Universality and herd immunity threshold : Revisiting the SIR model for COVID-19

TL;DR

This paper revisits the SIR model for COVID-19, incorporating time-dependent parameters to analyze herd immunity, re-outbreaks, and universal patterns across countries, with a focus on India’s pandemic trajectory.

Contribution

It introduces a modified SIR model with time-dependent rates, redefining key epidemiological quantities and analyzing their implications for herd immunity and re-outbreaks.

Findings

Identifies universal aspects in disease spread across countries.

Highlights the importance of herd immunity in preventing re-outbreaks.

Provides insights into COVID-19 dynamics in India.

Abstract

COVID-19 pandemic has been raging all around the world for almost a year now, as of November 1, 2020. In this paper, we try to analyze the variation of the COVID-19 pandemic in different countries in the light of some modifications to the susceptible-infected-recovered (SIR) model. The SIR model was modified by taking time-dependent rate parameters. From this modified SIR model, the basic reproduction number, effective reproduction number, herd immunity, and herd immunity threshold are redefined. The re-outbreak of the COVID-19 is a real threat to various countries. We have used the above-mentioned quantities to find the reasons behind the re-outbreak of this disease. Also, the effectiveness of herd immunity to prevent an epidemic has been analyzed with respect to this model. We have also tried to show that there are certain universal aspects in the spread and containment of the disease in various countries for a short period of time. Finally, we have also analyzed the current pandemic situation in India and have attempted to discuss the possibilities in order to predict its future behaviour using our model.