As a part of public health measures to contain corona virus disease 2019 (COVID-19), several countries have imposed lockdown restrictions which resulted in unstable economies. Now, the world is preparing to find different solutions to open up the economy while simultaneously containing the COVID-19.   In this regard, a few concepts like, “basic reproduction number” (R₀), “effective reproduction number” (R_e) and “herd immunity” applicable for any infectious disease outbreaks are important.  A clear scientific definition of R₀, R_e and herd immunity may be worth revisiting, to correctly understand novel proposals suggested to control the COVID-19 outbreak.  The difference in the definitions are so subtle that it may miss the attention of rigorous peer review process and careful scrutiny of editorial boards of even reputed journals.  For example, a recent publication highlighted the misuse of the term ‘rate’ as in case-fatality rate in publications related to COVID-19 [1].  The scientific definition of the term ‘rate’ has a notion of time and should not be used in cross-sectional studies.  Again, in another related publication, the issue of wrong assumptions for distribution of COVID-19 incidence rates with ‘binomial’ or ‘normal’ instead of ‘Poisson’ distribution for computation of confidence intervals was brought out [2].  The aim of this article is to highlight the importance of correct usage of scientific definitions related to R₀, R_e and ‘herd immunity’.

 A recent publication discussed the issue of potential use of face shields in the community for containment of COVID-19 [3]. In their narration, the authors defined R₀ as “effective reproduction number” when it should have been “basic reproduction number”.  In the modelling with SEIR, i.e., Susceptible, Exposed, Infected, Recovered, two parameters R₀ (basic reproductive number) and R_e (effective reproductive number) give us information about the effectiveness of control measures (Table 1) [4,5]. Both R₀ and R_e are dimensionless numbers and exclude new cases produced by secondary cases.  For example, a similar SIR modeling was used to illustrate the dynamics of the coronavirus pandemic in Italy and make some global predictions [6]. The zero in “R₀” means that it is estimated when there is zero immunity in the population even though not everyone will necessarily be susceptible to infection.

Current estimates of R₀ for COVID-19 are believed to be about 2·2 [7] and can range from 2 to 3. With the estimate of 2.2 for R₀, if 80% of the population is susceptible, then R_e will be 1.76, (2.2 x 0.8).  The R_e can be reduced by reducing the number of susceptible individuals.  Obviously, the number of susceptible individuals will be reduced by an increased pool of recovered patients with protective natural immunity or by vaccination.  The R₀ can be reduced by public health measures such as social distancing with lockdown, preventing congregations, mass gatherings and similar interventions including the use of face shields. The rationale for using face shields is that infection can be transmitted via respiratory droplets (>5 μm), aerosols (≤ 5 μm) or submicron aerosol (<1 μm) exhaled from infected individuals. Submicron virus-containing aerosols can be transferred deep into the alveolar region of the lungs, where immune responses seem to be temporarily bypassed [8].  In an open letter to the WHO, 239 scientists from 32 countries have claimed that the Covid-19 coronavirus is airborne [9]. This issue of potential aerosol transmission is of serious concern during presymptomatic/asymptomatic stage [10].  Hence, face shields can potentially reduce transmission in the community setting.  The implicit goal of face shields alone or in combination with other non-vaccination interventions is to interrupt transmission by reducing the R₀ to less than 1. The face shields attempt to reduce the transmission rate, but they have no effect on the recovery rate. Obviously, face shields do not increase the immune status of the population.  Hence, the authors proposing the face-shield solution were actually referring to “basic reproduction number”, R₀, not the “effective reproduction number”, R_e, in the context of their narration [3].

Another important aspect in the present context is “herd immunity” as there is an indication that some policy makers are relying on it as a solution to go hand-in-hand while opening up their economies.  For example, some policy makers even suggested that the detection of antibodies to COVID-19 could serve as the basis for an “immunity passport” or “risk free certificate” that would enable individuals to travel or to return to work.  However, such a concept did not get the support from the World Health Organization. Herd immunity occurs when a significant proportion of the population is immune by some mechanism, resulting in protection for susceptible individuals who are not immune. Herd immunity is actually ‘herd protection’ from scientific standpoint as it gives protection to vulnerable population.  The herd immunity threshold is the proportion of a population that needs to be immune in order for an infectious disease to become stable in that community and is given by the formula [11]

Thus, with the current estimate of R₀ for COVID-19 being about 2.2, the herd immunity threshold will be 54.5%. If the threshold for herd immunity is surpassed, then R_e will be <1 and the epidemic will not be sustained.  This is an important measure used in immunization programs with a primary aim to eradicate the infection.  At present without vaccination, immunity can be expected only by recovery from infection.  In other words, that proportion of the population according to the estimate for R₀, 54.5% should get infected and then recover with protective immunity (IgG seroconversion) to achieve herd immunity.  In addition, such a strategy will put several vulnerable people at risk for serious complications of the infection including mortality. A recent review indicated that recovery from COVID-19 might confer immunity against reinfection, at least temporarily, but several questions remain unanswered [12].  The essential questions are: Does immunity occur after recovery from COVID-19 infection?; why some patients seem not to develop humoral immune response?; what is the durability of neutralizing antibodies?; does robust IgG response correspond with immunity?.   A recent, nationwide, population-based seroepidemiological study showed that the seroprevalence was 5% (95% confidence interval, 4.7 to 5.4).  Spain is one of the European countries most affected by the COVID-19 pandemic [13].  An accompanying commentary stated that any proposed approach to achieve herd immunity through natural infection is not only highly unethical, but also unachievable [14]. Hence, relying on herd immunity conferred only by natural immunity is not a scientific approach.

In summary, scientific definitions of R₀ and R_e should be noted and care must be taken not to use them interchangeably as they have distinct implications with regard to control measures for the COVID-19 outbreak and attempts to reopen the hampered economies.  Relying on herd immunity without vaccination is not a scientific solution in these circumstances.

The author declared no conflicts of interest

Srinivas Mantha, MD:  This author conceived the idea and written and finalized the manuscript.

Authors thank Venkat R Mantha, MD, FFARCSI, Anesthesiologist, Houston, TX for thoughtful comments on the manuscript.