Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes
In this paper, an SIR rumor propagation model is established with the three recovery modes that the spreader turns into a stifler under the influence of the spreader, stifler and media nonlinear rumor-refuting mechanism. Firstly, we calculate the basic regeneration number, and we determine the stabi...
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2024-11-01
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| Series: | Mathematics |
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| author | Jingping Lu Qinlong Wang Wentao Huang |
| author_facet | Jingping Lu Qinlong Wang Wentao Huang |
| author_sort | Jingping Lu |
| collection | DOAJ |
| description | In this paper, an SIR rumor propagation model is established with the three recovery modes that the spreader turns into a stifler under the influence of the spreader, stifler and media nonlinear rumor-refuting mechanism. Firstly, we calculate the basic regeneration number, and we determine the stability of the rumor-free equilibrium and the existence of the rumor-endemic equilibrium. Secondly, by applying the strict symbolic calculation methods of singular quantities, we investigate the Hopf bifurcation at the rumor-endemic equilibrium, and we determine the existence of single and double periodic solutions under certain parameter conditions. Thirdly, we discuss the practical dynamic behaviors of rumors spreading from the perspectives of the basic reproduction number and periodic solutions, especially the correlation between these two and multi-periodic oscillations. To our knowledge, such complex dynamic properties have rarely been analyzed in rumor models. |
| format | Article |
| id | doaj-art-690f93085d594049a5ca902260fd75b7 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-690f93085d594049a5ca902260fd75b72024-12-13T16:27:30ZengMDPI AGMathematics2227-73902024-11-011223371210.3390/math12233712Dynamic Analysis of Rumor Spreading Model Based on Three Recovery ModesJingping Lu0Qinlong Wang1Wentao Huang2Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, ChinaCenter for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, ChinaCenter for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, ChinaIn this paper, an SIR rumor propagation model is established with the three recovery modes that the spreader turns into a stifler under the influence of the spreader, stifler and media nonlinear rumor-refuting mechanism. Firstly, we calculate the basic regeneration number, and we determine the stability of the rumor-free equilibrium and the existence of the rumor-endemic equilibrium. Secondly, by applying the strict symbolic calculation methods of singular quantities, we investigate the Hopf bifurcation at the rumor-endemic equilibrium, and we determine the existence of single and double periodic solutions under certain parameter conditions. Thirdly, we discuss the practical dynamic behaviors of rumors spreading from the perspectives of the basic reproduction number and periodic solutions, especially the correlation between these two and multi-periodic oscillations. To our knowledge, such complex dynamic properties have rarely been analyzed in rumor models.https://www.mdpi.com/2227-7390/12/23/3712rumor spreadingSIR modelrumor-refuting mechanismHopf bifurcation |
| spellingShingle | Jingping Lu Qinlong Wang Wentao Huang Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes Mathematics rumor spreading SIR model rumor-refuting mechanism Hopf bifurcation |
| title | Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes |
| title_full | Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes |
| title_fullStr | Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes |
| title_full_unstemmed | Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes |
| title_short | Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes |
| title_sort | dynamic analysis of rumor spreading model based on three recovery modes |
| topic | rumor spreading SIR model rumor-refuting mechanism Hopf bifurcation |
| url | https://www.mdpi.com/2227-7390/12/23/3712 |
| work_keys_str_mv | AT jingpinglu dynamicanalysisofrumorspreadingmodelbasedonthreerecoverymodes AT qinlongwang dynamicanalysisofrumorspreadingmodelbasedonthreerecoverymodes AT wentaohuang dynamicanalysisofrumorspreadingmodelbasedonthreerecoverymodes |