### Global asymptotic stability of a networked fractional SIR model

Document Type : Research Paper

Authors

College of Science, Northwest A&F University, Yangling 712100, Shaanxi, P.R. China

10.22075/ijnaa.2024.31829.4722

Abstract

In this paper, we consider a networked fractional SIR model. After proving the existence and uniqueness of the solution, we obtain the basic reproduction number, the disease-free equilibrium point and the endemic equilibrium point. By constructing the Lyapunov function, we show that the endemic equilibrium is globally asymptotically stable when the basic reproduction number is greater than 1, and the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than 1. Finally, numerical simulations are carried out to verify these theoretical results. Thus, the stability theory of Laplacian diffusion is extended to the graph Laplacian model.

Keywords

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###### Articles in Press, Corrected Proof Available Online from 13 April 2024
• Receive Date: 18 September 2023
• Accept Date: 02 February 2024