A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism
As communication continues to develop, the high freedom and low cost of the communication network environment also make rumors spread more rapidly. If rumors are not clarified and controlled in time, it is very easy to trigger mass panic and undermine social stability. Therefore, it is important to...
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MDPI AG
2022-10-01
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/603 |
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| author | Linna Li Yuze Li Jianke Zhang |
| author_facet | Linna Li Yuze Li Jianke Zhang |
| author_sort | Linna Li |
| collection | DOAJ |
| description | As communication continues to develop, the high freedom and low cost of the communication network environment also make rumors spread more rapidly. If rumors are not clarified and controlled in time, it is very easy to trigger mass panic and undermine social stability. Therefore, it is important to establish an efficient model for rumor propagation. In this paper, the impact of rumor clarifiers on the spread of rumors is considered and fractional order differentiation is introduced to solve the problem that traditional models do not take into account the “anomalous propagation” characteristics of information. A fractional-order Susceptible-Infected-Removal-Clarify (SIR-C) rumor propagation prediction model featuring the clarification mechanism is proposed. The existence and asymptotic stability conditions of the rumor-free equilibrium point (RFEP) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>0</mn></msub></semantics></math></inline-formula>; the boundary equilibrium points (BEPs) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>2</mn></msub></semantics></math></inline-formula> are also given. Finally, the stability conditions and practical cases are verified by numerical simulations. The experimental results confirm the analysis of the theoretical study and the model fits well with the real-world case data with just minor deviations. As a result, the model can play a positive and effective role in rumor propagation prediction. |
| first_indexed | 2024-03-09T19:16:26Z |
| format | Article |
| id | doaj.art-b2d6eae29cff456c846cbef9c1acb449 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T19:16:26Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj.art-b2d6eae29cff456c846cbef9c1acb4492023-11-24T03:44:08ZengMDPI AGAxioms2075-16802022-10-01111160310.3390/axioms11110603A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification MechanismLinna Li0Yuze Li1Jianke Zhang2Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Post and Telecommunications, Xi’an 710121, ChinaSchool of Communication and Information Engineering, Xi’an University of Post and Telecommunications, Xi’an 710121, ChinaSchool of Science, Xi’an University of Post and Telecommunications, Xi’an 710121, ChinaAs communication continues to develop, the high freedom and low cost of the communication network environment also make rumors spread more rapidly. If rumors are not clarified and controlled in time, it is very easy to trigger mass panic and undermine social stability. Therefore, it is important to establish an efficient model for rumor propagation. In this paper, the impact of rumor clarifiers on the spread of rumors is considered and fractional order differentiation is introduced to solve the problem that traditional models do not take into account the “anomalous propagation” characteristics of information. A fractional-order Susceptible-Infected-Removal-Clarify (SIR-C) rumor propagation prediction model featuring the clarification mechanism is proposed. The existence and asymptotic stability conditions of the rumor-free equilibrium point (RFEP) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>0</mn></msub></semantics></math></inline-formula>; the boundary equilibrium points (BEPs) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>E</mi><mn>2</mn></msub></semantics></math></inline-formula> are also given. Finally, the stability conditions and practical cases are verified by numerical simulations. The experimental results confirm the analysis of the theoretical study and the model fits well with the real-world case data with just minor deviations. As a result, the model can play a positive and effective role in rumor propagation prediction.https://www.mdpi.com/2075-1680/11/11/603fractional-orderSIR modelrumor propagationstability |
| spellingShingle | Linna Li Yuze Li Jianke Zhang A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism Axioms fractional-order SIR model rumor propagation stability |
| title | A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism |
| title_full | A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism |
| title_fullStr | A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism |
| title_full_unstemmed | A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism |
| title_short | A Fractional-Order SIR-C Cyber Rumor Propagation Prediction Model with a Clarification Mechanism |
| title_sort | fractional order sir c cyber rumor propagation prediction model with a clarification mechanism |
| topic | fractional-order SIR model rumor propagation stability |
| url | https://www.mdpi.com/2075-1680/11/11/603 |
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