A Fuzzy Fractional Order Approach to SIDARTHE Epidemic Model for COVID-19

Abstract

In this paper, a novel coronavirus SIDARTHE epidemic model system is constructed using a Caputo-type fuzzy fractional differential equation. Applying Caputo derivatives to our model is motivated by the need to more thoroughly examine the dynamics of the model. Here, the fuzzy concept is applied to the SIDARTHE epidemic model for finding the transmission of the coronavirus in an easier way. The existence of a unique solution is examined using fixed point theory for the given fractional SIDARTHE epidemic model. The dynamic behaviour of COVID-19 is understood by applying the numerical results along with a combination of fuzzy Laplace and Adomian decomposition transform. Hence, an efficient method to solve a fuzzy fractional differential equation using Laplace transforms and their inverses using the Caputo sense derivative is developed, which can make the problem easier to solve numerically. Numerical calculations are performed by considering different parameter values.