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Dynamical Behaviour of Fractional Order SEIR Mathematical Model for Infectious Disease Transmission | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 2، دوره 9، شماره 1، مرداد 2024، صفحه 35-48 اصل مقاله (971.4 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2023.64849.1210 | ||
| نویسندگان | ||
| Reza Akbari* 1؛ Leader Navaei2؛ Mohammad Shahriari3 | ||
| 1Department of Mathematics, Payame Noor University (PNU), Tehran, Iran | ||
| 2Department of Statistics, Payame Noor University (PNU), Tehran, Iran, | ||
| 3Department of Mathematics, Maragheh University, Maragheh, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fractional calculus؛ Caputo derivatives؛ SEIR model؛ Lyapunov function؛ Stability | ||
| مراجع | ||
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