R₀ of COVID-19 and its impact on vaccination coverage: compared with previous outbreaks

ABSTRACT

Background: Vaccination has been known to reduce morbidity and mortality of infectious diseases since the emergence of the 1st vaccine in the 18th century. That’s why global efforts are directed toward finding a vaccine for COVID-19 in order to eliminate its threat.

The current pandemic of COVID-19 has changed the world affecting all fields significantly as a result of the preventive measures including locking down, social distancing, obligatory mask wearing, stopping flights, etc. The medical field is clearly the most significantly affected starting from altering most of the research efforts toward the new virus passing through the inadequate number of physicians as well as unavailable intensive care unit (ICU) beds. In order to break the restricted preventive measures, we need to minimize the newly infected cases which can be achieved by reaching adequate herd immunity. Moreover, calculating the basic reproduction number (R0) of COVID-19 is crucial to estimate the herd immunity threshold (Ic).

Methods: In this review, we searched PubMed for studies that mentioned the R0 of COVID_19, SARS, and MERS as well as measles, Zika and dengue virus to calculate the herd immunity threshold and the minimal vaccination coverage.

Results: The value of R0 could vary for the same disease and consequently the herd immunity threshold as well as the vaccination coverage. The R0 of COVID-19 ranged widely through various articles from 1.4 to 6.68. As a result, the herd immunity threshold would range from 28.57% to 85.03%. However, the vaccination coverage depends also on the effectiveness of the vaccine which is still unknown.

Conclusion: The calculations of vaccination coverage include many variables such as the R0 of the disease, Ic that depends on that value as well as sensitivity and specificity of the vaccine itself.

KEYWORDS:

• Basic reproduction number
• herd immunity
• vaccination coverage
• COVID-19

Introduction

Basic reproduction number (R0)

Estimating the basic reproduction number (R₀) of a certain infectious disease is a crucial step to identify its contagiousness depending on the human behavior as well as the biological characteristics of its pathogen. Consequently, the value of R₀ varies according to the pathogen itself as well as the local socio-behavioral and environmental circumstances.¹ According to Anderson et al.² R₀ can be defined as “the average number of infections that is produced in a susceptible host population when an infected individual is introduced into that population”.² It can be calculated mainly depending on three interconnected parameters, namely the duration of contagiousness, the possibility of infection per contact as well as the contact rate.³ The value of R₀ gives information about the state of the infection whether it will likely result in an epidemic when R₀ > 1 or will probably recede when R₀ < 1.²

Vaccination

Vaccination is defined by Merriam-Webster dictionary as a preparation of a microorganism that has been killed or attenuated to increase immunity against a particular disease.⁴ The first vaccine that was developed in history was the smallpox vaccine. It was manufactured in the year 1796 as a live-attenuated vaccine. Since then, vaccines for several diseases were developed and new types of vaccines have emerged. Different types of vaccinations include killed vaccines, live attenuated vaccines, purified proteins or polysaccharides, and genetically engineered vaccines.⁵ Since vaccines were introduced they have reduced death and disability caused by infectious diseases; a study was carried in the states showed a more than 90% decrease (between the 20th century and the year2016) in the cases caused by 9 different vaccine-preventable diseases including smallpox. Some of these diseases have been eliminated or reached a 99% reduction.⁶

Impact on ICU admission

Ritter et al.⁷ used a simple statistical model which predicted that during the exponential phase of the novel coronavirus, ICU admissions will rise above the capabilities of the health system causing a crisis.⁷ While in New South Wales, Fox et al.⁸ predicted that the pinnacle interest in ICU beds was a gauge to be 6,965 ICU beds with a serious mitigation strategy (797% of the ICU limit preceding COVID-19).⁸ The compartmental model evaluated that under a strategy that could diminish transmission by 33%, at any rate; 5,109 ICU beds would be required (584% of the earlier ICU limit). Therefore, immunization of preventable illnesses and Intensive care medicine has been consistently connected. For example, a single-center study in a Chinese pediatric ICU showed that 9.3% of all admissions were due to vaccine-preventable infections.⁹ Consequently, introducing vaccines to communicable diseases significantly reduces the need for ICU beds. For instance, Thompson et al.¹⁰ showed that introducing the influenza virus vaccine had a significant effect on ICU admission.¹⁰ Among hospitalized patients who were flu positive, flu immunization was connected to a 59% abatement in the odds of ICU affirmation and with shorter ICU lengths of remain (LOS).

Methods

Search

We manually searched PubMed for articles discussing the basic reproduction number of the current pandemic SARS-CoV2 as well as other infectious diseases including measles, dengue virus, SARS, and MERS. Then, we extracted the values of R₀ from selected studies to calculate the herd immunity as well as vaccination coverage.

Calculations

The value of R0 was used to calculate the herd immunity threshold (I_c) using the following formula:

$I_c=\frac{R0-1}{R0}$

Then, the I_c was used to calculate the vaccination coverage (V_c) depending on the effectiveness of the vaccine (E) as follows:$V_c=\frac{I_c}{E}$.¹¹

Results

We reviewed the basic reproduction number of various infectious diseases in six articles which were further classified according to the mode of transmission into airborne, bloodborne, and sexually transmitted diseases as shown in Table 1.^12–17 Additionally, 4 studies carried out in different countries were reviewed regarding the R0 of COVID-19.^12,15,18,19

Table 1. The table compares between the R₀ of different infections according to the mode of transmission

Mode of transmission	Pathogen	R0
Airborne	SARS	2.9^Citation12
	MERS	<1^Citation13
	Measles	14^Citation14
	H1N1	1.9005^Citation15
Bloodborne	Ebola	1.3522^Citation15
Vector borne	Zika	2.33^Citation16
	Dengue	1.70^Citation16
Sexually transmitted	HIV	36.75^Citation17

R₀ of previous infection outbreaks

The value of the basic reproduction number (R₀) varies according to the type of pathogen as well as the method of measurement being used. Regarding the pathogen, Villela et al.²⁰ compared the R₀ value of both Zika and dengue viruses in Rio de Janeiro, Brazil.²⁰ The value of R₀ varied even between the subtypes of dengue virus as R₀ of DENV-3 = 1.70 (95% CI: 1.50–2.02) and R₀ of DENV-4 = 1.25 (95% CI: 1.18–1.36) while it reached 2.33 (95% CI: 1.97–2.97) for Zika virus. Moreover, the basic reproduction number may be different for the same pathogen according to time, place, and method of measurement. For instance, the R₀ of the dengue virus reached 27.2 (95%CI: 14.8, 49.3) during the early phase of the epidemic in Easter Island, Chile.⁹ On the other hand, Guerra et al. (2017) showed the wide variability of R₀ values of measles through literature with different methods of measurement for each study, e.g., R₀ = 4.6, 13, and 27 according to Broutin et al. (2005), Merler et al. (2014) and Hooker et al. (2011), respectively.^14,21 Similarly, the R₀ value of HIV in rural South West Uganda fluctuated from 0.45 in 1992 reaching 36.75 in 2008.¹⁷ Furthermore (Table 1) shows the variability of the R₀ value comparing between different modes of transmission.

R₀ of COVID-19

The outbreak of COVID-19 started in Wuhan, China causing an epidemic in China later on. At the start of the epidemic, the R₀ of COVID-19 in Wuhan was calculated at 2.2, with an average incubation period of 5.2 days.¹⁸ Then, the infection spread from China overseas and several studies were conducted to calculate R₀ in different countries. Liu et al. (2020) reported the R₀ as a range of values between 1.5 and 6.68. Additionally, the average R₀ was calculated from 12 different studies to be 3.28 and the median to be 2.79 which is higher than the estimates of the WHO which ranged between 1.4 and 2.5.¹⁹ Moreover, the basic reproductive number (R₀) was estimated in several countries outside China using different methods and the results were almost equal to the average R₀ found in China. The overall outbreak R₀ in Peru was approximated to 2.97 according to Roman et al. Also, the stochastic model (a tool used for estimating probability distributions of potential outcomes)‎ was used in the Republic of Korea and Italy to estimate the R₀ during the outbreak in the country and it reached 3.2 in Korea and 3.3 in Italy.

This high R₀ value for the new coronavirus is very alarming for the rapid spread of the disease and gives an idea about the rapid transmissivity of the infection causing a widespread pandemic. On the other hand, the R₀ value of the two previous coronaviruses which elicited two epidemics earlier (in 2003 and 2012, respectively) namely the SARS (Severe Acute Respiratory Syndrome) and MERS (Middle–East Respiratory Syndrome) viruses were a bit lower. Regarding SARS, the R₀ was estimated at 2.9 by analyzing data from 1600 cases at the early phase of the epidemic in Hong Kong,¹² while it was <1 in the case of the MERS outbreak.¹³ This emphasizes the importance of restriction measures to halt the spread of this new virus which is turning into a world-dominating pandemic.

R₀ and herd immunity

In spite of the variability of R₀ values, it is still important for calculating the vaccination coverage needed to achieve herd immunity (the indirect protection of susceptible individuals brought about by the presence of immune individuals in the population).¹¹ To clarify, providing vaccination for the whole population is hard to achieve. However, vaccinating a specific proportion of the population could work as a protective wall for other susceptible persons against getting the infection. This proportion can be calculated depending on the basic reproduction number (R₀) of the disease as follows:

$I_c=\frac{R0-1}{R0}$

where (I_c) is the herd immunity threshold (the fraction of the population that should be vaccinated, if present, to achieve the herd immunity).¹¹ The relation between the basic reproduction number and the herd immunity threshold can be illustrated through the curve drawn in (Figure 1).

Figure 1. The curve shows the relation between the basic reproduction number and herd immunity threshold.

For example, If the R₀ of DENV-4 = 1.25 as mentioned above, then 20% of the population at least should be vaccinated.¹³

$\frac{1.25-1}{1.25}=\hspace{0.17em}\frac{0.25}{1.25}=\hspace{0.17em}20\%$

On the other hand, the percentage will jump to 96.3% in the case of measles with R₀ = 27.

$\frac{27-1}{27}=\hspace{0.17em}\frac{26}{27}=96.3\%$

Therefore, the higher the R₀, the more the vaccination coverage needed to establish required herd immunity as shown in (Figure 1, Figure 2):

Figure 2. Herd immunity threshold (Ic) of the disease according to the basic reproduction number (R0).

Minimal vaccination coverage for COVID-19

The minimal vaccination coverage against the novel coronavirus can be calculated by estimating the value of herd immunity threshold (I_c) which in turn depends on the value of R₀. For example, when the value of R₀ = 2.97, 3.2, or 6.68, the proportion of the population that should be vaccinated will be I_c = 66.32%, 68.75%, or 85.03%, respectively (Figure 3).²⁰

Figure 3. Herd immunity threshold (Ic) of COVID-19 depending on different values of the basic reproductive number (R0).

As explained by Plans-Rubió (2012), these percentages will be valuable if only the vaccine efficacy is 100% which is simply impossible to achieve.²¹ As a result, the vaccine effectiveness (E) should be put into consideration to calculate the vaccination coverage (Vc) as follows:

$V_c=\frac{I_c}{E}$

Not only that but we should also increase the percentage to overcome the false positive and true negative results of serological tests by estimating the additional vaccination coverage (Va) as follows:

$V_a=\frac{P_c-P}{E}$

where (P) is the prevalence of positive results and (Pc) is the critical prevalence of positive results which can be calculated through the following equation depending on the specificity (Sp) and sensitivity (Se) of the vaccine:

$P_c=I_{c}Se+\left(1-I_c\right)\left(1-Se\right)$

Consequently, once the vaccine is provided, the basic reproduction number (R0,), herd immunity threshold (Ic), and vaccine effectiveness (E), specificity (Sp), and sensitivity (Se) should be estimated to determine the least percentage of the population that should receive that vaccine in order to achieve herd immunity essential for protecting susceptible persons.

Discussion

R0 of COVID-19 compared with previous outbreaks

The value of R0 of COVID-19 varied widely from 1.4 to 6.68 with a mean (from mentioned values) of 2.98 which makes the current pandemic higher than previous outbreaks mentioned above including SARS, dengue, Zika, H1N1 with exception to measles that had the highest value reaching R0 = 13. As a result, the vaccination coverage needed to achieve the herd immunity against COVID-19 will be more than that of other diseases regardless of additional factors related to the vaccine itself.

The variability of R0 and herd immunity

The values of R₀ and the subsequent calculation of values required for herd immunity are not absolute. The simplest method used for the calculation depends on the “core model – homogeneous population” which assumes that the whole population is homogeneous disregarding the socioeconomic and ethnic differences which can affect the virus distribution and spread. Therefore, the calculations of herd immunity based on these models are not always accurate. As regards the R₀ value of the virus, several factors can cause variability in the numbers thus altering the measurements and calculations. Two studies were conducted in UK and Germany proved that the social distancing and control measures applied in the community have great effects on the R₀ value which unfortunately means that all calculations performed can have a margin of error as many variables affecting the outcomes are not taken into consideration.

Summary

The basic reproduction number as well as the herd immunity threshold is essential to calculate the minimal vaccination coverage to help in protecting susceptible persons from catching the disease. However, there are some other factors that we should be aware of while calculating this percentage. In the case of the novel coronavirus, the value of R₀ is more than 1 which means it is spreading causing infection to more people. Herd immunity aims to make R₀ = 1 maximally. As a result, the state of infection will be stable, and no preventive measures will be needed.

Disclosure of potential conflicts of interest

No potential conflicts of interest were disclosed.

Additional information

Funding

No funding was received.