Asymptotic Stability of a Rumor Spreading Model with Three Time Delays and Two Saturation Functions

Teng Sheng, Chunlong Fu, Xiaofan Yang (), Yang Qin and Luxing Yang
Additional contact information
Teng Sheng: Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China
Chunlong Fu: Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China
Xiaofan Yang: Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China
Yang Qin: School of Big Data and Software Engineering, Chongqing University, Chongqing 400044, China
Luxing Yang: School of Information Technology, Deakin University, Melbourne, VIC 3125, Australia

Mathematics, 2025, vol. 13, issue 12, 1-25

Abstract: Time delays and saturation effects are critical elements describing complex rumor spreading behaviors. In this article, a rumor spreading model with three time delays and two saturation functions is proposed. The basic properties of the model are reported. The structure of the rumor-endemic equilibria is deduced. A criterion for the global asymptotic stability of the rumor-free equilibrium is derived. In the presence of very small delays, a criterion for the local asymptotic stability of a rumor-endemic equilibrium is provided. The influence of the delays and the saturation effects on the dynamics of the model is made clear through simulation experiments. In particular, it is found that (a) extended time delays lead to slower change in the number of spreaders or stiflers and (b) lifted saturation coefficients lead to slower change in the number of spreaders or stiflers. This work helps to deepen the understanding of complex rumor spreading phenomenon and develop effective rumor-containing schemes.

Keywords: rumor spreading; time delay; saturation effect; basic reproduction number; equilibrium; asymptotic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/12/2015/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/12/2015/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:12:p:2015-:d:1682105

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().