An Efficient Approach to Solving the Fractional SIR Epidemic Model with the Atangana–Baleanu–Caputo Fractional Operator

Author:

Riabi Lakhdar1ORCID,Hamdi Cherif Mountassir1ORCID,Cattani Carlo23ORCID

Affiliation:

1. Department of the Preparatory Cycle in Science and Technology, Higher School of Electrical and Energetic Engineering of Oran (ESGEE-Oran), Oran 31000, Algeria

2. DEIM, University of Tuscia, Largo dell’Universita, 01100 Viterbo, Italy

3. Department of Mathematics and Informatics, Azerbaijan University, J. Hajibeyli Str., AZ1007 Baku, Azerbaijan

Abstract

In this article, we study the fractional SIR epidemic model with the Atangana–Baleanu–Caputo fractional operator. We explore the properties and applicability of the ZZ transformation on the Atangana–Baleanu–Caputo fractional operator as the ZZ transform of the Atangana–Baleanu–Caputo fractional derivative. This study is an application of two power methods. We obtain a special solution with the homotopy perturbation method (HPM) combined with the ZZ transformation scheme; then we present the problem and study the existence of the solution, and also we apply this new method to solving the fractional SIR epidemic with the ABC operator. The solutions show up as infinite series. The behavior of the numerical solutions of this model, represented by series of the evolution in the time fractional epidemic, is compared with the Adomian decomposition method and the Laplace–Adomian decomposition method. The results showed an increase in the number of immunized persons compared to the results obtained via those two methods.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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