if that growth continues, how long would it take?  In that case, just about two months.  But the case load toward the end of that would clearly overwhelm the Virginia hospital system.  So that’s short, but not really feasible.

A modified-growth scenario:  Let the current growth rate continue until we reach some plausible estimate of hospital capacity.  I (gu)estimate that at around five times the current daily new case count.  Under that scenario, it would take just under half a year to achieve herd immunity.  Arguable, that’s well before we can reasonably expect a vaccine to be available in the US.

But haven’t you read that there’s no guarantee that you’re immune, once you’ve gotten over this?  Yep, you’ve probably read that.  My guess is, that’s exceptionally unlikely to occur.  It did not occur in the 2003 SARS epidemic, and it probably isn’t occurring in this epidemic.  Most of what you’ve read about people being “re-infected” comes from Korea, and my best guess is that they simply have not properly accounted for a small false negative rate in their testing regiment.  See the extended small-type discussion in this post for details.

Hand it off to the younger generation

But there is an alternative, which is to let the younger generations get on with their lives.  At least, those without direct household contact with the older generation.

Today (5/4/2020), the Commonwealth reports a cumulative total of about 6,000 diagnosed cases age 21-40, resulting in 318 total hospitalizations.  Assuming that the un-diagnosed population is four times as large (see prior post), that would be a hospitalization rate, per infected person, of just about 1%.  We have 2,250,000 adults of that age in the Commonwealth.  Infecting 70% of them would generate 16,700 hospitalizations.  But if we did that at an even pace, over the course of two months, that would be just 300 new hospitalizations per day, plausibly within the limits of the Virginia hospital system to absorb.

In other words, if we could pace the infection of the younger (21-40) population, we could achieve herd immunity within that population in just two months, plausibly without overwhelming the hospital system.  (It’s not clear that the herd immunity concept really applies, unless they can be kept separate from the rest of the population.)

Based on the same calculation, you would expect a total of 315 deaths, to achieve “herd immunity in that population.”  In a normal year, we would expect about 2800 deaths from all causes in that population.