https://doi.org/10.1140/epjs/s11734-026-02170-9
Regular Article
Dynamic security in wireless sensor networks: stochastic worm propagation and Lyapunov stability in 
models
1
MSU-BIT-SMBU Joint Research Center of Applied Mathematics, Shenzhen MSU-BIT University, 518172, Shenzhen, China
2
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
3
School of Mathematical Sciences, East China Normal University, 200241, Shanghai, China
a
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Received:
22
September
2025
Accepted:
30
January
2026
Published online:
16
February
2026
Abstract
In this study, we apply the tools of stochastic calculus to address critical security challenges in wireless sensor networks (WSNs) that arise due to operational constraints, particularly focusing on the rapid spread of worms through network nodes. To achieve this, we present an innovative model that incorporates two exposed states, based on a stochastic susceptible–exposed state 1–exposed state 2–infectious–recovered (SE
E
IR) system to describe the dynamics of worm propagation within WSNs. The approach involves establishing the existence and uniqueness of an ergodic stationary distribution using suitably constructed Lyapunov functions. We find that incorporating random environmental perturbations into the model yields a more accurate representation of the dynamics than deterministic models, which often overestimate the propagation potential of these threats. Numerical simulations affirm the effectiveness of the analytical approach in understanding worm propagation within WSNs. This study not only enhances the understanding of worm propagation dynamics in WSNs but also provides a methodological framework for network security applications.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
