The effect of the Caputo fractional difference operator on a new discrete COVID-19 model

Abderrahmane Abbes; Adel Ouannas; Nabil Shawagfeh; Giuseppe Grassi

doi:10.1016/j.rinp.2022.105797

The effect of the Caputo fractional difference operator on a new discrete COVID-19 model

Results Phys. 2022 Aug:39:105797. doi: 10.1016/j.rinp.2022.105797. Epub 2022 Jul 6.

Authors

Abderrahmane Abbes¹, Adel Ouannas², Nabil Shawagfeh¹, Giuseppe Grassi³

Affiliations

¹ Department of Mathematics, The University of Jordan, Amman, 11942, Jordan.
² Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi, 04000, Algeria.
³ Dipartimento Ingegneria Innovazione, Universita del Salento, Lecce, 73100, Italy.

Abstract

This study aims to generalize the discrete integer-order SEIR model to obtain the novel discrete fractional-order SEIR model of COVID-19 and study its dynamic characteristics. Here, we determine the equilibrium points of the model and discuss the stability analysis of these points in detail. Then, the non-linear dynamic behaviors of the suggested discrete fractional model for commensurate and incommensurate fractional orders are investigated through several numerical techniques, including maximum Lyapunov exponents, phase attractors, bifurcation diagrams and $C_{0}$ algorithm. Finally, we fitted the model with actual data to verify the accuracy of our mathematical study of the stability of the fractional discrete COVID-19 model.

Keywords: COVID-19; Chaotic dynamics; Fractional discrete SEIR model; Stability.