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.

中文翻译：

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一类具有时间分数阶导数的反应-扩散多群 SIR 流行病模型的全局动力学

本文研究了一类具有时间分数阶导数和反应-扩散的多群 SIR 流行病模型的全局动力学。本文考虑的分数阶在(0; 1]，这个过程的传播速度比布朗运动慢，导致异常子扩散。此外，考虑了广义关联函数，以便数据本身可以灵活地确定泛函首先研究了所提出系统解的存在性、非负性和最终有界性。当 R0 ≤ 1 时，提出的系统是全局渐近稳定的，而当 R0 > 1 时，提出的系统是一致持久的，并且地方性平衡点是全局渐近稳定的。最后通过数值模拟验证了理论结果。