Dynamic analysis of stochastic rumor model with education effect

Hui Zhu; Zonghe Guo; Yunping Liu; Wei Ou; Hui Zhu; Zonghe Guo; Yunping Liu; Wei Ou

doi:10.3934/math.2026416

AIMS Mathematics

2026, Volume 11, Issue 4: 10079-10099. doi: 10.3934/math.2026416

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Research article

Dynamic analysis of stochastic rumor model with education effect

1.
School of Engineering Science, Shandong Xiehe University, Jinan 250107, China
2.
School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China
3.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received: 12 December 2025 Revised: 30 January 2026 Accepted: 04 February 2026 Published: 14 April 2026
MSC : 60H10, 60H30, 92D30, 93E15

With the development of the economy and society, rumors have become increasingly popular. Therefore, quantitative research on rumors has become essential. In this paper, a new rumor model with age of education is introduced by considering two different types of populations. First, we obtain the existence of global positive solutions by utilizing Itô's formula and the Lyapunov functional method. Then, several sufficient conditions for the disappearance and persistence of rumors are given, where the threshold will be affected by the age of education. Finally, to support the main results of this article, several illustrative numerical simulations are conducted.
- age-dependent education,
- rumor model,
- stochastic model,
- extinction,
- persistence in the mean
Citation: Hui Zhu, Zonghe Guo, Yunping Liu, Wei Ou. Dynamic analysis of stochastic rumor model with education effect[J]. AIMS Mathematics, 2026, 11(4): 10079-10099. doi: 10.3934/math.2026416

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Abstract

With the development of the economy and society, rumors have become increasingly popular. Therefore, quantitative research on rumors has become essential. In this paper, a new rumor model with age of education is introduced by considering two different types of populations. First, we obtain the existence of global positive solutions by utilizing Itô's formula and the Lyapunov functional method. Then, several sufficient conditions for the disappearance and persistence of rumors are given, where the threshold will be affected by the age of education. Finally, to support the main results of this article, several illustrative numerical simulations are conducted.

References

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