Herd Immunity Ratio
As an intellectual exercise let’s think of an imaginary state, “State A.” Our fictional State A is devastated that 100 of its citizens are infected with Covid-19. For this exercise, we accept that these 100 citizens are representative of State A‘s demography, classes, ethnicities and so on. Apparently, State A’s nightmare is just the beginning because out of its 100 Covid-19 carriers, not one survives the next three weeks.
Let’s now imagine another case, we will call “State B.” State B is similar to state A in terms of its size, population, geography, climate, culture, ethnicity, nutrition, etc. In State B 100 citizens also tested positive for Covid-19. Following the experience of State A, State B braces itself for the possibility that all its infected citizens may perish but then for reasons that are not yet clear to us, no one in state B dies. And if this is not different enough, hardly any of the 100 develop any symptoms.
The crude difference between State A and B may tell us something about the herd immunity in States A and B. It is easy to detect that the ratio created by the number of fatalities (F) divided by the number of those infected (I) is an indication of the level of immunity or ‘herd immunity’ in a given region or a state.
State A: F/I = 100/100=1
State B: F/I = 0/100=0
State A’s immunity ratio equals 1. This means that anyone who contracts the virus in State A will likely die. In state B, on the other hand, one is likely to survive the virus. In fact, they may, without knowing it, have already survived.
But let us now consider some more realistic cases. In “State C,” again, a state similar to A and B, out of 100 who tested Covid-19 positive, 10 people died within the next few weeks.
State C: F/I=10/100=0.1
The herd immunity ratio in State C is 0.1. In terms of herd immunity, State C is far better off than State A as a virally infected subject may benefit from a 0.9 chance to survive. But State C’s situation is not as good as in State B where no one is expected to die as the F/I ratio in State B is O. We can see that the smaller the F/I ratio is, the greater is the herd immunity in a given state or a region.
But let us look at another realistic case. In “State D” out of 100 patients only 1 died within a few weeks.
State D: F/I=1/100=0.01.
This means that in State D the herd immunity is close to perfect. Someone who contracts the Covid-19 virus has only a remote chance that he will lose his life. In other words, the survival rate is 0.99
State C and D are not completely imaginary cases. The F/I ratio in State C is a good representation of the numbers we saw in Northern Italy, NYC, Spain, UK and other vulnerable regions that have suffered heavily in the last few weeks. The ratio in State D is very similar to South Korea and Israel. Though many people are identified with Covid-19 in these two states alone, very few have died.
Such a methodical search for herd immunity ratio may help to identify the survival rate in different states, regions and cities. It may help us to determine policy; to decide who, what and how to lockdown or maybe not to lockdown at all. It can also help to locate the origin and the spreaders of the disease as we have a good reason to believe that the regions with the most immunity to a given viral infection have likely experienced the disease in the past and have developed some form of resistance.
In reality, this model is problematic for many reasons and can hardly be applied. As things stand (in reality), we are comparing data that was collected under different circumstances and using various procedures designed with completely different strategies and philosophies. Both Israel and South Korea, for instance, conducted testing on mass scale and hence, identified many more carriers. More crucially both Israel and S. Korea made a huge effort to identify super spreaders and applied strict isolation measures to those spreaders and those who were infected by them. Britain, USA and Italy on the other hand conducted limited testing and have generally tested those who developed symptoms or were suspected of being infected.