Stochastic modeling of worm propagation in PLC-based industrial systems with general incidence and Lévy noise

Abdulwasea Alkhazzan, You Guoqiang, Wanna Zhou, Sayed Murad Ali Shah and Yassine Sabbar

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: The Fourth Industrial Revolution has accelerated the integration of IIoT technologies, cyber–physical systems, and real-time automation, boosting industrial productivity while exposing critical infrastructures to self-replicating malware. To address these threats, we propose a stochastic SIQHR model (Susceptible–Infected–Quarantined–Halted–Recovered) for worm propagation in PLC-based industrial control systems. The model incorporates white noise to capture frequent fluctuations, Lévy noise for rare but severe cyber events, and a generalized nonlinear incidence to account for heterogeneous device interactions. We establish the existence, uniqueness, and positivity of global solutions, and derive conditions for malware extinction or persistence using Lyapunov functions and stopping times. Numerical simulations and parametric analyses validate the theoretical results, revealing how random disturbances and system parameters shape outbreak dynamics and resilience thresholds. This study provides a rigorous and practically relevant framework for understanding malware spread and informing adaptive cybersecurity strategies in industrial environments.

Keywords: Extinction; Persistence; Lévy noise; PLCs networks; Cybersecurity (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925015760

DOI: 10.1016/j.chaos.2025.117563

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