Peng-Yue Li , Feng Hu , Fa-Xu Li , You-Feng Zhao , Yu-Rong Song
{"title":"超网络中敌对状态的SEIAR谣言传播模型","authors":"Peng-Yue Li , Feng Hu , Fa-Xu Li , You-Feng Zhao , Yu-Rong Song","doi":"10.1016/j.amc.2025.129637","DOIUrl":null,"url":null,"abstract":"<div><div>Rumors pose serious harm to society, often affecting public safety and social stability as they spread. Most existing studies on rumor propagation models are based on binary relationships within ordinary graphs, constructing complex network information propagation models. However, these models struggle to capture the multi-dimensional, multi-attribute, and multi-relational complex interaction characteristics of real-world social networks. This paper proposes an SEIAR (Susceptible-Exposed-Informed-Antagonistic-Removed) rumor propagation model, built upon hypergraph theory, which effectively captures complex interaction relationships. The model builds on the SEIR framework by introducing a debunking state, enabling a more comprehensive reflection of the dynamic characteristics of rumor propagation and debunking behavior. Using mean-field theory, the dynamic equations of the SEIAR model are derived, along with an analytical expression for its basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, and a stability analysis is conducted. The study shows that when <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></math></span>, the rumor-free equilibrium state of the model is locally and globally stable, ultimately leading to the disappearance of the rumor. When <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></math></span>, the rumor persists and continues to spread. Numerical simulations using the Runge-Kutta method were performed to validate the effectiveness of the theoretical findings. Subsequently, the model was validated using actual rumor datasets, and the results showed that the model can effectively simulate the rumor propagation process in real social networks. In addition, this paper systematically analyzes the impact of factors such as the influence of debunkers, information control strength and control time, individual interests, information timeliness, and network structure on rumor propagation, and compares the propagation characteristics of different models through simulation. The model presented in this paper broadens the perspective of information propagation research, providing a detailed depiction of the rumor propagation mechanism that includes a debunking state, and offers significant theoretical support for developing rumor control strategies.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"508 ","pages":"Article 129637"},"PeriodicalIF":3.4000,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SEIAR rumor spreading model with antagonistic states in hypernetworks\",\"authors\":\"Peng-Yue Li , Feng Hu , Fa-Xu Li , You-Feng Zhao , Yu-Rong Song\",\"doi\":\"10.1016/j.amc.2025.129637\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Rumors pose serious harm to society, often affecting public safety and social stability as they spread. Most existing studies on rumor propagation models are based on binary relationships within ordinary graphs, constructing complex network information propagation models. However, these models struggle to capture the multi-dimensional, multi-attribute, and multi-relational complex interaction characteristics of real-world social networks. This paper proposes an SEIAR (Susceptible-Exposed-Informed-Antagonistic-Removed) rumor propagation model, built upon hypergraph theory, which effectively captures complex interaction relationships. The model builds on the SEIR framework by introducing a debunking state, enabling a more comprehensive reflection of the dynamic characteristics of rumor propagation and debunking behavior. Using mean-field theory, the dynamic equations of the SEIAR model are derived, along with an analytical expression for its basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, and a stability analysis is conducted. The study shows that when <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≤</mo><mn>1</mn></math></span>, the rumor-free equilibrium state of the model is locally and globally stable, ultimately leading to the disappearance of the rumor. When <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>></mo><mn>1</mn></math></span>, the rumor persists and continues to spread. Numerical simulations using the Runge-Kutta method were performed to validate the effectiveness of the theoretical findings. Subsequently, the model was validated using actual rumor datasets, and the results showed that the model can effectively simulate the rumor propagation process in real social networks. In addition, this paper systematically analyzes the impact of factors such as the influence of debunkers, information control strength and control time, individual interests, information timeliness, and network structure on rumor propagation, and compares the propagation characteristics of different models through simulation. The model presented in this paper broadens the perspective of information propagation research, providing a detailed depiction of the rumor propagation mechanism that includes a debunking state, and offers significant theoretical support for developing rumor control strategies.</div></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":\"508 \",\"pages\":\"Article 129637\"},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2025-07-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0096300325003637\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300325003637","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
SEIAR rumor spreading model with antagonistic states in hypernetworks
Rumors pose serious harm to society, often affecting public safety and social stability as they spread. Most existing studies on rumor propagation models are based on binary relationships within ordinary graphs, constructing complex network information propagation models. However, these models struggle to capture the multi-dimensional, multi-attribute, and multi-relational complex interaction characteristics of real-world social networks. This paper proposes an SEIAR (Susceptible-Exposed-Informed-Antagonistic-Removed) rumor propagation model, built upon hypergraph theory, which effectively captures complex interaction relationships. The model builds on the SEIR framework by introducing a debunking state, enabling a more comprehensive reflection of the dynamic characteristics of rumor propagation and debunking behavior. Using mean-field theory, the dynamic equations of the SEIAR model are derived, along with an analytical expression for its basic reproduction number , and a stability analysis is conducted. The study shows that when , the rumor-free equilibrium state of the model is locally and globally stable, ultimately leading to the disappearance of the rumor. When , the rumor persists and continues to spread. Numerical simulations using the Runge-Kutta method were performed to validate the effectiveness of the theoretical findings. Subsequently, the model was validated using actual rumor datasets, and the results showed that the model can effectively simulate the rumor propagation process in real social networks. In addition, this paper systematically analyzes the impact of factors such as the influence of debunkers, information control strength and control time, individual interests, information timeliness, and network structure on rumor propagation, and compares the propagation characteristics of different models through simulation. The model presented in this paper broadens the perspective of information propagation research, providing a detailed depiction of the rumor propagation mechanism that includes a debunking state, and offers significant theoretical support for developing rumor control strategies.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.