• 论文 •

### 一类具有自发行为的SIRI谣言传播模型研究

1. 1. 忻州师范学院数学系, 忻州   034000; 2. 太原理工大学数学学院,太原  030024
• 出版日期:2020-07-25 发布日期:2020-09-23

LIU Fang, LI Mingtao. Research on SIRI Rumor Spreading Model with Spontaneous Behavior[J]. Journal of Systems Science and Mathematical Sciences, 2020, 40(7): 1257-1269.

### Research on SIRI Rumor Spreading Model with Spontaneous Behavior

LIU Fang1, LI Mingtao2

1. 1. Department of Mathematics, Xinzhou Teachers University, Xinzhou 034000; 2. College of Mathematics, Taiyuan University of Technology, Taiyuan 030024
• Online:2020-07-25 Published:2020-09-23

Based on the theory of epidemic dynamics, a dynamic SIRI model of differential equation about rumor spreading with spontaneous behavior was established. By analyze the existence of non-negative equilibria, the threshold which effect the rumor spreading result is determined. Jacobian matrix and bendixson-dulac discriminant method were used to analyze the stability of the non-negative equilibria. Furthermore, the main factors affecting the rumor spreading and the strategies in order to control rumor spreading are given. The theoretical analysis shows that the existence of spontaneous behavior is a necessary condition for rumor spreading. If the threshold is more than 1, the rumor will last, otherwise the rumor will die out. Numerical simulations are provided to support the theoretical results. The complicated dynamics properties exhibit that the model is very sensitive to variation of parameters, which play an important role on controlling and administering the rumor spreading.

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