Numerical investigation of a wireless sensor network epidemic model with $ \alpha $-stable noise: A case study

Hassan Tahir; Anwarud Din; Wajahat Ali Khan; Mati ur Rahman; Hassan Tahir; Anwarud Din; Wajahat Ali Khan; Mati ur Rahman

doi:10.3934/math.2025908

AIMS Mathematics

2025, Volume 10, Issue 9: 20312-20345. doi: 10.3934/math.2025908

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Research article

Numerical investigation of a wireless sensor network epidemic model with $ \alpha $-stable noise: A case study

1.
MSU-BIT-SMBU Joint Research Center of Applied Mathematics, Shenzhen MSU-BIT University, Shenzhen, China
2.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
3.
Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
4.
Department of Mathematics, University of Malakand, Chakdara 18800, KPK, Pakistan
5.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

Received: 01 July 2025 Revised: 27 August 2025 Accepted: 29 August 2025 Published: 05 September 2025
MSC : 60G51, 60H10, 92D30

This study examines a stochastic susceptible-exposed-infected-recovered-vaccinated $ ({\mathbf S} {\mathbf E}_1 {\mathbf E}_2 {\mathbf I} {\mathbf R} {\mathbf V}) $ model exhibiting the dynamics of the computer virus within the wireless sensor networks (WSNs) while considering the unpredictability of nodes and the impact of anti-virus measures. The model is formulated with reasonable assumptions, and the stochastic stability is performed with a derivation of a six-dimensional Fokker-Planck equation. To obtain an analytical representation of the probability density functions, a scheme is developed and subsequently implemented in MATLAB. The behavior of the model around the quasi-endemic state is numerically investigated, which reflects the main objective and unique novelty of the present work. On the basis of various parameter settings, graphical illustrations of the model are presented showing the authenticity of the analytical results and complex aspects of the phenomenon. The paper concludes with a brief summary of the study and important insights for future research.
- computer virus model,
- wireless sensor networks,
- Lévy noise,
- Fokker-Planck equation,
- numerical simulation
Citation: Hassan Tahir, Anwarud Din, Wajahat Ali Khan, Mati ur Rahman. Numerical investigation of a wireless sensor network epidemic model with $ \alpha $-stable noise: A case study[J]. AIMS Mathematics, 2025, 10(9): 20312-20345. doi: 10.3934/math.2025908

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Abstract

This study examines a stochastic susceptible-exposed-infected-recovered-vaccinated $ ({\mathbf S} {\mathbf E}_1 {\mathbf E}_2 {\mathbf I} {\mathbf R} {\mathbf V}) $ model exhibiting the dynamics of the computer virus within the wireless sensor networks (WSNs) while considering the unpredictability of nodes and the impact of anti-virus measures. The model is formulated with reasonable assumptions, and the stochastic stability is performed with a derivation of a six-dimensional Fokker-Planck equation. To obtain an analytical representation of the probability density functions, a scheme is developed and subsequently implemented in MATLAB. The behavior of the model around the quasi-endemic state is numerically investigated, which reflects the main objective and unique novelty of the present work. On the basis of various parameter settings, graphical illustrations of the model are presented showing the authenticity of the analytical results and complex aspects of the phenomenon. The paper concludes with a brief summary of the study and important insights for future research.

References

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