  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.
