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The global pandemic due to the outbreak of COVID-19 ravages the whole worldfor more than two years in which all the countries are suffering a lot sinceDecember 2019. In order to control this ongoing waves of epidemiologicalinfections, attempts have been made to understand the dynamics of this pandemicin deterministic approach with the help of several mathematical models. In thisarticle characteristics of a multi-wave SIR model have been studied whichsuccessfully explains the features of this pandemic waves in India. Stabilityof this model has been studied by identifying the equilibrium points as well asby finding the eigen values of the corresponding Jacobian matrices. Complexeigen values are found which ultimately give rise to the oscillatory solutionsfor the three categories of populations, say, susceptible, infected andremoved. In this model, a finite probability of the recovered people forbecoming susceptible again is introduced which eventually lead to theoscillatory solution in other words. The set of differential equations has beensolved numerically in order to obtain the variation for numbers of susceptible,infected and removed people with time. In this phenomenological study, finallyan additional modification is made in order to explain the aperiodicoscillation which is found necessary to capture the feature of epidemiologicalwaves particularly in India.

Study of COVID-19 epidemiological evolution in India with a multi-wave SIR model