Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks

Abstract

Due to inherent operating constraints, wireless sensor networks (WSNs) need help assuring network security. This problem is caused by worms entering the networks, which can spread uncontrollably to nearby nodes from a single node infected with computer viruses, worms, trojans, and other malicious software, which can compromise the network’s integrity and functionality. This article discusses a fractional SE1E2IR{\mathsf{S}}{{\mathsf{E}}}_{1}{{\mathsf{E}}}_{2}{\mathsf{I}}{\mathsf{R}} model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. To illustrate our analytical conclusions, we ran numerical simulations.

Keywords

• epidemic model
• wireless sensor networks
• fractional derivative
• differential operator
• computational method