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Analysis of Time-Delay Epidemic Model in Rechargeable Wireless Sensor Networks

Author

Listed:
  • Guiyun Liu

    (School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China)

  • Junqiang Li

    (School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China)

  • Zhongwei Liang

    (School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China)

  • Zhimin Peng

    (School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China)

Abstract

With the development of wireless rechargeable sensor networks (WRSNs), many scholars began to attach attention to network security under the spread of viruses. This paper mainly studies a novel low-energy-status-based model SISL (Susceptible, Infected, Susceptible, Low-Energy). The conversion process from low-energy nodes to susceptible nodes is called charging. It is noted that the time delay of the charging process in WRSNs should be considered. However, the charging process and its time delay have not been investigated in traditional epidemic models in WRSNs. Thus, the model SISL is proposed. The basic reproduction number, the disease-free equilibrium point, and the endemic equilibrium point are discussed here. Meanwhile, local stability and global stability of the disease-free equilibrium point and the endemic equilibrium point are analyzed. The addition of the time-delay term needs to be analyzed to determine whether it affects the stability. The intervention treatment strategy under the optimal control is obtained through the establishment of the Hamiltonian function and the application of the Pontryagin principle. Finally, the theoretical results are verified by simulations.

Suggested Citation

  • Guiyun Liu & Junqiang Li & Zhongwei Liang & Zhimin Peng, 2021. "Analysis of Time-Delay Epidemic Model in Rechargeable Wireless Sensor Networks," Mathematics, MDPI, vol. 9(9), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:978-:d:544444
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    References listed on IDEAS

    as
    1. Guiyun Liu & Baihao Peng & Xiaojing Zhong & Xuejing Lan, 2020. "Differential Games of Rechargeable Wireless Sensor Networks against Malicious Programs Based on SILRD Propagation Model," Complexity, Hindawi, vol. 2020, pages 1-13, July.
    2. Zhu, Linhe & Zhou, Xiao & Li, Yimin, 2019. "Global dynamics analysis and control of a rumor spreading model in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    3. Guiyun Liu & Baihao Peng & Xiaojing Zhong & Lefeng Cheng & Zhifu Li, 2020. "Attack-Defense Game between Malicious Programs and Energy-Harvesting Wireless Sensor Networks Based on Epidemic Modeling," Complexity, Hindawi, vol. 2020, pages 1-19, September.
    4. Zhu, Linhe & Guan, Gui, 2019. "Dynamical analysis of a rumor spreading model with self-discrimination and time delay in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    5. Zizhen Zhang & Yougang Wang, 2017. "Bifurcation Analysis for an SEIRS-V Model with Delays on the Transmission of Worms in a Wireless Sensor Network," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-15, January.
    6. Zhu, Linhe & Liu, Mengxue & Li, Yimin, 2019. "The dynamics analysis of a rumor propagation model in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 118-137.
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