The dynamical behaviors of fractional-order SE1E2IQR epidemic model for malware propagation on Wireless Sensor Network

In order to investigate the effectiveness of quarantine strategy and the heterogeneity of scale-free network on epidemic spreading, this paper focuses on the investigation of a new fractional epidemiology model, namely fractional SE(1)E(2)IQR epidemic model. Our proposed model introduces an isolation class (Q) and an exposure class with two distinct compartments E-1 (Type 1-exposed) and E-2 (Type 2-exposed). The dynamics of the network-based fractional-order SE(1)E(2)IQR epidemic model are studied from the viewpoint of stability analysis and bifurcation. Firstly, by using the next-generation method, we derive the basic reproductive ratio R-0 of the proposed epidemic model, which plays an important role in determining not only the unique existence of epidemic equilibrium point E* but also the locally asymptotically stability of malware-free equilibrium point E-0. However, the paper points out that the condition R-0 < 1 is not sufficient to eliminate the malware from the network. In addition, the direction of bifurcation at R-0 = 1 is also presented. Furthermore, by graphical simulations and computations, we can evaluate the importance of parameters in the basic reproductive ratio R0 and show that the quarantine treatment plays a key role in controlling the epidemic disease. (C) 2022 Elsevier B.V. All rights reserved.