محمد شهریاری

This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α 2 (0, 1]. We study the stability of equilibrium points, including the disease-free equilibrium (Ef ), and the infected steady-state equilibrium (Ee) using the stability theorem of Fractional Differential Equations. The model is also analyzed under certain conditions, and it is shown that the disease-free equilibrium is locally asymptotically stable. Additionally, the extended Barbalat’s lemma is applied to the fractional-order system, and a suitable Lyapunov functional is constructed to demonstrate the global asymptotic stability of the infected steady-state equilibrium. To validate the theoretical results, a numerical simulation of the problem is conducted.