Abstract
The susceptible-infected-recovered (SIR) epidemic model of childhood disease is analysed in this chapter with the Atanagana-Baleanu (AB) fractional operator. The considered non-linear model has been efficiently applied to describe the evolution of childhood disease in a population and its influence on the community. The Adams-Bashforth scheme is applied to find and analyse the solution for the proposed model. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the derived solution for the future fractional-order model. Two distinct explanatory cases are considered and for both cases, the simulations have been demonstrated in terms of plots. The present investigation illuminates that the AB derivative plays a vital role in the analysis and describes the behaviour of the diverse model arising in human disease.
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