Lévy impact on the transmission of worms in wireless sensor network: Stochastic analysis

Abstract

This manuscript addresses the security challenges wireless sensor networks (WSNs) face due to their operational limitations. The primary challenge stems from the infiltration of worms into the network, where one infected node could uncontrollably propagate the malware to neighboring node(s). First, we proposes a stochastic system based on Lévy noise to explain the spread of worms in WSNs. Then, we establish a unique positive global solution for the proposed model. We also examine the presence and potential extinction of worms within the networks. The results reveal that random environmental perturbations can confine the spread of worms and that the deterministic model tends to overestimate the worms’ spreading capacity. Using different parameter sets, the study obtains approximate solutions to validate these analytical findings and demonstrate the effectiveness of the suggested SEIRS system. The findings of the work reveal that the proposed model surpasses existing models in mitigating worm transmission in WSNs. Our inference suggests that the transmission dynamics of the system are influenced by both white noise and Lévy noise.

Keywords

• Sensor networks
• Stochastic epidemic model
• Lévy jump
• Persistence
• Performance analysis