Global dynamics for a class of reaction–diffusion multigroup SIR epidemic models with time fractional-order derivatives
Articles
Zhenzhen Lu
Beijing Jiaotong University
https://orcid.org/0000-0003-0520-8911
Yongguang Yu
Beijing Jiaotong University
Guojian Ren
Beijing Jiaotong University
Conghui Xu
Beijing Jiaotong University
Xiangyun Meng
Beijing Jiaotong University
Published 2022-01-01
https://doi.org/10.15388/namc.2022.27.25192
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Keywords

SIR epidemic model
multigroup
reaction–diffusion
fractional order
asymptotic stability

How to Cite

Lu Z., Yu Y., Ren G., Xu C. and Meng X. (2022) “Global dynamics for a class of reaction–diffusion multigroup SIR epidemic models with time fractional-order derivatives”, Nonlinear Analysis: Modelling and Control, 27(1), pp. 142-162. doi: 10.15388/namc.2022.27.25192.

Abstract

This paper investigates the global dynamics for a class of multigroup SIR epidemic model with time fractional-order derivatives and reaction–diffusion. The fractional order considered in this paper is in (0; 1], which the propagation speed of this process is slower than Brownian motion leading to anomalous subdiffusion. Furthermore, the generalized incidence function is considered so that the data itself can flexibly determine the functional form of incidence rates in practice. Firstly, the existence, nonnegativity, and ultimate boundedness of the solution for the proposed system are studied. Moreover, the basic reproduction number R0 is calculated and shown as a threshold: the disease-free equilibrium point of the proposed system is globally asymptotically stable when R0 ≤ 1, while when R0 > 1, the proposed system is uniformly persistent, and the endemic equilibrium point is globally asymptotically stable. Finally, the theoretical results are verified by numerical simulation.

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