COVID-19 Herd Immunity
Is Herd Immunity a response to a Pandemic?
Herd immunity is an issue that has been discussed for a long time, and that as a consequence of poor education in basic mathematics is being poorly evaluated even by people who have a fundamental role in decision-making, at the regional level, at the level of the country, and even internationally.
It has to do with the famous group immunity or herd immunity, I prefer to use the term group immunity although sometimes we human beings behave little as rational.
People who are interested in studying the way in which infectious diseases spread in a population have long known that epidemics suddenly seem to stop almost as if by magic, every day more and more and more people get sick and of soon this process is reversed.
And for a long time, it could not be understood why this happens.
Over the years we discover the cause of infectious diseases, microorganisms, or even smaller structures that are not alive, such as viruses.
Mathematical behavior, at least in terms of how an infection spreads, can be described with the same kinds of formulas that you can use to describe the way a bacterial epidemic spreads, such as bubonic plague, basic concepts are the same.
Since we discovered what causes infectious diseases and how they work, we began to create mathematical models that describe the evolution of an epidemic.
For a long time, the idea of making mathematical models in the world of science was not very well regarded by the scientific community, because it gave the impression that a model mathematical is a kind of little toy whose behavior can sometimes resemble the phenomenon that it is trying to model, but in the end, a mathematical model is generally a simplification, it is a machine that produces numbers and whose behavior is a simplified version of what it happens in nature.
To pretend that a few scribbles on paper make a useful prediction about the evolution of an epidemic seemed in the late 19th, early 20th century to be truly absurd.
Over the years it became increasingly clear to us that the behavior of nature is logical, there are distinguishable chains of cause and effect, chains whose structure is accessible to the human intellect, that is, human beings can understand the cause of things in nature, and on the other hand we have a tool that we normally pack into the world of science, and I mean mathematics.
Although strictly speaking mathematics is not a science, although it sometimes seems like it. Mathematics is a discipline that allows us to represent a chain of logical reasoning as accurately as possible. You start from a series of principles, of axioms, and you also start from a series of basic principles for processing information, for example, the principles of algebra, if you in your axioms and in the initial mathematical description of what you think they are are The elements that describe an epidemic put all the correct elements, this little machine that produces numbers, numbers that are supposed to represent the number of patients in the locality, for example, can come to reflect in a fairly reliable way what is really happening.
In the natural world, you can even anticipate a phenomenon if you have a mathematical model based on a firm understanding of the cause of the phenomenon.
The behavior of a phenomenon, you can predict it, even roughly
For example, we understand quite clearly in mathematical terms how electrons move, if we try to translate it into the language of the newspaper or you get into some delicious trouble because electrons have a very peculiar way of moving very strange when we describe it in terms of every day, but it has its logic, a logic that is represented with great precision by a collection of mathematical concepts that
We collectively call quantum mechanics, and the reality is that quantum mechanics allows us to predict with great precision that a lot of atoms will pass through it under certain circumstances, and that’s why we have computers.
Nature, in short, works in a logical way, and the best tool we have to represent strictly logical reasoning is mathematics, therefore if we get to understand the mechanics of a natural phenomenon reasonably well and we can describe that mechanics with a formula, This formula can allow us to anticipate the behavior of a natural phenomenon. Whatever the movement of electrons on a chip, the movement of planets around the sun, or the behavior of an epidemic.
Epidemiology is a discipline that has a strong dose of mathematics and remembers that, just as in the world of geology, you have several different aspects, several disciplines, you have geophysics, you have volcanology, seismology, edaphology, the study of soils, etc …
The world of mathematics also has its areas of expertise, for example, there are statistics, number theory, algebraic topology, there are several disciplines, many disciplines.
To describe an epidemic you use tools that come from different disciplines, for example from the world of statistics and other branches of mathematics, there are already well-established formulas that really describe the behavior of an epidemic very well, as long as you place the correct values in certain variables, these variables describe some fundamental factor of the disease you are studying. One of these factors that have to do with the mathematical behavior of an epidemic is a number called r 0 if you study the formulas that describe the dynamics of an epidemic.
r 0 is the basic number of reproduction of the epidemic, the basic number of contagion, and in short, it is the average of a contagious person and how many people he infects during the course of his illness.
If this number is higher than 1 then the total number of infected people will grow over time. This number r 0 evolves as the epidemic evolves in the early stages, this number is generally constant.
When the Covid-19 epidemic began, the r 0 of was more or less stable, in some countries it will be a little higher and in others lower, and that reflects, among other things, the social circumstances where an epidemic occurs, if there is a country where massive use is made of means of transport that involve many people in confined spaces, the number of r 0 has to be very high, it is enough for a person to get on the subway on a Friday morning to, that in principle, it can infect dozens of people, then when you start to study the evolution of the epidemic in different countries, you find different values of r 0 and even for different cities or different areas within a city, depending on the circumstances that facilitate that a contagious person passes the disease to a susceptible person.
We take an average and that average gives us an idea of the general evolution of the epidemic, considering all the variations that can occur in the contagion mechanisms in human society.
Well, once the epidemic has evolved and people have been contagious, some non-infectious, some with mild infections, others with serious infections, there may come a time when the number of available people susceptible to contagion begins to decrease. In an epidemic like Covid-19, many people become infected like this, they are a healthy carrier of the disease, they can infect others, but in this person, it has no visible effect on their health, the so-called “asymptomatic”.
At first, these healthy carriers infect many people, most of the infected people will be healthy carriers, and only a relatively small fraction show any symptoms, and fortunately only a fraction of the people who show symptoms develop serious disease, but after a while, you already have a lot of infected people, and infected people, supposedly, become resistant to the disease. We know, but we do not know to what extent and under what circumstances.
There is also the case of reinfections
It is being studied very closely these days, but there comes a time when so many people have already been infected that the probability that an infectious person will come into contact in circumstances that allow contagion with Someone susceptible begins to decrease because there are less and less susceptible people, when this happens what is observed is that suddenly the number of clearly ill people begins to decrease even though protection measures have not been taken, the number of people who are He obviously declares the disease begins to diminish.
This was observed in the plague epidemics in the Renaissance, they were brutal waves, one after another and at their worst, they wiped out a quarter and a half of the European population, it was something truly dramatic that left indelible marks on art. , in social behavior, in our laws, in all human activities. There comes a time when so many people have been infected asymptomatically or symptomatically that the probability of someone else becoming infected begins to decrease rapidly and it is then that the epidemic begins to stop, as happened with the plague epidemics, which seemed to they were going to end the world and suddenly they disappeared as if by magic.
Today we know that this magic is actually mathematical, mumps is an extraordinarily contagious disease, and that on average a sick person can infect between 12 and 18 people, in the case of Covid-19 this number is much lower, between 2 and 4 people depending on where it is.
The possibility that arises if we do not have a vaccine and an effective treatment has not been developed is to allow people who belong to groups not very susceptible to severe disease to begin to return to their normal activities with minimum protection and only restricts the movement of people who have risk circumstances, for example, people of 60 years, people with diabetes, hypertension, people who have a high probability of developing a serious disease if infected.
People who have a low probability of developing the disease begin to lead their normal lives, they begin to be infected and to infect others, but as the people who are on the street are the only people who have a low probability of developing the serious disease this, of somehow, it blocks the process of the epidemic. The total number of seriously ill people begins to decrease, the total number of people who have already been exposed to the virus and have developed immunity grows more and more and there comes a time when
The one that the virus no longer has anywhere to go, resides in a sick person and that sick person cannot infect anyone else because the people who approach them are people who have already been infected before and already have resistance after a while relatively short.
That should make the virus disappear from the population and then susceptible people could go back out onto the streets. That is the logic of the so-called herd immunity or group immunity.
Works?
Well, this can be solved with mathematics, there is a formula to calculate what is the percentage of the population that must be exposed to a virus so that this mechanism begins to activate, that of herd immunity or group immunity.
When there are many people who have already been infected with the virus, they no longer have anywhere to go and the virus disappears, it is as if the entire population has become immune, it is not that everyone is protected against the disease but simply by probability no longer there are circumstances for the virus to infect the few susceptible people out there. The problem is over.
Well, why not bet on immunity herd?
There are countries that did it and are regretting it.
There is a way to calculate this and it is a truly ridiculous formula, it is not advanced math. In the case of mumps that has a contagion between 12 and 18, each person can infect between 12 and 18 people on average, you put this number in the formula and it comes out as between 92% and 94%, that is, between 92% and 94% of the population must be exposed to the virus and become ill so that the virus stops finding victims to infect. This last sentence is figurative because viruses, of course, are not intelligent and are not looking for someone to annoy, but well it means that you have to allow the virus to run freely through the population and infect a very large fraction of people so that only it stops. This solution is obviously foolish and irresponsible.
And what about the Covid-19 pandemic?
The problem is that other variables need to be introduced into the formula to account for this group immunity issue.
Other factors such as the social circumstances of each country, a country like Sweden, for example, or Norway with a high standard of living, with a very small population, is not the same as countries where the population naturally tends to crowd out of necessity, for example in transport to get around, because if in a subway car with 100 people only two are susceptible, if you put those two susceptible people in a car with 100 people and 98 of those people have had the virus and some of them still have it active, the probability of these two people being infected is enormous, especially if they have to make two or more trips a day. In these crowded cars, they are sure to get infected.
Therefore herd immunity is not feasible in these circumstances.
There are research journals that are dedicated to this type of thing, such as the Journal of Epidemiology that several research papers have published in recent months where it is intended to calculate what would be the percentage of the population that would have to be exposed to the virus for it to be reached group immunity in a country.
The first estimates were very extreme, in some places they said that with the data we have from this or that country, with 10% of the population that is exposed to the virus we would already have group immunity, and in other cases, in other estimates, data of up to 70% have been offered and in the data that have been obtained in closed environments, for example in the San Quintín prison in California, they indicate that very high percentages are needed. In the San Quintín prison, a micro epidemic began inside the prison that stopped until more than 60% of the people had been exposed to the virus.
If we translate this to the whole of society, the result is that we would need a huge number of people around the world to become infected for herd immunity to start working.
If we try to do this very gradually it may happen, we still don’t know, that we run into another problem. There is a suspicion that perhaps the immunity acquired through a Covid-19 vaccine is temporary, lasting a few months or a year. If this is true, we cannot count on a vaccine that supports us in betting on group immunity by gradually exposing the population, it will never work, because people who are now immune to the virus within a year will no longer being immune, and that creates new risks because if you were asymptomatically ill the first time, there is no guarantee that the same will happen the second time.
There are cases that suggest that a second infection can seriously intervene
If you bet on herd immunity as happened in the case of Sweden, you can face a real disaster, Sweden for example and Norway are two countries with a truly high standard of living, not only in terms of money, in economic terms, but also in terms of quality of life, they are two very comparable societies, only that Norway opted for social distancing, isolation, etc… and Sweden did not, and the number of deaths per 100,000 inhabitants in Sweden was ten times higher than the number of deaths per 100,000 inhabitants in Norway. In Sweden, there were 58.12 deaths per 100,000 inhabitants until the end of a study that was published in a major journal, while in the same interval there were only 5.23 deaths per 100,000 inhabitants in Norway.
If we project this on a large scale then one of two, or it goes very slowly exposing people little by little to the virus and that can produce the problem that I mentioned before, that people are again susceptible to the virus and we would never end the pandemic, or we allow people to get infected easily and that can make the numbers jump up 10, 15, 20 times and then if the hospitals are going to saturate and we will have truly terrible scenes.
So it is not the time to bet on group immunity, it does not work at this time, it will work when we have a vaccine, even if the vaccine has a short life, with an appropriate administration of people’s exposure to the virus it could win the battle.
With the vaccine it seems that we are going to have at least one year of protection, things are much easier, we simply establish a revaccination plan similar to the flu but against Covid-19 every year, and with that, we will end the epidemic.
So ignore the people who say that you can bet on herd immunity, it does not work, do not listen to rumors, what appears on social networks, which as well as they are wonderful to inform are also wonderful to misinform. Better listen to the health authorities, listen to the experts and remember the recommendation, calm down, and if we have a way to win the battle against Covid-19 what we need is patience and discipline, nothing more.
Eppur Si Muove
