Lyapunov-based analysis and worm extinction in wireless networks using stochastic SVEIR model

In this study, we present a novel stochastic SVEIR (Susceptible–Vaccinated–Exposed–Infectious–Recovered) model specifically designed to analyze worm propagation in wireless sensor networks (WSNs) influenced by both white and Lévy noises, along with a general incidence rate. By incorporating stochastic elements, our model closely mimics real-world network conditions, and we demonstrate its robustness by proving the existence of a global positive solution using Lyapunov functions and stopping times. We introduce a reproduction number to delineate the necessary condition for worm extinction, along with a modified reproduction number aimed at identifying the conditions for the existence of an ergodic stationary distribution (ESD). To demonstrate the practical implications of our theoretical findings, we develop a numerical scheme using the Milstein method and conduct extensive MATLAB simulations. Our results highlight the significant impacts of various parameters on model dynamics, providing critical insights to bolster network security against worm attacks. This research addresses key gaps in the current literature by integrating stochastic components into the SVEIR framework, making substantial contributions to the field of cybersecurity. By offering a structured methodology for mitigating worm threats in WSNs, our study sets the stage for future advancements in enhancing network protection.