A Dynamic Countermeasure-Based Worm Propagation Model in Wireless Sensor Networks: Critical Threshold Analysis and Validation of Benign Worm Effectiveness

In this paper, we propose an innovative i-SIR model to characterize the co-propagation dynamics of malicious worms (“bad worms”) and defensive worms (“good worms”) in wireless sensor networks (WSNs)—where “bad worms” refer to malware that invades sensor nodes to steal data, disrupt communication, or paralyze network functions, while “good worms” are benign programs designed to repair infected nodes, block “bad worm” intrusion, and build immune barriers. The model is designed to comprehensively analyze worm spread and its countermeasures in the complex and resource-constrained WSN environments, especially addressing the critical threat of “bad worms”: in WSNs widely used for environmental monitoring, industrial control, and smart agriculture, “bad worm” outbreaks can lead to irreversible data loss, large-scale node failure, and even cascading damage to physical systems connected to the network. Through rigorous mathematical analysis, we derive the basic reproduction number R0, which serves as a critical threshold determining the extinction or persistence of worm propagation, and further explore its sensitivity to key network parameters such as node density, communication range, and energy constraints that are inherent to WSNs. Numerical simulations confirm the theoretical validity of R0 and demonstrate that the i-SIR model is superior to classical statistical immune models in controlling both the speed and scale of worm outbreaks—specifically, it reduces the worm outbreak speed by 50% and curbs the final infection scale by 60%. Furthermore, we investigate the impact of the infection rate ratio between bad and good worms on propagation dynamics, considering temporal variations in worm activity patterns. Results reveal that reducing the infection rate ratio between bad and good worms significantly suppresses the virulence and the scale of malicious worm spread, with more pronounced effects in densely deployed networks. This work provides a robust theoretical foundation for designing dynamic defense strategies in WSNs, highlighting the efficacy of deploying benign worms as active countermeasures against cyber-physical threats and offering performable insights for optimizing the timing and density of good worm deployment in real-world sensor network operations.