Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks
An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R0...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/3935750 |
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| author | Zhongxue Chang Haijun Jiang Shuzhen Yu Shanshan Chen |
| author_facet | Zhongxue Chang Haijun Jiang Shuzhen Yu Shanshan Chen |
| author_sort | Zhongxue Chang |
| collection | DOAJ |
| description | An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations. |
| format | Article |
| id | doaj-art-997ca5ad1ec8493fae378bb3791b8d4b |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-997ca5ad1ec8493fae378bb3791b8d4b2025-08-20T02:10:19ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/39357503935750Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex NetworksZhongxue Chang0Haijun Jiang1Shuzhen Yu2Shanshan Chen3College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaAn Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations.http://dx.doi.org/10.1155/2021/3935750 |
| spellingShingle | Zhongxue Chang Haijun Jiang Shuzhen Yu Shanshan Chen Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks Discrete Dynamics in Nature and Society |
| title | Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks |
| title_full | Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks |
| title_fullStr | Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks |
| title_full_unstemmed | Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks |
| title_short | Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks |
| title_sort | dynamic analysis and optimal control of iscr rumor propagation model with nonlinear incidence and time delay on complex networks |
| url | http://dx.doi.org/10.1155/2021/3935750 |
| work_keys_str_mv | AT zhongxuechang dynamicanalysisandoptimalcontrolofiscrrumorpropagationmodelwithnonlinearincidenceandtimedelayoncomplexnetworks AT haijunjiang dynamicanalysisandoptimalcontrolofiscrrumorpropagationmodelwithnonlinearincidenceandtimedelayoncomplexnetworks AT shuzhenyu dynamicanalysisandoptimalcontrolofiscrrumorpropagationmodelwithnonlinearincidenceandtimedelayoncomplexnetworks AT shanshanchen dynamicanalysisandoptimalcontrolofiscrrumorpropagationmodelwithnonlinearincidenceandtimedelayoncomplexnetworks |