Assessing the impact of non‐pharmaceutical (NPI) interventions and the role of mutations on the SARS‐CoV‐2 Virus spread in India using a discrete renewal process

In recent years, the world has not suffered so much compared to the devastation caused by Covid 19. The present study aims to investigate the impact of various comprehensive and stringent interventions (as advised by the government of India) implemented to decelerate the spread of the SARS-CoV-2 virus. Studying the effects of different mutations found in India is equally important. We consider a stochastic model based on a discrete renewal process that includes various controlling measures to systematically evaluate their effects on the disease transmission dynamics through three inter-linked components. A Bayesian model has been considered for the infection cycle to observe deaths with upper and lower bounds of the total population infected (attack rates), case detection probabilities, and the reproduction number over time. The MCMC technique was adopted to analyze the data. This model is related to the widely used susceptible-infected-recovered (SIR) model, except the renewal is not expressed in differential form. In this study, we treat interventions as covariates in modeling the average reproduction number. Here, the time-varying reproduction number ($R_t$) has been assumed to be a piece-wise constant function that starts from a baseline prior, and mutations are used as covariates alongwith the NPIs.