This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for the disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter τ concerns the effects of time delay and we demonstrate that the locally asymptotic stability holds for the present equilibrium. The reproduction number is brief in less than or greater than one, and it effectively is controlling the COVID-19 infection outbreak and subsequently reveals insight into understanding the patterns of the flare-up. We have included eight parameters and the least square method allows us to estimate the initial values for the Indian COVID-19 pandemic from real-life data. It is one of India’s current pandemic models that have been studied for the time being. This Covid19 SEIR model can apply with or without delay to all country’s current pandemic region, after estimating parameter values from their data. The sensitivity of seven parameters has also been explored. The paper also examines the impact of immune response time delay and the importance of determining essential parameters such as the transmission rate using sensitivity indices analysis. The numerical experiment is calculated to illustrate the theoretical results.

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This paper deals with the mathematical modeling of the second wave of COVID-19 and verifies the current Omicron variant pandemic data in India. We also we discussed such as uniformly bounded of the system, Equilibrium analysis and basic reproduction number R0. We calculated the analytic solutions by HPM (homotopy perturbation method) and used Mathematica 12 software for numerical analysis up to 8th order approximation. It checked the error values of the approximation while the system has residual error, absolute error and h curve initial derivation of square error at up to 8th order approximation. The basic reproduction number ranges between 0.8454 and 2.0317 to form numerical simulation, it helps to identify the whole system fluctuations. Finally, our proposed model validated (from real life data) the highly affected five states of COVID-19 and the Omicron variant. The algorithm guidelines are used for international arrivals, with Omicron variant cases updated by the Union Health Ministry in January 2022. Right now, the third wave is underway in India, and we conclude that it may peak by the end of May 2022.

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