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

Akbari, Reza; Navaei, Leader; Shahriari, Mohammad

doi:10.30473/coam.2023.64849.1210

Document Type : Research Article

Authors

¹ Department of Mathematics‎, ‎Payame Noor University (PNU), Tehran‎, ‎Iran

² Department of Statistics, Payame Noor University (PNU), Tehran, Iran,

³ Department of Mathematics‎, ‎Maragheh University‎, ‎Maragheh‎, ‎Iran‎.

10.30473/coam.2023.64849.1210

Abstract

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.

Keywords

Main Subjects

Mathematical Modeling

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

References

References

Articles in Press, Accepted Manuscript Available Online from 04 October 2023

Articles in Press, Accepted Manuscript
Available Online from 04 October 2023