The vaccine explained with a musical


We expect scientists to provide certainties, exact numbers.

How reliable is a test when it gives a positive answer? How effective is a certain type of mask, even if moistened by breath? What is the value of Rt, the reproduction index of the epidemic, today in Italy?

When will herd immunity be achieved? What is the efficacy of a vaccine? And how effective is it in reducing or preventing the possibility of transmitting the virus?

How many variants of the coronavirus are there? And how effective are vaccines against these variants? How many viruses are yet to be eradicated?

We expect public health issues to receive an undisputable and straight answer.

Should we vaccinate first the elderly, who pay the highest price in terms of fatalities, or young people, who have the right to study and to a greater mobility? Or rather certain specific  categories of workers, who cater for our primary needs?

We would like the answers to these questions to be at least as reliable as those we are used to in, say, the weather forecasts, which determine those everyday dilemmas such as cycling to work or take the umbrella.

But current scientific results cannot provide that sort of certainty, yet!

It is estimated that the order of magnitude of viruses living permanently in the human body is 100 trillion, or 1 followed by 14 zeros, that is 100,000,000,000,000,000. Many are useful, some are harmless, some are dangerous.

Our Knowledge of the world is not complete and is can never be 100% exact.

For this reason, scientists often have difficulty making firm predictions about the future. However, they can calculate numerical ranges and state, with a certain level of confidence/belief, that the actual values are within those predicted ranges. This does not give us foolproof certainty, but it does at least allow for making predictions with a known measurable margin of error. For this reason, it is important to understand that every estimate always has a margin of uncertainty associated with it. The smaller the uncertainty, the narrower the confidence interval and the more informative the estimates and predictions.

The only certainty is that science indicates what is the best strategy among the available ones. This remark is crucial in understating the role of Science in Society and Policies.

And today the best strategy is: Don't hesitate to get vaccinated when your turn will come!

We do this to protect ourselves but also to help protect others. And after you get vaccinated, remember: keep using your mask!

Sharing is caring: make the difference in the age of the virus

Frequently Asked Questions

1. D: What is herd immunity?

A: By herd immunity, or rather community immunity, we mean a general resistance to contagion on the part of a population where only a portion of people are immunized, either because they have contracted the disease or, as is more often the case, because they have been vaccinated.

With herd immunity, non-immunized people are protected from infection because the infectious agent (virus or other) does not find a sufficient number of individuals capable of becoming infected and transmitting the virus.

The percentage of the immunized population required to achieve herd immunity varies depending on many conditions, one of the most important of which refers to the characteristics of the infectious agent.

In the case of viruses, the threshold of community immunity is generally never below 60-80% and can be, in some cases, even as high as 95%, as in the case of measles.

2. D: Is it possible for herd immunity to develop through administration of the SARS-CoV-2 vaccine?


In order to understand whether community immunity for SARS-CoV-2 (the virus that causes COVID-19 disease) can be achieved, there are still some points to be clarified.

In particular, we do not know exactly the mechanisms by which our bodies react to the virus or how long immunity lasts after infection or vaccine.

The latest data on the spread of immunity offer no reassurance that community immunity will be achieved soon through direct contagion, as the percentage of people immune to SARS-CoV-2 is still low. Moreover, the price to be paid in terms of lives would be very high. More reasonable seems to be the possibility of achieving community immunity with a vaccination campaign as wide as possible so that no pockets of population remain where the virus can continue to replicate and survive. But even then, some questions remain.

The first is how long the vaccine will be able to produce enough immunity to defend against subsequent infections. Preliminary data are very promising in this regard.

The second question is whether the vaccine will not only immunize the person but also make him or her unable to transmit the virus. Preliminary studies (not yet published) carried out in England and Israel go towards an encouraging direction.

In any case, even if the threshold of community immunity is not reached, a substantial number of immune people is an important goal to achieve because it would contribute to reducing the rate of spread of the disease, and avoid the risk of new health emergencies, such as the overloading of hospitals, straining the health system to its limit.

3. D: Can a person become contagious because of the vaccine?

A: NO.

Vaccines for SARS-CoV-2 approved so far in Europe use one or more coronavirus proteins as the immunizing agent (called antigen), so live or attenuated virus is not used.

These proteins, which are not infectious agents, serve to teach our immune system to recognize the virus before it can cause COVID-19 disease or to alleviate its most severe symptoms by producing the antibodies needed to neutralize it in time.

In this way, when our body comes into contact with the virus, it is already trained to recognize it and blocks it before it can spread through the whole organism causing the disease for which it is responsible.

4. D: Can I avoid protecting myself with masks and spacing after vaccination?

A: NO.

During the development of the vaccines approved to date, the study protocol was to evaluate their efficacy in preventing SARS-CoV-2 infection from causing the more severe symptoms of COVID-19 disease. For the Moderna and Pfizer-BioNTech vaccines, the efficacy in blocking the onset of a severe form of COVID-19 was about 95%. The efficacy of a vaccine is the percentage reduction of disease in a vaccinated group of people compared to an unvaccinated group.

However, the studies did not measure the vaccine's ability to prevent infection (specific studies are ongoing).

Therefore, vaccinating decreases the probability of becoming seriously ill, but we still do not know if you can still be contagious in case you have the coronavirus inside you.

Waiting for confirmation in this regard, it is therefore necessary to continue to wear the mask, maintain physical distance and follow the rules of hygiene.

5. D: What are "R with zero" and "R with t"?

A: The term "R with zero," R0, “R nought” denotes the basic reproduction index of a virus.

R0 represents the number of new infections - called secondary infections - that, on average, are caused by a single case over its entire period of infectivity, in a fully susceptible population. This index depends on three main elements: the characteristics of the virus (understood as the ability to transmit from one person to another), the number of contacts that each infected person has with other members of the population, the protection that each individual adopts with respect to contagion (masks, spacing, quarantines, etc.). It follows that R0 is different according to the context (e.g., the average number of contacts between people is not the same in Pavia and Paris does not remain stable even within the same context (e.g., due to changes in the adoption of individual protective measures) and could still change even under the same conditions, in relation to virus mutations (e.g., due to the emergence of new viral variants). In addition, over time, an increasing number of individuals become resistant to infection, either because they have recovered and become immune or because they have been vaccinated. This means that not all the contacts that each infected person will have will be with susceptible individuals. If anything, if each infected person only encountered immune or protected individuals, he or she could not transmit the infection to anyone.

For this reason, it is almost more important to assess and monitor the Rt parameter ("R with t").

The Rt index is a close relative of R0; in fact, it represents the average number of new infections (cases of disease) caused by each infected individual during its period of infectivity, in a given population and at a given time t. In other words, this parameter, in epidemiology, indicates the potential transmissibility of an infectious disease at a given time. For this reason it is more suitable to measure the state of the epidemic at a late stage, when part of the people are immune having already developed antibodies, others have been vaccinated, and various approaches to mitigate transmission are still in place. In a sense we can think of R0 as the special case of Rt when t=0, i.e. at the beginning of the epidemic phase. R0 and Rt are difficult to measure, but we know that if Rt (or R0) is less than 1, the number of cases tends to decrease because the next generation of newly infected will be, on average, less numerous than the current generation.

6. D: To estimate the threshold of community immunity, do you use R0 or Rt ?

A: To estimate the threshold for community immunity, either R0 or Rt can be used. If we use R0, it means that we are estimating what percentage of the population must be immune for the infection not to be transmitted if no restrictive measures were used. In other words: in order to return to the normal condition of the pre-epidemic era. We can call this the threshold of initial community immunity. In the case of Covid, if the estimate of R0 = 4 were confirmed, we could say that if at least 75% of the population were immune, then, under certain assumptions about how members of the population socially interact, we would no longer need masks, spacings, curfews, etc.

It should be mentioned in this regard that the spread of new variants of the virus often results in a change in the ability of the virus itself to transmit from one person to another. This leads to a change in R0 and thus also in the initial community immunity threshold.

If instead we calculated the threshold of community immunity using Rt, the value we would obtain would correspond to the percentage of the population that would have to be immune at that precise moment (thus with the restrictive measures in place, the level of social interaction present and the variants circulating) to stop the epidemic.

7. D: Are the values we hear and read about vaccine efficacy, R0, and Rt certain?

A: NO.

Efficacy values as well as R0 and Rt values are estimates obtained with statistical models that are approximate descriptions of reality.

These values therefore have an associated margin of error that mostly depends on the assumptions underlying the model, the data available to calculate it, and their quality.

As with exit-pool forecasts in which the number of people estimated to vote for a certain candidate is associated with a "range" which, technically, is called a confidence interval, a "range" is also calculated for estimates of effectiveness, R0 and Rt, and the value that is normally reported is the value in the center of that range.

As an example, the 95% confidence interval (meaning that we are 95% confident that the true value of efficacy is contained within this interval), for the Pfizer-BionTech vaccine is estimated to be between 90.3% and 97.6%, while for the Moderna vaccine it is estimated to be between 89.3% and 96.8%. 

8. D: Does the threshold for herd immunity depend on vaccine efficacy?

A: NO.

The threshold for herd immunity refers only to the percentage of the population that must be immune in order for all individuals, even those who are not immune, to be protected. In the text of the song we have referred to the formula for calculating the Herd Immunity Threshold (HIT).

However, if we want to achieve herd immunity through vaccination, we must take into account the effectiveness of the vaccine in preventing the transmission of the virus and calculate the vaccine coverage threshold.

Since the efficacy of the vaccine is never 100%, the number of people to be vaccinated to reach the threshold of herd immunity is higher than the threshold itself. If, for example, the efficacy of the vaccine in blocking transmission were 95%, by vaccinating all the people in a population, only 95% of them would not be able to transmit the virus. It follows that if a vaccine has an efficacy that we denote with E, the formula to be used to calculate the vaccination coverage threshold, i.e. the vaccination coverage required to achieve herd immunity, is:

Vaccination coverage = HIT/E

that is:

Vaccination coverage = (1 – 1/R0)/E

Where, remember, HIT = (1 - 1/ R0). So if R0 = 4, we can calculate that HIT = (1 - 1/4) = 0.75 (rounding up) this means that we must ensure that 75% of the population is unable to transmit the virus (threshold of herd immunity). It follows that, if we use a vaccine with 95% efficacy, we must vaccinate a proportion of the population equal to HIT/E = 0.75/0.95 = 0.79 (vaccination coverage threshold). In other words, it is not enough to vaccinate 75% of the population (herd immunity threshold) but it is necessary to vaccinate 79% of the population (vaccination coverage threshold).

We note that the estimate of the R0 value of 4 for Italy does not yet take into account the variants of the virus. It is likely that the variants will lead to an increase in the value of R0 and this will determine a consequent increase in the threshold of community immunity.

We report below, as an example, the estimate of the vaccine coverage required if we were to use individually the two vaccines that currently have the highest effectiveness: Pfizer-BionTech and Moderna (approved in Europe and Italy). This means that for the other vaccines the vaccination coverage is estimated to be higher than the values reported below: we leave the reader to do the computation.

Moreover, the various vaccines approved by the competent authorities will be used together according to their availability so the computation to estimate the vaccination coverage needed to achieve community immunity become more complex.

The Pfizer-BionTech vaccine has an efficacy estimate of 0.95 - or 95% - with a confidence interval that has a minimum efficacy of 90.3% and a maximum of 97.6%. This is a 95% confidence interval in the sense that we have 95% confidence that the vaccine's efficacy is between 90.3% and 97.6% (Source: New England J. Medicine, article published on 10.12.20 entitled: "Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine").

Assuming that the vaccine has equal efficacy in protecting against infection and in blocking transmission of the virus, if only this vaccine were used, the vaccination coverage threshold would be 0.79 = 0.75/0.95 (assuming that R0 is equal to 4 and remembering that we always approximate by excess in this case).

The Moderna vaccine has an estimated efficacy of 0.941 - or 94.1% - with a confidence interval ranging from a minimum of 89.3% to a maximum of 96.8%. This interval also has a 95% confidence level (Source: New England J. Medicine, article published on 12/30/20 entitled "Efficacy and Safety of the mRNA-1273 SARS-CoV-2 Vaccine").

Always making the assumption of equal protective and transmissive efficacy, if only this vaccine were used, the vaccination coverage threshold would be 0.8 (assuming R0 is equal to 4).

Scientific Committee

  • Antonella Viola - Immunologist, University of Padova  and Director  Istituto di Ricerca Pediatrica
  • Antonietta Mira - Statistician, Università della Svizzera italiana, Director, Data Science Lab, University of Insubria and Queensland University of Technology (adjunct professor)
  • Armando Massarenti - Journalist and Philosopher, membro della commissione per l’etica e l’integrità della ricerca del CNR
  • Furio Honsell - computer scientist and politician, University of Udine; University of Udine Vice Chancellor, 2001-2008; Udine  Mayor, 2008-2018; Friuli Region Councillor & member of Regional Health Commission 2018 - ; Member of the  Political Board of WHO-Healthy Cities Network, 2014-2018
  • Paolo Giudici – Statistician, University of Pavia and PI of the Covid-19 “PERISCOPE” H2020 project 
  • Dario Gregori -  Biostatistician, University  of Padova and  Director of the Biostatistics, Epidemiology and Public Health Unit
  • Daniele Cassani - Mathematician, University of Insubria and President of the Riemann International School of Mathematics, RISM
  • Raffaele Bruno - Infectivologist, University of Pavia and Director of Clinica di Malattie Infettive Fondazione IRCCS Policlinico San Matteo di Pavia
  • Guido Bertolini - Epidemiologist, Istituto di Ricerche Farmacologiche Mario Negri  IRCCS, Responsabile del Laboratorio di Epidemiologia Clinica
  • Riccardo Bellazzi - Bioengineer, University of Pavia and Director of the Department of Ingegneria Industriale e dell'Informazione, Università di Pavia and Responsabile del Laboratorio di Informatica e Sistemistica per la Ricerca Clinica, Istituti Clinici Scientifici Maugeri, Pavia
  • Alan Agresti - Distinguished Professor Emeritus of Statistics, University of Florida


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