Dynamical Behaviour of Fractional Order SEIR Mathematical Model for Infectious Disease Transmission
نویسندگان
1 Department of Statistics, Payame Noor University (PNU), Tehran, Iran,
2 Department of Mathematics, Maragheh University, Maragheh, Iran.
3 Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
doi
10.30473/coam.2023.64849.1210چکیده
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.
