Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs
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 propaga...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/9/929 |
| _version_ | 1797536778104602624 |
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| author | Guiyun Liu Jieyong Chen Zhongwei Liang Zhimin Peng Junqiang Li |
| author_facet | Guiyun Liu Jieyong Chen Zhongwei Liang Zhimin Peng Junqiang Li |
| author_sort | Guiyun Liu |
| collection | DOAJ |
| description | 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 <i>R</i><sub>0</sub>, 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. |
| first_indexed | 2024-03-10T12:05:38Z |
| format | Article |
| id | doaj.art-4e657e883e45484a97271ee53c2d4d18 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T12:05:38Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4e657e883e45484a97271ee53c2d4d182023-11-21T16:38:10ZengMDPI AGMathematics2227-73902021-04-019992910.3390/math9090929Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNsGuiyun Liu0Jieyong Chen1Zhongwei Liang2Zhimin Peng3Junqiang Li4School of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Mechanical and Electric Engineering, Guangzhou University, Guangzhou 510006, ChinaWith 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 <i>R</i><sub>0</sub>, 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.https://www.mdpi.com/2227-7390/9/9/929wireless sensor networksvirus mutationstability analysisoptimal control |
| spellingShingle | Guiyun Liu Jieyong Chen Zhongwei Liang Zhimin Peng Junqiang Li Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs Mathematics wireless sensor networks virus mutation stability analysis optimal control |
| title | Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs |
| title_full | Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs |
| title_fullStr | Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs |
| title_full_unstemmed | Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs |
| title_short | Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs |
| title_sort | dynamical analysis and optimal control for a seir model based on virus mutation in wsns |
| topic | wireless sensor networks virus mutation stability analysis optimal control |
| url | https://www.mdpi.com/2227-7390/9/9/929 |
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