The basic reproduction number and herd immunity for COVID-19 in India

Objectives: To estimate the basic reproduction number and herd immunity in India relative to the viral disease COVID-19. Methods: In this study, we analyzed literature from March-2020 to January-2021, which were related to the basic reproduction number and herd immunity of COVID-19 in India. Also, we found the mean value of the basic reproduction number and herd immunity as a result. Findings: According to our study, the basic reproduction number and the percentage of the herd immunity ranged from 1.2561 to 3 and from 20% to 66%, respectively. The mean value of the basic reproduction number and the percentage of the herd immunity is 2.0546 and 51% respectively. Novelty: To the best of our knowledge, no such studies have been conducted in India.


Introduction
COVID-19 is a viral disease that has been rampant around the world since its inception. India is also not untouched by COVID-19. Even though the vaccine was produced, the cases of infection are steadily increasing. The higher population density, carelessness of people, lack of medical resources, lack of testing and tracing, are some responsible factors for the coronavirus explosion.
The second wave of the epidemic COVID-19 has caused havoc in India. The first peak of COVID-19 cases was on 16 September 2020. After that, lots of fluctuations came, but from 11 February 2021 (9353 cases), the confirmed cases began to increase. After the 1st confirmed case on 30 January 2020, on 4 April 2021, it crossed the 1 lac mark. (1) . Now, on the 13th April 2021, in the number of total confirmed cases, India holds the 1st place in the Asia and the 2nd place in the world (2) . The size of the epidemic and the rising statistics of deaths once again forced many states in India to take rigorous and drastic decisions.
The basic reproduction number (R 0 ) indicates 'the average number of secondary infectious people' generated by an infected person in a completely susceptible population. The dynamics of an epidemic are studied by the researchers and the epidemiologists by applying the compartmental model. R 0 plays a very important role to control and prevent the spread of a disease. It helps to make strategies and policies against the epidemic. It ensures that if the policies are properly implemented by the government and carefully followed by the citizens, the viral disease can be overcome easily. Levine-Tiefenbrun et al. (6) showed that the vaccination can reduce the value of R 0 .
Balbas L. et al. (7) used the formula that indicates the vaccination percentage required in the population to meet the state of herd immunity. Kadkhoda (8) mentioned that social distancing, mask wearing, and frequent hand washing are important infection prevention measures to control the epidemic COVID-19.
Steven Suan Zhu and Enahoro Iboi (9) estimated R 0 by using dynamic and statistical modeling. Ives et al. (10) applied timeseries analysis to estimate R 0 . India consists of 28 states and 8 union territories. These states and union territories are further divided into divisions, districts, tehsils, and villages. That's why the value of the basic reproduction number (R 0 ) can't be determined uniformly or applicable for all regions. It changes between a range. It depends on the various aspects like population density, availability of medical resources, the distribution of different ages into the community, awareness of the people, etc. Gennaro et al. (11) researched the attitude towards COVID-19 vaccination among healthcare professionals in Itali. Awareness and positive attitudes of people can help the government to drive vaccination campaigns successfully.

Method
The value of R 0 for COVID-19 is taken from various internet sources such as Google Scholar, MedRxiv, and other online sources. The data are presented in tabular form (see Table 1 ) for analysis of the outcome.

Data
Data collection is done by Google Scholar and MedRxiv. The keywords "the basic reproduction number for COVID-19 in India" have been searched on various internet sources. After that, 16 research papers were selected, out of which 11 research papers are related to mathematical modeling through the compartment models, 2 research papers are related to the exponential growth method, 1 research paper is related to both the exponential growth method and the epidemic model. The one-one research articles are based on the statistical distribution and the review methodology respectively.

Result and discussion
The estimated average value of the basic reproduction number R 0 is 2.0546 that is greater than one and creates a worrying situation for Indian citizens. Although, all the 16 research paper has different methods to estimate the full Di Fi do value of, yet the R 0 value more than 1.2 in all these research papers indicate a threat to citizens of India. Herd immunity is also interpreted as 'population immunity' . It is the indirect protection against a communicable disease that occurs when a community is protected either by vaccination or by protection obtained by an earlier infection. The W.H.O. (World Health Organization) approvals acquiring 'population immunity' through vaccination, by not permitting the infection to spread into any part of the community, as this may be resulted in the unnecessary patients and deaths. According to John and samuel (12) , herd immunity can be measured by testing a sample of the population for the presence of the chosen immune parameter. The percentage of herd immunity is another key factor in controlling the COVID-19 pandemic, which is linked to the basic reproduction number by the relationship: The range of R 0 varying from 1.2561 to 3 and so, the value of herd immunity percentage varies from 20% to 66% (see table 1).
https://www.indjst.org/  Figure 1 shows the strong regression relationship between the percentage of herd immunity and the percentage required to control emerging COVID-19 viral disease.

Conclusion
The estimated value of the basic reproduction number R 0 for COVID-19 in India is in a worrisome state. To reduce the spread of disease, the government of India has to impose all the controlling factors like lockdown/Janta curfew, vaccination, social distancing, wearing masks, frequent hand washing, and improving medical facilities effectively. An average immunization of 51% of the total population is necessary to reach the state of herd immunity. However, the immunity requirement for the herd must be met to prevent and control the spread of the disease. This survey mainly includes data from 2020. This study excludes recently published research papers. Thus, in the future, recently published research papers can be included to estimate the basic reproduction number and the percentage of herd immunity.

Conflict of interest
No conflict of interest exists.