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. 2025 May 16;20(5):e0322391.
doi: 10.1371/journal.pone.0322391. eCollection 2025.

Mathematical analysis of the dynamics of cyberattack propagation in IoT networks

Yousef AbuHour  1 , Sadeq Damrah  2 , Mahmoud H DarAssi  1 , Zuhur Alqahtani  3 , Areej Almuneef  3
Affiliations

Mathematical analysis of the dynamics of cyberattack propagation in IoT networks

Yousef AbuHour et al. PLoS One. .

Abstract

The growing threat of cyberattacks is a severe concern to governments, military organizations, and industries, especially with the increasing use of Internet of Things (IoT) devices. To tackle this issue, researchers are working on ways to predict and prevent these attacks by studying how malware spreads. In this study, we use a discrete-time approach to better model how cyberattacks spread across IoT networks. We also focus on the role of firewalls, developing a strategy to optimize their effectiveness in slowing down the spread of malware. Additionally, we analyze the reproduction number's sensitivity and explore the proposed discrete system's local and global stability. The model was simulated and analyzed using Python packages, providing practical solutions to improve cybersecurity in IoT networks. These insights are supported by numerical simulations based on real-world data.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. Illustration of model compartment links.
Fig 2
Fig 2. Simulated network for 2000 devices.
Fig 3
Fig 3. Simulated network for interactions between attackers and targets (330 devices).
Fig 4
Fig 4. Comparison of stochastic (Monte Carlo) and deterministic solutions for the dynamics of attackers and IoT devices.
Fig 5
Fig 5. The reproduction number of attacking population analysis.
Fig 6
Fig 6. The reproduction number RTarget of targeted population analysis.
Fig 7
Fig 7. PRCC elasticity analysis of R0Target.
Fig 8
Fig 8. PRCC of R0a analysis.
Fig 9
Fig 9. Sensitivity analysis of the reproduction number R0 to key parameters.
Fig 10
Fig 10. Sensitivity analysis of Ma (malicious attackers) to βa.
Fig 11
Fig 11. R0>1 compartment analysis when we have successful attack.
Fig 12
Fig 12. R0<1 compartment analysis when the cyberattack failed.
Fig 13
Fig 13. The proportion of compromised devices during a cyber IoT attack.
Fig 14
Fig 14. An optimal control strategy for firewall protection fp
Fig 15
Fig 15. Comparison of attacker and target populations with and without control strategy.
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