{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T14:48:07Z","timestamp":1781621287755,"version":"3.54.5"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["OIA-1946391, OIA-1920920"],"award-info":[{"award-number":["OIA-1946391, OIA-1920920"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-22-1-0332"],"award-info":[{"award-number":["FA9550-22-1-0332"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-23-1-0011, W911NF-24-1-0078"],"award-info":[{"award-number":["W911NF-23-1-0011, W911NF-24-1-0078"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-21-1-2121, N00014-21-1-2765, N00014-22-1-2318"],"award-info":[{"award-number":["N00014-21-1-2121, N00014-21-1-2765, N00014-22-1-2318"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006602","name":"Air Force Research Laboratory","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006602","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000185","name":"Defense Advanced Research Projects Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000185","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008480","name":"Arkansas Research Alliance","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008480","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Jerry L. Maulden\/Entergy Endowment"},{"name":"Australian Department of Defense Strategic Policy Grants Program"},{"name":"Donaghey Foundation"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soc. Netw. Anal. Min."],"abstract":"Abstract<\/jats:title>\n \n The spread of narratives online has been extensively studied. However, prior research typically relies on metadata and often overlooks the dynamics of post stances. In this paper, we introduce a novel stance-based epidemiological model, which explicitly incorporates the stance of posts\u2014a critical element often ignored by models that focus solely on isolated narratives. Our model,\n \n \n $$SEI_A I_D Z$$<\/jats:tex-math>\n \n \n S<\/mml:mi>\n E<\/mml:mi>\n \n I<\/mml:mi>\n A<\/mml:mi>\n <\/mml:msub>\n \n I<\/mml:mi>\n D<\/mml:mi>\n <\/mml:msub>\n Z<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (\n \n \n $$S$$<\/jats:tex-math>\n \n S<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = susceptible,\n \n \n $$E$$<\/jats:tex-math>\n \n E<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = exposed,\n \n \n $$I_A$$<\/jats:tex-math>\n \n \n I<\/mml:mi>\n A<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = agree with the narrative,\n \n \n $$I_D$$<\/jats:tex-math>\n \n \n I<\/mml:mi>\n D<\/mml:mi>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = posting disagree or alternative narrative,\n \n \n $$Z$$<\/jats:tex-math>\n \n Z<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n = skeptic), captures the dynamic interactions among competing narratives, including the introduction of countermeasures or opposing viewpoints, thereby offering a more comprehensive framework for analyzing online narrative dissemination. Comparative evaluations demonstrate that our model outperforms the baseline\n \n \n $$SEIZ$$<\/jats:tex-math>\n \n \n SEIZ<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n model, achieving lower predictive error rates. Furthermore, we identify two key parameters:\n \n \n $$\\beta$$<\/jats:tex-math>\n \n \u03b2<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (transmission rate) and\n \n \n $$\\psi$$<\/jats:tex-math>\n \n \u03c8<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n (the rate at which exposed individuals transition to the Agreed and Skeptic compartment). Both parameters significantly influence the basic reproduction number (\n \n \n $${\\mathcal {R}}_0$$<\/jats:tex-math>\n \n \n R<\/mml:mi>\n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ), a measure of transmission potential. Our findings indicate that \u03b2 plays a significant role in driving propagation across all platforms, underscoring the need to control it in order to mitigate the spread of misinformation. To ensure the generalization of our model, we validate our approach using three distinct platforms and scenarios: Health-related conspiracy theories about COVID-19 and 5G on the text-based platform X (formerly Twitter), Geopolitical narratives related to the Russia-Ukraine conflict on the messaging platform Telegram, and Election misinformation campaigns during Taiwan\u2019s 2024 elections on the multimedia-based platform TikTok. Our research provides critical insights into the role of stance and content dynamics in online narrative dissemination, paving the way for more effective strategies to combat harmful narratives and inform policymaking.\n <\/jats:p>","DOI":"10.1007\/s13278-025-01479-y","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T14:56:55Z","timestamp":1750431415000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Modeling polarized information diffusion with SEI(A)I(D)Z: a stance-based epidemiological approach"],"prefix":"10.1007","volume":"15","author":[{"given":"Mayor Inna","family":"Gurung","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nitin","family":"Agarwal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuel","family":"Addai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"1479_CR1","doi-asserted-by":"crossref","unstructured":"Abdullah S, Wu X (2011) An epidemic model for news spreading on twitter. In: Proceedings of the 23rd IEEE international conference on tools with artificial intelligence. ICTAI 2011:163\u2013169","DOI":"10.1109\/ICTAI.2011.33"},{"issue":"5","key":"1479_CR2","doi-asserted-by":"publisher","first-page":"19458","DOI":"10.2196\/19458","volume":"22","author":"W Ahmed","year":"2020","unstructured":"Ahmed W, Vidal-Alaball J, Downing J, Segu\u00ed FL et al (2020) Covid-19 and the 5g conspiracy theory: social network analysis of twitter data. J Med Internet Res 22(5):19458","journal-title":"J Med Internet Res"},{"issue":"2","key":"1479_CR3","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1257\/jep.31.2.211","volume":"31","author":"H Allcott","year":"2017","unstructured":"Allcott H, Gentzkow M (2017) Social media and fake news in the 2016 election. J Econ Perspect 31(2):211\u2013236","journal-title":"J Econ Perspect"},{"key":"1479_CR4","doi-asserted-by":"crossref","unstructured":"Bawa A, Kursuncu U, Achilov D, Shalin V, Agarwal N, Akbas E (2025) Telegram as a battlefield: Kremlin-related communications during the russia-ukraine conflict. In: 2025 AAAI international conference on web and social media (ICWSM 2025) . AAAI","DOI":"10.1609\/icwsm.v19i1.35939"},{"key":"1479_CR5","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1016\/j.physa.2005.08.083","volume":"364","author":"LM Bettencourt","year":"2006","unstructured":"Bettencourt LM, Cintr\u00f3n-Arias A, Kaiser DI, Castillo-Ch\u00e1vez C (2006) The power of a good idea: quantitative modeling of the spread of ideas from epidemiological models. Phys A 364:513\u2013536","journal-title":"Phys A"},{"key":"1479_CR6","doi-asserted-by":"crossref","unstructured":"Cakmak MC, Okeke O, Onyepunuka U, Spann B, Agarwal N (2023) Investigating bias in youtube recommendations: emotion, morality, and network dynamics in China-Uyghur content. In: International conference on complex networks and their applications. Springer, pp 351\u2013362","DOI":"10.1007\/978-3-031-53468-3_30"},{"key":"1479_CR7","doi-asserted-by":"crossref","unstructured":"Cardone A, Alba P, Paternoster B (2022) Influence of age group in the spreading of fake news: Contact matrices in social media. In: Proceedings of the IEEE 16th international conference on signal image technology and internet based systems (SITIS), Dijon, France, pp 515\u2013521","DOI":"10.1109\/SITIS57111.2022.00083"},{"issue":"9","key":"1479_CR8","doi-asserted-by":"publisher","first-page":"2023301118","DOI":"10.1073\/pnas.2023301118","volume":"118","author":"M Cinelli","year":"2021","unstructured":"Cinelli M, De Francisci Morales G, Galeazzi A, Quattrociocchi W, Starnini M (2021) The echo chamber effect on social media. Proc Natl Acad Sci 118(9):2023301118","journal-title":"Proc Natl Acad Sci"},{"issue":"1","key":"1479_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41598-020-73510-5","volume":"10","author":"M Cinelli","year":"2020","unstructured":"Cinelli M, Quattrociocchi W, Galeazzi A, Valensise CM, Brugnoli E, Schmidt AL, Zola P, Zollo F, Scala A (2020) The covid-19 social media infodemic. Sci Rep 10(1):1\u201310","journal-title":"Sci Rep"},{"key":"1479_CR10","unstructured":"DataReportal: global social media users: October 2024 Update (2024). https:\/\/datareportal.com\/social-media-users"},{"issue":"3","key":"1479_CR40","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1073\/pnas.1517441113","volume":"113","author":"M Del Vicario","year":"2016","unstructured":"Del Vicario M, Bessi A, Zollo F, Petroni F, Scala A, Caldarelli G, Stanley HE, Quattrociocchi W (2016) The spreading of misinformation online. Proc Natl Acad Sci 113(3):554\u2013559","journal-title":"Proc Natl Acad Sci"},{"key":"1479_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2021.103970","volume":"23","author":"R Din","year":"2021","unstructured":"Din R, Algehyne EA (2021) Mathematical analysis of covid-19 by using sir model with convex incidence rate. Results Phys 23:103970. https:\/\/doi.org\/10.1016\/j.rinp.2021.103970","journal-title":"Results Phys"},{"key":"1479_CR12","doi-asserted-by":"publisher","first-page":"222","DOI":"10.3390\/fi13090222","volume":"13","author":"R D\u2019Ambrosio","year":"2021","unstructured":"D\u2019Ambrosio R, Giordano G, Mottola S, Paternoster B (2021) Stiffness analysis to predict the spread out of fake information. Fut Internet 13:222. https:\/\/doi.org\/10.3390\/fi13090222","journal-title":"Fut Internet"},{"key":"1479_CR13","doi-asserted-by":"crossref","unstructured":"D\u2019Ambrosio R, Alba P, Giordano G, Paternoster B (2022) A modified seir model: stiffness analysis and application to the diffusion of fake news. In: Gervasi O, Murgante B, Hendrix EMT, Taniar D, Apduhan BO (eds) Proceedings of the 22nd international conference on computational science and its applications, , vol 13375. Springer, Malaga, pp 90\u2013103","DOI":"10.1007\/978-3-031-10522-7_7"},{"key":"1479_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.socscimed.2021.114546","volume":"293","author":"E Flaherty","year":"2022","unstructured":"Flaherty E, Sturm T, Farries E (2022) The conspiracy of covid-19 and 5g: Spatial analysis fallacies in the age of data democratization. Soc Sci Med 293:114546","journal-title":"Soc Sci Med"},{"key":"1479_CR15","unstructured":"Gan N (2025) This 2024 Presidential Election Could Change the World-and It\u2019s Not Happening in the US. Accessed: April 15"},{"issue":"6","key":"1479_CR16","first-page":"002","volume":"8","author":"JP Gleeson","year":"2020","unstructured":"Gleeson JP, Onaga T, Fennell P, Cotter J, Burke R, O\u2019Sullivan DJ (2020) Branching process descriptions of information cascades on twitter. J Complex Networks 8(6):002","journal-title":"J Complex Networks"},{"key":"1479_CR17","doi-asserted-by":"publisher","first-page":"115541","DOI":"10.1016\/j.cma.2022.115541","volume":"401","author":"M Grave","year":"2022","unstructured":"Grave M, Viguerie A, Barros G.F., Reali A, Andrade\u00a0Roberto F.S., Coutinho\u00a0Alvaro L.G.A. (2022) Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network. Comput Methods Appl Mech Eng 401:115541. https:\/\/doi.org\/10.1016\/j.cma.2022.115541","journal-title":"Comput Methods Appl Mech Eng"},{"key":"1479_CR18","doi-asserted-by":"crossref","unstructured":"Gurung MI, Bhuiyan MMI, Al-Taweel A, Agarwal N (2024) Decoding youtube\u2019s recommendation system: a comparative study of metadata and gpt-4 extracted narratives. In: Companion proceedings of the ACM on web conference 2024, pp 1468\u20131472","DOI":"10.1145\/3589335.3651913"},{"key":"1479_CR19","doi-asserted-by":"crossref","unstructured":"Gurung MI, Agarwal N, Al-Taweel A (2024) Are narratives contagious? Modeling narrative diffusion using epidemiological theories. In: International conference on advances in social networks analysis and mining . Springer, pp 303\u2013318","DOI":"10.1007\/978-3-031-78554-2_20"},{"issue":"4","key":"1479_CR20","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1137\/S0036144500371907","volume":"42","author":"HW Hethcote","year":"2000","unstructured":"Hethcote HW (2000) The mathematics of infectious diseases. SIAM Rev 42(4):599\u2013653","journal-title":"SIAM Rev"},{"key":"1479_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2022.111331","volume":"557","author":"EM Hill","year":"2023","unstructured":"Hill EM (2023) Modelling the epidemiological implications for sars-cov-2 of christmas household bubbles in england. J Theor Biol 557:111331. https:\/\/doi.org\/10.1016\/j.jtbi.2022.111331","journal-title":"J Theor Biol"},{"key":"1479_CR22","doi-asserted-by":"crossref","unstructured":"Kempe D, Kleinberg J, Tardos, \u00c9 (2003) Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining, pp 137\u2013146","DOI":"10.1145\/956750.956769"},{"key":"1479_CR23","doi-asserted-by":"crossref","unstructured":"Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics, vol 115. The Royal Society London, pp 700\u2013721","DOI":"10.1098\/rspa.1927.0118"},{"key":"1479_CR24","unstructured":"Klepper D, Wu H (2024) How Taiwan Preserved Election Integrity by Fighting Back Against Disinformation. PBS NewsHour"},{"key":"1479_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.111063","volume":"150","author":"D Lacitignola","year":"2021","unstructured":"Lacitignola D, Diele F (2021) Using awareness to z-control a seir model with overexposure: insights on covid-19 pandemic. Chaos Solitons Fract 150:111063. https:\/\/doi.org\/10.1016\/j.chaos.2021.111063","journal-title":"Chaos Solitons Fract"},{"key":"1479_CR26","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2023.3321767","author":"Y Liu","year":"2023","unstructured":"Liu Y, Ding W, Zhang Y, Chen Z, Wu J (2023) Diffusion source inference for large-scale complex networks based on network percolation. IEEE Trans Neural Networks Learn Syst. https:\/\/doi.org\/10.1109\/TNNLS.2023.3321767","journal-title":"IEEE Trans Neural Networks Learn Syst"},{"key":"1479_CR27","doi-asserted-by":"publisher","DOI":"10.1109\/TIFS.2023.3338423","author":"Y Liu","year":"2023","unstructured":"Liu Y, Ding W, Zhang Y, Chen Z, Wu J (2023) Diffusion containment in complex networks through collective influence of connections. IEEE Trans Inf Forensics Secur. https:\/\/doi.org\/10.1109\/TIFS.2023.3338423","journal-title":"IEEE Trans Inf Forensics Secur"},{"key":"1479_CR28","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2024.3382546","author":"Y Liu","year":"2024","unstructured":"Liu Y, Ding W, Zhang Y, Chen Z, Wu J (2024) Fast outbreak sense and effective source inference via minimum observer set. IEEE\/ACM Trans Networking. https:\/\/doi.org\/10.1109\/TNET.2024.3382546","journal-title":"IEEE\/ACM Trans Networking"},{"key":"1479_CR29","unstructured":"Loucaides D (2022) Telegram: the digital battlefront between Russia and Ukraine. Politico Europe . Accessed 2024 Dec 12"},{"key":"1479_CR30","doi-asserted-by":"crossref","unstructured":"Maleki M, Arani M, Buchholz E, Mead E, Agarwal N (2021) Applying an epidemiological model to evaluate the propagation of misinformation and legitimate Covid-19-related information on twitter. In: International Conference on Social Computing, Behavioral-Cultural Modeling and Prediction and Behavior Representation in Modeling and Simulation. Springer, pp 23\u201334","DOI":"10.1007\/978-3-030-80387-2_3"},{"key":"1479_CR31","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1140\/epjb\/e20020122","volume":"26","author":"Y Moreno","year":"2002","unstructured":"Moreno Y, Pastor-Satorras R, Vespignani A (2002) Epidemic outbreaks in complex heterogeneous networks. Eur Phys Jl B-Condens Matter Complex Syst 26:521\u2013529","journal-title":"Eur Phys Jl B-Condens Matter Complex Syst"},{"key":"1479_CR32","doi-asserted-by":"crossref","unstructured":"Muhlmeyer M, Agarwal S (2021) Information spread in a social media age. In: Modelling and Control. CRC Press, Boca Raton","DOI":"10.1201\/9780429263842"},{"key":"1479_CR33","unstructured":"MyGoPen: [Verification] It Is Rumored on the Internet that the Ticket for Singing No. 3 and Painting No. 2 Is Issued? It Has Been Corrected Immediately! The Video Does Not Present the Complete Picture (2024)"},{"key":"1479_CR34","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1016\/j.matcom.2022.12.004","volume":"204","author":"A Omame","year":"2023","unstructured":"Omame A, Abbas M, Din A (2023) Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of sars-cov-2. Math Comput Simul 204:302\u2013336. https:\/\/doi.org\/10.1016\/j.matcom.2022.12.004","journal-title":"Math Comput Simul"},{"key":"1479_CR35","doi-asserted-by":"crossref","unstructured":"Pathak N, Banerjee A, Srivastava J (2010) A generalized linear threshold model for multiple cascades. In: 2010 IEEE International Conference on Data Mining . IEEE, pp 965\u2013970","DOI":"10.1109\/ICDM.2010.153"},{"issue":"11","key":"1479_CR36","doi-asserted-by":"publisher","first-page":"4944","DOI":"10.1287\/mnsc.2019.3478","volume":"66","author":"G Pennycook","year":"2020","unstructured":"Pennycook G, Bear A, Collins ET, Rand DG (2020) The implied truth effect: attaching warnings to a subset of fake news headlines increases perceived accuracy of headlines without warnings. Manage Sci 66(11):4944\u20134957","journal-title":"Manage Sci"},{"key":"1479_CR37","doi-asserted-by":"crossref","unstructured":"Pogorelov K, Schroeder D.T, Filkukov\u00e1 P, Brenner S, Langguth J (2021) Wico text: a labeled dataset of conspiracy theory and 5g-corona misinformation tweets. In: Proceedings of the 2021 workshop on open challenges in online social networks, pp 21\u201325","DOI":"10.1145\/3472720.3483617"},{"key":"1479_CR38","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/s00285-022-01739-0","volume":"85","author":"P Song","year":"2022","unstructured":"Song P, Xiao Y (2022) Analysis of a diffusive epidemic system with spatial heterogeneity and lag effect of media impact. J Math Biol 85:17. https:\/\/doi.org\/10.1007\/s00285-022-01739-0","journal-title":"J Math Biol"},{"key":"1479_CR39","doi-asserted-by":"crossref","unstructured":"Tran C, Zheleva E (2022) Heterogeneous peer effects in the linear threshold model. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 36, pp. 4175\u20134183","DOI":"10.1609\/aaai.v36i4.20336"},{"issue":"6380","key":"1479_CR41","doi-asserted-by":"publisher","first-page":"1146","DOI":"10.1126\/science.aap9559","volume":"359","author":"S Vosoughi","year":"2018","unstructured":"Vosoughi S, Roy D, Aral S (2018) The spread of true and false news online. Science 359(6380):1146\u20131151","journal-title":"Science"},{"key":"1479_CR42","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-38852-2","volume-title":"Modeling information diffusion in online social networks with partial differential equations","author":"H Wang","year":"2020","unstructured":"Wang H, Wang F, Xu K (2020) Modeling information diffusion in online social networks with partial differential equations, vol 7. Springer, Cham"},{"key":"1479_CR43","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2022.108459","volume":"136","author":"J Yang","year":"2023","unstructured":"Yang J, Shi X, Song X, Zhao Z (2023) Threshold dynamics of a stochastic siqr epidemic model with imperfect quarantine. Appl Math Lett 136:108459. https:\/\/doi.org\/10.1016\/j.aml.2022.108459","journal-title":"Appl Math Lett"},{"key":"1479_CR44","doi-asserted-by":"crossref","unstructured":"Yousefi N, Agarwal N, Addai E (2024) Developing epidemiological models with differentiated infected intensity. In: International conference on social computing, behavioral-cultural modeling and prediction and behavior representation in modeling and simulation. Springer, pp 58\u201368","DOI":"10.1007\/978-3-031-72241-7_6"},{"issue":"13","key":"1479_CR45","doi-asserted-by":"publisher","first-page":"2619","DOI":"10.1016\/j.physa.2011.03.010","volume":"390","author":"L Zhao","year":"2011","unstructured":"Zhao L, Wang Q, Cheng J, Chen Y, Wang J, Huang W (2011) Rumor spreading model with consideration of forgetting mechanism: a case of online blogging livejournal. Phys A 390(13):2619\u20132625","journal-title":"Phys A"}],"container-title":["Social Network Analysis and Mining"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13278-025-01479-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13278-025-01479-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13278-025-01479-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:28:33Z","timestamp":1765960113000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13278-025-01479-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,20]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["1479"],"URL":"https:\/\/doi.org\/10.1007\/s13278-025-01479-y","relation":{},"ISSN":["1869-5469"],"issn-type":[{"value":"1869-5469","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,20]]},"assertion":[{"value":"19 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 May 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The writers state that they do not have any Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Generative AI and AI-assisted technologies were not used in the preparation of this manuscript.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Use of generative AI in scientific writing"}}],"article-number":"60"}}