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 behavior using our model.

中文翻译：

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普遍性和群体免疫阈值：重新审视 COVID-19 的 SIR 模型

截至 2020 年 11 月 1 日，COVID-19 大流行已在全球肆虐近一年。在本文中，我们尝试根据一些修改来分析不同国家 COVID-19 大流行的变化。易感感染恢复（SIR）模型。通过采用与时间相关的速率参数来修改 SIR 模型。从这个修改后的 SIR 模型中，重新定义了基本繁殖数、有效繁殖数、群体免疫和群体免疫阈值。COVID-19 的再次爆发对各国构成了真正的威胁。我们已经使用上述数量来寻找这种疾病再次爆发的原因。此外，还针对该模型分析了群体免疫预防流行病的有效性。我们还试图表明，在短期内，各国对疾病的传播和遏制具有某些普遍性。最后，我们还分析了印度当前的大流行情况，并试图讨论可能性，以便使用我们的模型预测其未来的行为。