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Abstract：
The global pandemic due to the outbreak of COVID-19 ravages the whole world for more than two years in which all the countries are suffering a lot since December 2019. In this article characteristics of a multi-wave SIR model have been studied which successfully explains the features of this pandemic waves in India. Origin of the multi-wave pattern in the solution of this model is explained. Stability of this model has been studied by identifying the equilibrium points as well as by finding the eigenvalues of the corresponding Jacobian matrices. In this model, a finite probability of the recovered people for becoming susceptible again is introduced which is found crucial for obtaining the oscillatory solution in other words. Which on the other hand incorporates the effect of new variants, like delta, omicron, etc in addition to the SARS-CoV-2 virus. The set of differential equations has been solved numerically in order to obtain the variation of susceptible, infected and removed populations with time. In this phenomenological study, some specific sets of parameters are chosen in order to explain the nonperiodic variation of infected population which is found necessary to capture the feature of epidemiological wave prevailing in India. The numerical estimations are compared with the actual cases along with the analytic results.
摘要：
由于COVID-19的爆发而导致的全球大流行肆虐全球超过两年，自2019年12月以来，所有国家都遭受了巨大的痛苦。在本文中，研究了多波SIR模型的特征，该模型成功地解释了印度大流行波的特征。解释了该模型解中多波模式的起源。通过确定平衡点以及找到相应的雅可比矩阵的特征值，研究了该模型的稳定性。在这个模型中,引入了恢复的人再次变得易感的有限概率，换句话说，这对于获得振荡解至关重要。另一方面结合了新变体的效果，像三角洲，omicron,除了SARS-CoV-2病毒。为了获得易感的变化，已经对微分方程组进行了数值求解，随着时间的推移，被感染和移除的人群。在这个现象学研究中,选择了一些特定的参数集来解释感染人群的非周期性变化，这对于捕获印度流行的流行病学浪潮的特征是必要的。将数值估计与实际情况以及分析结果进行比较。
