Dynamical Behaviour of Fractional Order ‎‎SEIR‎ ‎Mathematical Model for Infectious Disease Transmission

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 ∈ (0, 1]‎. ‎We study the stability of equilibrium points‎, ‎including the disease-free equilibrium $(E_{f})$‎, ‎and the‎ ‎infected steady-state equilibrium $(E_{e})$ 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.