A treatise on herd immunity

The concept of herd immunity has recently taken the world at its stride and has garnered hopes in the masses about a possible relief devoid of medicines, vaccines to counter the COVID19 dread that has turned from a threat to a fearful reality where the social life of human has been disrupted, not to mention of the general health insecurity.

But, however much my heart would wish to rely on the herd immunity concept, the brain would just not listen! It requires proof, evidence and if that is not available, step by step logical reasoning. This and some other factors motivated me to briefly understand the concept and how it fares in the combat against COVID19.

Now, the term, herd immunity refers to the indirect protection from an infectious disease that happens when a population is immune either through vaccination or immunity developed through previous infection [1].

Trying to understand it more clearly, consider a virus infected person standing in the centre of a circular room with all doors and windows closed. Now, surrounding the person are others who are either never infected with the same virus or if infected, have recovered. Now, those who have recovered, if they surround the infected person, will have the chance of getting contaminated by the transmission agent of the virus, droplets in the case of COVID19, but, if the antibodies developed in these persons are still retained, will make the virus inactive. So, this human shield will be enough to prevent the infection to spread to the other non-infected persons. Thus immunity is developed in the population inside that particular room. Immunity developed in this way is thus called 'population immunity'[1] which means the same. But the only note of caution is that the shield remains in position till the virus is eliminated from the system of the infected person completely.

Now, please understand, if the persons who are acting as a shield had been vaccinated to develop the antibodies, the result would be the same. So the main idea behind the herd immunity is to develop enough antibody filled humans around infected persons so that they shield the other vulnerable (who have yet to develop antibodies) persons to get infected.

So, the problem boils down to finding this number of humans, or more correctly the proportion of humans, that constitute earlier mentioned cleverly camouflaged insertion, 'enough', in the preceding paragraph. Clearly, this will be based on how many persons, an infected person can transmit the disease to. The more this number is, the more will be the number of humans required for the shield. This is obvious as if a virus is non-transmittable, you will require no person to act as shield. But if it can be easily transmitted from person to person, an infected person will required to be guarded on all sides by shields to keep the transmission at check. This is called the basic reproduction number (R₀) and it varies with each new virus and each new setting of the human civilization that modifies its characteristics. Actually it measures the transmission potential of a viral infection. R₀ is the number of cases that may occur in a homogenous population as a result of infection by a single individual, when

• the population is susceptible to the disease
• before widespread immunity develops
• before immunization drive is attempted

Now, R₀ is estimated following a mathematical model and lots of inputs[2].

R₀ is affected by:

• the proportion of susceptible people at the start and the density of the population;
• the infectiousness of the organism;
• the rate of disappearance of cases by recovery or death, the first of which depends on the time for which an individual is infective;[2]

R₀ < 1 means the chance of transmission is going to reduce. If R₀ = 0.5 and there are 10 infected persons, they have the potential to infect 5 persons, who in turn can infect 2.5 persons (on the average of course, you can't infect selective parts of a person, keeping the remaining parts uninfected), who in turn will infect fewer still, leading to a single individual who will most probably cannot infect anybody and thus the infection vanishes.

R₀ = 1 means each person, infected, will infect exactly 1 person and the infection will not stop but will be maintained at a constant rate.

R₀ > 1 is pandemic situation! Each infected person will infect multiple others!

But what about the threshold size of the shield which will bar this transmission to spread?

Obviously, this will increase with R0 for any specific case. Actually it is given by

P = 1 - 1/R₀[3], where

P: threshold above which the population must be immuned to achieve herd immunity.

Thus,

R₀ = 0.5 gives P = -1, interpreted as nobody is required to act as shield, you need to give the poor virus some shield to get itself protected from infected entities. This goes for any 0 < R₀ < 1.

R₀ = 1 gives P = 0, interpreted as above without the concern about the virus.

R₀ = 2 gives P = 0.5, meaning 50% of the population must be immunized to save the other 50% susceptible populace.

If R₀ is 4, P climbs to 75%.

This must be noted that P actually increases exponentially with R₀.

But here comes the twist!

The basic reproduction number is defined when there was no immunity and only a single infection. When immunity is developed in a populace, R₀ must change dynamically. Actually, R₀ doesn't change but the transmission is indeed affected by the change in the immunized population. This is specified as the effective reproduction number, R_e, given by

R_e = R₀(1 - P_i)[2], where

P_i: immunized populace

But, though it is a twist, it is more common sense (and science) than anything as, without going to the principles behind it, the mathematics is pretty simple to understand.

For 100% population with no immunity, if the average number of persons to whom the virus can be transmitted by a single infected individual be R₀ at start,

then when it starts to develop immunity and by that can immune P_i part of the population, then the population with no immunity is reduced from 100% to 100(1 - P_i)%, effectively making the average for the same virus to be R₀(1 - P_i).

Thus, hopefully, it is obvious now that

R_e ≤ R₀.

Our aim will be to make it < 1 for harmful viruses by making P_i as high as possible.

How can this be achieved?

These can be done in the following 2 ways:

1. By vaccines, which are biological information injected into the human body, without the intention of making the body sick, but mimic the virus so that the body develops antibodies to fight it. Once developed, the antibodies will be ready to counter the virus, if they get inside the system in future. But some vaccines have a life span, after which it needs to be given a boost by another dose after a definite period.
2. By developing immunity by directly fighting off the virus, once infected. Here, not only there is the chance of getting sick, but dying also. Thus a part of the population is getting immuned after they are infected and recovered by developing the antibodies in their bodies. Those, who cannot recover will die and will reduce the size of the population but the others will develop immunity to achieve herd immunity. But this immunity will remain till the antibodies persist due to the natural virus and it will be solely controlled by the nature of the virus and the human physiology. There will be no man-made information passed to the system which is deterministic to certain extent so that the recovered person is certain how long the immunity might be sustained.

Though in principle both the methods will achieve herd immunity, but curiously enough this 2^nd measure devoid of artificial mimic approach has gained popularity among the masses while any reference is made of herd immunity.

In either of the above cases, even if we consider nobody dies, but it will require the particular P_i to be reached to make R_e < 1.
Thus, in each case P_i are subjected to a process of immunization so that (1 - P_i) remains safe without being subjected to anything adverse.
Also, in either case the period of immunity needs to be determined for a full proof combat.
In these 3 aspects, where does COVID19 lie?
In the question of determining R0, it is reported as 2.0 - 5.9[4-7].
This gives P_i = 50.0% to 83.1% ensuring safety of remaining 50.0% and 16.9% population respectively.

Now, coming to the final query of period of immunity in each case, the vaccinated cases will be deterministic and could be monitored while the natural process will not only be its opposite to say the least and more difficult to monitor but will also be unethical as we are going to sacrifice human beings for the sake of other human beings without the least responsibility for them without the guarantee of ascertaining the period of immunity to the herd. In the extreme case where risking is the only choice, I personally find no reason whatsoever for risking at least 50.0% of the population and thus the majority of the herd. Vaccine might give rise to adverse effects, infact if I am adversely affected, I will spontaneously respond adversely to this article, but logically it will be incorrect to completely depend on herd immunity by getting sick or allowing other persons to get sick.

Infact organizations like the authorities on public health, WHO "supports achieving 'herd immunity' through vaccination, not by allowing a disease to spread through any segment of the population, as this would result in unnecessary cases and deaths[8]", authority on world science, Nature discusses herd immunity "as a desirable result of wide-scale vaccination programmes[9]". Anything else might not only cost life but will have long-lasting medical and financial consequences, emphasizes the article[9]. Authorities on medical practices, John Hopkins University insists "herd immunity against COVID-19 will not be achieved at a population level in 2020, barring a public health catastrophe[10]".

National Geographic says that based on mathematics, experiences with outbreaks and emerging evidence in the ongoing one, the claim of herd immunity is just a fantasy[11]. It also adds that vaccines can only do that if they have at least 75% efficacy.

But the only silver lining is the effect of heterogeneity (non-uniformity in terms of age, mobility, social activity, disease susceptibility) in the population which might favourably[12, 13] bring down the Pi to a large extent. Infact, this might be the effect that we are seeing and not natural herd immunity by getting infected in several countries where the numbers are gradually declining. But remember, as dynamic parameters like age and activity are closely linked with heterogeneity, it might drastically change with time. But this might be utilized advantageously, as I am understanding while writing, if we induce heterogeneity in our social circles by maintaining a planned activity throughout the day as our social and professional circles permit and we must insist on these for a healthy living.

A cavaet might be in order, as being faced with a barely 1.5 years old officially recorded virus and a 0.1 year old emergency released battery of vaccines, I am questioning a method of immunity that might already have produced effects.

The benefit of wearing a mask and sanitization by washing hands and objects shared by many at frequent intervals have taught us that for combating virus, with droplet mode of transmission, this is a feasible method. So, it must be our primary mode of sustaining life and celebrating it so that man-made or natural methods of immunization will only be required as a complimentary to maintaining basic hygiene for preventing spread of infections.

Disclaimer: This is about the concept according to my interpretation, it is not peer reviewed, it can be very well discarded, readers are requested to hurl criticism and point at the flaws that they may find but the basic intent is to learn about the thing in a logical way. The article may very well be considered biased but would like a more unbiased reader to educate otherwise.

Ref: [1] Coronavirus disease (COVID-19): Herd immunity, lockdowns and COVID-19, accessed 19.1.21 

[2] “When will it be over?”: An introduction to viral reproduction numbers, R0 and Re, accessed 20.1.21 

[3] “Herd Immunity”: A Rough Guide, accessed 22.1.21

[4] Challenges in creating herd immunity to SARS-CoV-2 infection by mass vaccination, accessed 22.1.21

[5] The reproduction number of COVID-19 and its correlation with public health interventions, accessed 22.1.21

[6] Herd Immunity and Implications for SARS-CoV-2 Control, accessed 22.1.21

[7] Global convergence of COVID-19 basic reproduction number and estimation from early-time SIR dynamics, accessed 22.1.21

[8] Coronavirus disease (COVID-19): Herd immunity, lockdowns and COVID-19, accessed 24.1.21

[9] The false promise of herd immunity for COVID-19, accessed 24.1.21

[10] EARLY HERD IMMUNITY AGAINST COVID-19: A DANGEROUS MISCONCEPTION, accessed 24.1.21

[11] A 'herd mentality' can’t stop the COVID-19 pandemic. Neither can a weak vaccine., accessed 24.1.21

[12] A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2, 24.1.21

[13] Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold, accessed 24.1.21