Background. Several mathematical representations of contagious disease COVID-19 were evolved in order to capture the pragmatic aspect of unfurling of the disease. It is learned that individuals who became receptive were infected with a rate proportional to the fraction of the individuals affected by the infection, in the comprehensive population as well as the infected individuals recuperate at a sustained rate. It is also observed that in the SIR model, all contacts impart the disease with an identical probability.

Objective. We will estimate the dynamic epidemic behaviour of inflected population for India with the use of fractional-order SIR simulations and compare our results with the results obtained for extrapolated actual cases of the infected people.

Methods. We have obtained the approximate solutions of the fractional-order Susceptible-Infectious-Recovered model within the framework of the modified Riemann–Liouville fractional differential operator using a new iterative fractional complex transform technique.

Results. The optimal values of the fractional-order SIR model parameters were identified with the use of the New Iterative Method. The dynamic incident rate with high and low reproduction number is predicted as well as the illustrated graphical with actual data is provided. To sum, the fractional calculus model for a complex system proposed here is just an indication to show what might happen if we do not control the reproduction number in the community.

Conclusions. The control measures that have already been found like swift surveillance, quarantine and social distancing means, such as face masks and closures, assisted in curtailing coronavirus transmission – estimated by the average number of people each infected individual infects, or reproduction number, to close to the level of 1 in each month.

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