The dynamical behaviors of fractional-order SE[formula omitted]E[formula omitted]IQR epidemic model for malware propagation on Wireless Sensor Network

Abstract

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 SE1E2IQR epidemic model. Our proposed model introduces an isolation class (Q) and an exposure class with two distinct compartments E1 (Type 1-exposed) and E2 (Type 2-exposed). The dynamics of the network-based fractional-order SE1E2IQR 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 ℛ0 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 E0. However, the paper points out that the condition ℛ0<1 is not sufficient to eliminate the malware from the network. In addition, the direction of bifurcation at ℛ0=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.