Comprehensive analysis of a stochastic wireless sensor network motivated by Black-Karasinski process

Abstract Wireless sensor networks (WSNs) encounter a significant challenge in ensuring network security due to their operational constraints. This challenge stems from the potential infiltration of malware into WSNs, where a single infected node can rapidly propagate worms to neighboring nodes. To address this issue, this research introduces a stochastic $$\textsf{S}\textsf{E}\textsf{I}\textsf{R}\textsf{S}$$ S E I R S model to characterize worm spread in WSNs. Initially, we established that our model possesses a globally positive solution. Subsequently, we determine a threshold value for our stochastic system and derive a set of sufficient conditions that dictate the persistence or extinction of worm spread in WSNs based on the mean behavior. Our study reveals that environmental randomness can impede the spread of malware in WSNs. Moreover, by utilizing various parameter sets, we obtain approximate solutions that showcase these precise findings and validate the effectiveness of the proposed $$\textsf{S}\textsf{E}\textsf{I}\textsf{R}\textsf{S}$$ S E I R S model, which surpasses existing models in mitigating worm transmission in WSNs.