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Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Author

Listed:
  • Guiyun Liu

    (School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China
    Both authors contributed equally to this work.)

  • Jieyong Chen

    (School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, China
    Both authors contributed equally to this work.)

  • 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)

  • Junqiang Li

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

Abstract

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R 0 , the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

Suggested Citation

  • Guiyun Liu & Jieyong Chen & Zhongwei Liang & Zhimin Peng & Junqiang Li, 2021. "Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs," Mathematics, MDPI, vol. 9(9), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:929-:d:541095
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    References listed on IDEAS

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    1. Elena Gubar & Vladislav Taynitskiy & Quanyan Zhu, 2018. "Optimal Control of Heterogeneous Mutating Viruses," Games, MDPI, vol. 9(4), pages 1-18, December.
    2. 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.
    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. Farrah Kristel Batista & Angel Martín del Rey & Araceli Queiruga-Dios, 2020. "A New Individual-Based Model to Simulate Malware Propagation in Wireless Sensor Networks," Mathematics, MDPI, vol. 8(3), pages 1-23, March.
    5. Huang, Da-Wen & Yang, Lu-Xing & Yang, Xiaofan & Wu, Yingbo & Tang, Yuan Yan, 2019. "Towards understanding the effectiveness of patch injection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    6. Jose Diamantino Hernández Guillén & Ángel Martín del Rey & Roberto Casado Vara, 2020. "On the Optimal Control of a Malware Propagation Model," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
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    Cited by:

    1. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    2. Yingying Su & Zijing Qiu & Guiyun Liu & Zhongwei Liang, 2022. "Optimal Control of PC-PLC Virus-Mutation and Multi-Delay Propagation Model in Distribution Network CPS," Mathematics, MDPI, vol. 10(16), pages 1-24, August.
    3. Guiyun Liu & Zhimin Peng & Zhongwei Liang & Xiaojing Zhong & Xinhai Xia, 2022. "Analysis and Control of Malware Mutation Model in Wireless Rechargeable Sensor Network with Charging Delay," Mathematics, MDPI, vol. 10(14), pages 1-28, July.

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