Stochastic modeling of malware propagation on reduced scale-free topology-based wireless sensor networks: dynamics, resilience, and countermeasures

Volume 35, Issue 4, pp 388--410 https://dx.doi.org/10.22436/jmcs.035.04.02

Publication Date: May 31, 2024 Submission Date: November 26, 2023 Revision Date: December 20, 2023 Accteptance Date: May 05, 2024

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Authors

Ch. B'ayir - Condensed matter physics laboratory, Department of physics, Faculty of sciences, Abdelmalek Essaâdi University, B.P 2121, Tétouan, Morocco. M. Essouifi - Condensed matter physics laboratory, Department of physics, Faculty of sciences, Abdelmalek Essaâdi University, B.P 2121, Tétouan, Morocco. Y. El Ansari - IRF-SIC Laboratory, Faculty of Sciences, Ibn Zohr University, Agadir, 80000, Morocco. A. Achahbar - Condensed matter physics laboratory, Department of physics, Faculty of sciences, Abdelmalek Essaâdi University, B.P 2121, Tétouan, Morocco. J. El Khamkhami - Condensed matter physics laboratory, Department of physics, Faculty of sciences, Abdelmalek Essaâdi University, B.P 2121, Tétouan, Morocco.

Abstract

In this paper, we present an approach to model the stochastic spread of malware within a wireless sensor network (WSN). The network is characterized as a reduced scale-free topology, exhibiting just two average degrees. Our work delves into the realm of stochastic epidemic modeling building upon its deterministic counterpart \cite{18}. We leverage two distinct methodologies, namely the discrete-time Markov chain (DTMC) and the Stochastic Differential Equation (SDE) techniques, to explore the temporal dynamics of our proposed model. Our investigation extends to analyzing how various model parameters influence infection within WSNs. Through Monte Carlo simulations and the Euler-Maruyama discretization scheme, we validate the credibility of our two stochastic models by demonstrating their congruences and their fluctuations around the deterministic solution reliant on nonlinear coupled ordinary differential equations (ODEs). This comparison is guided for the best understanding of the stochastic fluctuations effect in the dynamics of the spread of malware in WSNs. Our findings offer valuable insights, indicating that the network exhibits enhanced resilience against network failures and more balanced energy consumption when specific countermeasures are implemented. This probabilistic framework proves both meticulous and systematic, providing a profound understanding of the intricate randomness inherent in the behavioral patterns of malware within WSNs.

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Keywords

• Stochastic spread of malware
• wireless sensor network
• reduced scale-free topology
• discrete time Markov chain
• stochastic differential equation
• Monte Carlo simulations\sep Euler-Maruyama discretization scheme

MSC

•  60G99
•  92-04
•  60H10

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