Data on COVID-19 was obtained from the data-sharing portal covid19india.org.Information is collected on daily confirmed cases and daily testing numbers at the state level from 14th March to 17th May 2020. For calculating the test per million population at the state level, the testing numbers were extracted at the state level from the data-sharing portal covid19india.org. The figures of the population for the selected states as on 1st March 2020 has been taken from the report “Population Projection for India and States (2011–2036)” provided by National Commission for Population (NCP). HDI Index 2018 at the state level is taken from the Global Data Lab, which provides the HDI Index at the state level for all countries from 1990-2018. Per Capita Health Expenditure (PCHE) data from the National Health Profile (NHP 2019) has also been used. All the calculations for estimating Rt are done using Jupyter notebook with Python 3.
Effective reproduction Number (Rt)
Effective reproduction number (Rt,) is the mean number of infections generated during the infectious period from a single infected person at time t. The effective reproduction number may vary across locations because contact rates among people may differ due to differences in population density, cultural differences, level of immunity and restrictions imposed on the movement of the people. When Rt>1, the pandemic will spread through a large part of the population. If Rt<1, the pandemic will slow quickly before it has a chance to infect many people. Lower the value of Rt, the situation is more controllable. In general, Rt<1 is the main goal of the policy planners working in the field of epidemiology. Epidemiologists argue that tracking Rt is the only way to manage the transmission of the communicable disease. More importantly, it is useful to understand Rt at the sub-national level to manage the transmission effectively.
Bayesian estimation of Rt with quantified uncertainty
Parameter estimation with quantified uncertainty can be achieved using the Bayesian approach in the context of probabilistic epidemiological models. Bayes’ theorem expresses the full probability distribution for model parameters, such as the effective reproduction number, Rt, in terms of the probabilistic epidemiological model, given the time series for new cases6.
Bettencourt & Ribeiro’s approach has been used to calculate Rt7, as described in8 as well. The data is available on how many new people have COVID-19 based on daily new cases. This new case count gives us information about the current value of Rt. Further, the value of today’s Rt is related to the value of yesterday’s Rt- and every previous value of Rt-m. Bayes’ rule updates the beliefs about the true value of Rt based on the information of how many new cases have been reported each day.
Bayes' Theorem suggests
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)
P (k| Rt): The likelihood of observing ‘k’ new cases given Rt, time points.
P(Rt): The prior beliefs of the value of P(Rt) at the beginning of the study period
P(k): The probability of observing ‘k’ new cases for a given day
Choosing a Likelihood Function P (kt |Rt)
Given an average arrival rate of λ new cases per day, the probability of observing ‘k’ new cases is distributed according to the Poisson distribution:
![](data:image/png;base64,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)
There exists a relationship between Rt and λ.
λ = kt-1. e ɤ (Rt– 1)
Where ɤ is the reciprocal of the serial interval, and the value of the serial interval has been considered to be four days based on the most reliable findings9. Further, new cases are known; therefore, the likelihood function as a Poisson parameterized by fixing k and varying Rt can be reformulated7.
![](data:image/png;base64,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)
Input variables required for its calculation are-
- Daily number of confirmed cases at the state and national level which is taken from http://api.covid19india.org/states_daily_csv/confirmed.csv
- Serial Interval for COVID -19 is required
- Basic Reproduction Number at the initial time (14th March) (R0) is required.
Serial Interval and Incubation Period for COVID 19
Literature suggests the mean serial interval for COVID-19 ranges from 4 to 8 days (9-12). Recent analyses by9 used a much larger sample that includes up to 468 pairs, making their estimates of between 4 and 5 days which are more statistically reliable. The estimated mean serial interval is shorter than the preliminary estimates of the mean incubation period (approximately 5 days) (11,12). When the serial interval is shorter than the incubation period for infectious disease, the pre-symptomatic transmission is likely to have taken place and may occur even more frequently than symptomatic transmission13. The Indian Council of Medical Research (ICMR) also confirmed that as much as 80% of all cases could be asymptomatic based on the fact that COVID-19 tests that delivered positive results in India show that 69% of positive cases were asymptomatic, whereas 31% are symptomatic representing a ratio of 2:114. In the present study, the mean value of the serial number is considered as four days.
Basic Reproduction Number (R0)
Reproduction Number for COVID 19 at the initial stage is estimated between 2 and 315. Using the raw CDC data, the estimated value of the basic reproduction number is between 2.2 and 2.3. Another study16 estimated that the median daily reproduction number (Rt) in Wuhan had declined from 2·35 (95% CI 1·15–4·77) at one week before travel restrictions were introduced on 23rd January 2020, to 1·05 (0·41–2·39) one week after. So, a basic reproduction number (R0) of 3 at the initial stage of infection (14th March in our case) will yield good results for the present study. However, the estimate of the effective reproduction number using the current adopted Bayesian approach is independent of the initial assumed basic reproduction number.
Multiple Linear Regression
Multiple linear regression analysis was carried out to quantify the impact that state-level factors made in the decline of Rt. The difference created in the value of Rt during lockdown phase (between 2nd April and 9th May) for states acts as the dependent variable, and state-level factors namely Tests Conducted (between 2nd April and 9th May) per million, HDI, PCHE and Good Governance Index as independent variables. All independent variables were normalized between 0 and 1 to bring all the values of independent variables in the dataset to a common scale15.