Department of Mathematics, AMNEA Group, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box 509, Boutalamine, 52000, Errachidia, Morocco.
MAIS Lab., MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box 509, Boutalamine, 52000, Errachidia, Morocco.
Sci Rep. 2022 Apr 6;12(1):5751. doi: 10.1038/s41598-022-08992-6.
We deal in this paper with a diffusive SIR epidemic model described by reaction-diffusion equations involving a fractional derivative. The existence and uniqueness of the solution are shown, next to the boundedness of the solution. Further, it has been shown that the global behavior of the solution is governed by the value of [Formula: see text], which is known in epidemiology by the basic reproduction number. Indeed, using the Lyapunov direct method it has been proved that the disease will extinct for [Formula: see text] for any value of the diffusion constants. For [Formula: see text], the disease will persist and the unique positive equilibrium is globally stable. Some numerical illustrations have been used to confirm our theoretical results.
本文研究了一类具有分数阶导数的反应扩散方程描述的扩散 SIR 传染病模型。证明了该模型解的存在唯一性和有界性。进一步，我们发现解的全局行为由基本繁殖数[Formula: see text]决定。事实上，利用李雅普诺夫直接法，我们证明了当扩散常数取任意值时，疾病将随着[Formula: see text]而灭绝。而当[Formula: see text]时，疾病将持续存在，且唯一的正平衡点是全局稳定的。我们还进行了一些数值模拟以验证我们的理论结果。
