Herd immunity.
The idea that after a certain number of people in a group are immune to a pathogen, it progressively becomes almost impossible for the pathogen to spread broadly.
If we could choose which of the members of society to be exposed to the pathogen and so become immune, but not all members have equal risk of harm or death from the disease, how would we decide?
Suppose there are 1000 people in the herd. As more of them recover, the disease is less and less likely to spread. But it takes until 50% (500) before the virus is basically no longer a threat.
100 of the herd, Zs, if they catch the virus, are known to be more likely to suffer harm or to die (maybe 5% of the infected Zs will die). When they die, they reduce the numerator and the denominator for the future (future being the realm where herd immunity continues to be useful).
200, the Xs, say, have almost zero risk of harm or death, but they can still contribute to the percentage of the herd that needs to be immune in order to have herd immunity.
The other 700, Ys, have a varying risk of death, but let’s say it’s at 1% of the infected, on average.
Scenario 1: If we select people at random to bear the burden of exposure, sickness, and hopeful survival into an immune state, a high percentage of the vulnerable Zs will die. Herd immunity may take longer to accomplish. 500/1000 will have to get and survive the disease. Around 50 will be Zs. Two or three Zs will die. About 350 Ys will catch it. Three or four of them will die. Around 100 Xs will catch it. None of them will die. Total death count would be five to seven.
Scenario 2: If we prevent most of the least vulnerable Xs from being exposed, but don’t prevent others (Ys and Zs) from being exposed, then an even higher portion of the most vulnerable will be exposed, sickened, and die from the disease. 500/800 will have to get and survive the disease. Around 62 or 63 Zs will catch it. About three will die. Around 438 Ys will catch it. Four or five will die. No Xs catch it. None die. Total death count seven or eight.
Scenario 3: If we choose to reverse this, and carefully prevent the most vulnerable from being exposed, while allowing the risks to be more or less evenly distributed among the Xs and Ys, we will have built herd immunity with less total harm and death. 500/900 will have to get and survive the disease. For the sake of argument, we are perfect at protecting the 100 Zs. None get it. None die. 389 Ys catch it. About four die. About 111 Xs catch it. None die. Total death count is four.
Which scenario do you support, and why?
Which is closest to what our leaders have chosen for us?
Please note. There is real data that could be substituted, for the percent of our population that is of a certain age, for example.
We could stratify the Ys into more age or vulnerability brackets.
The infection fatality rates assumed for the sake of simplification are not accurate, but they are somewhat close. They are least accurate for Ys, I believe.
We actually aren't perfect at sheltering any group of people. For simplicity, I assumed that all Zs, in Scenario 3, were protected, and all Xs, in Scenario 2. The real world is less sharply divided. However, I believe this example is demonstrative because it is such a small number relative to our total population.
Finally, there is some interesting thought about the most social* people being the most likely, quickest, and most necessary group to get infected for the purposes of herd immunity, which could affect this example, both in the total percentage required for herd immunity, and also for the natural tendencies that are not the same as mathematically random selections of the infected.
*Social defined here as having near physical contact. It doesn't have to be in a way that involves communication; proximity could work.
To God be all glory.
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