Stability Analysis of Worm Propagation in Wireless Sensor Network Model Utilizing Fractal-Fractional Operator

Wireless sensor networks have been extensively studied for their potential applications in both civil and military domains. However, due to their inherent resource constraints, sensor nodes are highly susceptible to cyber threats, particularly worm attacks, which pose significant security challenges. This study explores the dynamics of potential worm attacks within wireless sensor networks using a compartmental epidemic model. The model analyzes the temporal evolution of worm propagation while effectively capturing both spatial and temporal aspects. We determine the reproduction number and equilibrium of the system, with the local stability assessed using the Jacobian matrix. The linear growth and Lipschitz conditions are used to establish the existence and uniqueness of the solution. Furthermore, the Hyers–Ulam stability of the proposed model is also evaluated within the context of the fractal-fractional operator. Finally, a numerical method is developed to investigate the dynamic behavior of the wireless sensor network model under fractal-fractional orders, providing valuable insights into its robustness and security against potential worm attacks.