Since the first peak on April 19, 2021, the second wave of COVID-19, which began around February 11, 2021, has wreaked havoc on India, with daily cases nearly tripling. The epidemic evolution in India is particularly difficult due to regional inhomogeneities and the transmission of multiple coronavirus strains. We looked at some fundamental concepts of Mathematical modelling of virus transmission in the ongoing second wave in India and its states until October 31, 2021, as well as Mathematical modelling of COVID-19 in the present epidemic situation from the start of the control strategy outbreak.According to an exponential fit of recent data, the infection rate is likewise significantly higher than the prior wave. The features of COVID-19 mathematical modelling are then investigated, and four COVID-19 model examples are offered in this work.