Bifurcation analysis for some fractional SIRS models

Mahmoud M. El-Borai; Wagdy G. El-Sayed; Ahmed M. Ibrahim; Jawaher Th. Alhamdan

doi:10.62754/ais.v7i1.1223

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Published: 2026-02-19

DOI: https://doi.org/10.62754/ais.v7i1.1223

Keywords:

Dynamical systems, Fractional epidemic models, Stability, Mittag, Lefler function

Mahmoud M. El-Borai

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

Wagdy G. El-Sayed

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

Ahmed M. Ibrahim

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

Jawaher Th. Alhamdan

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, 21511 Alexandria, Egypt

Abstract

In this paper , some fractional-order epidemic models are investigated. In particular , a fractional SIRS epidemic model is considered to describe the transmission dynamics of infectious diseases incorporating memory effects through fractional derivatives . The existence and stability of equilibrium points of the proposed model are analyzed .Moreover, analytical solution are obtained for some special cases , highlighting the impact of fractional-order dynamics on the behavior of the epidemic system.