Affiliations: [a] College of Mathematical and System Sciences, Xinjiang University, Urumqi, China
| [b] College of Information Science and Engineering, Xinjiang University, Urumqi, China
Correspondence:
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Corresponding author. Yuhong Sheng, College of Mathematical and System Sciences, Xinjiang University, Urumqi 830046, China. Tel: +86 18167978160; E-mail: shengyh@xju.edu.cn.
Abstract: 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.
Keywords: Uncertain differential equation, Liu process, Uncertain SEIR model, Existence and uniqueness, Stability
