{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T23:09:47Z","timestamp":1773702587571,"version":"3.50.1"},"reference-count":33,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,8,11]]},"abstract":"<jats:p>In this paper, an uncertain SEIR rumor model driven by one uncertain process is formulated to investigate the influence of perturbation in the transmission of rumor. Firstly, the deduced process of the uncertain SEIR rumor model is presented. Then, we proposed the existence and uniqueness theorem for the solution of the model. Moreover, the study of the stability of the uncertain SEIR rumor model was carried out, and then we came to the conclusion that the model stable in mean. In addition, computer algorithm and numerical simulation is used to verify the accuracy of the theoretical results. The simulation results show that the proposed model can explain the trend of rumor propagation correctly and describe the rumor propagation accurately. Finally, we have compared the propagation process of the uncertain rumor model and the deterministic model according to the numerical algorithm, and drew the conclusion that the model with uncertain perturbation fluctuates around the deterministic model.<\/jats:p>","DOI":"10.3233\/jifs-201865","type":"journal-article","created":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T14:43:46Z","timestamp":1624027426000},"page":"399-412","source":"Crossref","is-referenced-by-count":3,"title":["An uncertain SEIR rumor model"],"prefix":"10.1177","volume":"41","author":[{"given":"Qianqian","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematical and System Sciences, Xinjiang University, Urumqi, China"}]},{"given":"Gang","family":"Shi","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Xinjiang University, Urumqi, China"}]},{"given":"Yuhong","family":"Sheng","sequence":"additional","affiliation":[{"name":"College of Mathematical and System Sciences, Xinjiang University, Urumqi, China"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-201865_ref1","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.physa.2017.09.077","article-title":"Studies on the population dynamics of a rumor-spreading model in online social networks","volume":"492","author":"Dong","year":"2018","journal-title":"Physica A"},{"key":"10.3233\/JIFS-201865_ref2","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.physa.2018.02.096","article-title":"M.F.H, Rumor spreading model with the different attitudes towards rumors","volume":"502","author":"Hu","year":"2018","journal-title":"Physica A"},{"key":"10.3233\/JIFS-201865_ref3","first-page":"1","article-title":"A coupled model for government communication and rumor spreading in emergencies","volume":"208","author":"Xu","year":"2016","journal-title":"Advances in Difference Equations"},{"issue":"4","key":"10.3233\/JIFS-201865_ref4","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/j.physa.2012.09.030","article-title":"SIR rumor spreading model in the new media age","volume":"392","author":"Zhao","year":"2013","journal-title":"Physica A"},{"key":"10.3233\/JIFS-201865_ref5","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.chaos.2019.05.027","article-title":"Global dynamics of the multi-lingual SIR rumor spreading model with crosstransmitted mechanism","volume":"126","author":"Wang","year":"2019","journal-title":"Chaos Solitons and Fractals"},{"key":"10.3233\/JIFS-201865_ref6","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1038\/2041118a0","article-title":"Epidemics and rumours","volume":"204","author":"Daley","year":"1964","journal-title":"Nature"},{"key":"10.3233\/JIFS-201865_ref7","unstructured":"Maki D.P. and Thompson M. , Mathematical models and applications, with emphasis on the social, life, and management sciences, Upper Saddle River: Prentice Hall 511 (1973)."},{"key":"10.3233\/JIFS-201865_ref8","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.physa.2013.09.058","article-title":"Stability analysis of an SIS epidemic model with feedback mechanism on networks","volume":"394","author":"Zhang","year":"2014","journal-title":"Physica A"},{"key":"10.3233\/JIFS-201865_ref9","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.physa.2015.12.078","article-title":"Dynamical analysis of a fractional SIR model with birth and death on heterogeneous complex networks","volume":"448","author":"Huo","year":"2016","journal-title":"Physica A"},{"issue":"1","key":"10.3233\/JIFS-201865_ref10","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/S0025-5564(03)00087-7","article-title":"Global dynamics of an SEIR epidemic model with saturating contact rate","volume":"185","author":"Zhang","year":"2003","journal-title":"Mathematical Biosciences"},{"issue":"6","key":"10.3233\/JIFS-201865_ref11","doi-asserted-by":"crossref","first-page":"2501","DOI":"10.1016\/j.cnsns.2011.07.025","article-title":"Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation","volume":"17","author":"Yuan","year":"2011","journal-title":"Communications in Nonlinear Science and Numerical Simulation"},{"issue":"10","key":"10.3233\/JIFS-201865_ref12","doi-asserted-by":"crossref","first-page":"3444","DOI":"10.1016\/j.cnsns.2014.02.025","article-title":"Asymptotic stability of a twogroup stochastic SEIR model with infinite delays","volume":"19","author":"Liu","year":"2014","journal-title":"Communications in Nonlinear Science and Numerical Simulation"},{"issue":"20","key":"10.3233\/JIFS-201865_ref13","doi-asserted-by":"crossref","first-page":"4928","DOI":"10.1016\/j.physa.2013.06.025","article-title":"Stability of an SEIR epidemic model with independent stochastic perturbations","volume":"392","author":"Witbooi","year":"2013","journal-title":"Physica A"},{"issue":"1","key":"10.3233\/JIFS-201865_ref14","first-page":"700","article-title":"A note on the stationary distribution of stochastic SEIR epidemic model with saturated incidence rate","volume":"7","author":"Han","year":"2017","journal-title":"Scientific Reports"},{"key":"10.3233\/JIFS-201865_ref15","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.amc.2014.04.061","article-title":"Stochastic SEIR model with jumps","volume":"239","author":"Zhang","year":"2014","journal-title":"Applied Mathematics and Computation"},{"key":"10.3233\/JIFS-201865_ref16","first-page":"1","article-title":"Rumor spreading of a SEIR model in complex social networks with hesitating mechanism","volume":"391","author":"Liu","year":"2018","journal-title":"Advances in Difference Equations"},{"key":"10.3233\/JIFS-201865_ref17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.physa.2014.07.041","article-title":"Analysis of the impact of education rate on the rumor spreading mechanism","volume":"414","author":"Afassinou","year":"2014","journal-title":"Physica A"},{"key":"10.3233\/JIFS-201865_ref18","doi-asserted-by":"crossref","unstructured":"Zhu L.H. , Zhou X. and Li Y.M. , Global dynamics analysis and control of a rumor spreading model in online social networks, Physica A 526 (2019).","DOI":"10.1016\/j.physa.2019.04.139"},{"key":"10.3233\/JIFS-201865_ref19","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.physa.2015.05.113","article-title":"Rumor spreading model considering hesitating mechanism in complex social networks","volume":"437","author":"Xia","year":"2015","journal-title":"Physica A"},{"key":"10.3233\/JIFS-201865_ref20","first-page":"1","article-title":"Global stability of a SEIR rumor spreading model with demographics on scale-free networks","volume":"253","author":"Wan","year":"2017","journal-title":"Advances in Difference Equations"},{"key":"10.3233\/JIFS-201865_ref21","unstructured":"Liu B. , Uncertainty Theory, 2nd ed. Springer-Verlag, Berlin, (2007)."},{"issue":"1","key":"10.3233\/JIFS-201865_ref22","first-page":"3","article-title":"Fuzzy process, hybrid process and uncertain process","volume":"2","author":"Liu","year":"2008","journal-title":"Journal of Uncertain Systems"},{"issue":"1","key":"10.3233\/JIFS-201865_ref23","first-page":"3","article-title":"Some research problems in uncertainty theory","volume":"3","author":"Liu","year":"2009","journal-title":"Journal of Uncertain Systems"},{"key":"10.3233\/JIFS-201865_ref24","unstructured":"Liu B. , Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, (2010)."},{"issue":"1","key":"10.3233\/JIFS-201865_ref25","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s10700-010-9073-2","article-title":"Existence and uniqueness theorem for uncertain differential equations","volume":"9","author":"Chen","year":"2010","journal-title":"Fuzzy Optimization and Decision Making"},{"issue":"3","key":"10.3233\/JIFS-201865_ref26","first-page":"223","article-title":"Existence and uniqueness theorems on uncertain differential equations without global Lipschitz condition","volume":"6","author":"Gao","year":"2012","journal-title":"Journal of Uncertain Systems"},{"issue":"3","key":"10.3233\/JIFS-201865_ref27","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s10700-014-9204-2","article-title":"Stability in mean for uncertain differential equation","volume":"14","author":"Yao","year":"2015","journal-title":"Fuzzy Optimization and Decision Making"},{"key":"10.3233\/JIFS-201865_ref28","first-page":"244","article-title":"An analytic method for solving uncertain differential equations","volume":"6","author":"Liu","year":"2012","journal-title":"Journal of Uncertain Systems"},{"issue":"1","key":"10.3233\/JIFS-201865_ref29","first-page":"1","article-title":"A type of uncertain differential equations with analytic solution","volume":"1","author":"Yao","year":"2013","journal-title":"Journal of Uncertainty Analysis and Applications"},{"issue":"1","key":"10.3233\/JIFS-201865_ref30","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10700-012-9139-4","article-title":"Some stability theorems of uncertain differential equation","volume":"12","author":"Yao","year":"2013","journal-title":"Fuzzy Optimization and Decision Making"},{"issue":"3","key":"10.3233\/JIFS-201865_ref31","doi-asserted-by":"crossref","first-page":"825","DOI":"10.3233\/IFS-120688","article-title":"A numerical method for solving uncertain differential equations","volume":"25","author":"Yao","year":"2013","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"15","key":"10.3233\/JIFS-201865_ref32","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.1002\/mma.3335","article-title":"Uncertain fractional differential equations and an interest rate model","volume":"38","author":"Zhu","year":"2015","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"10.3233\/JIFS-201865_ref33","doi-asserted-by":"crossref","unstructured":"Jin T. , Sun Y. and Zhu Y. , Extreme values for solution to uncertain fractional differential equation and application to American option pricing model, Physica A: Statistical Mechanics and its Applications 534(122357) (2019).","DOI":"10.1016\/j.physa.2019.122357"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-201865","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T03:22:07Z","timestamp":1770002527000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-201865"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,11]]},"references-count":33,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/jifs-201865","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,11]]}}}