A Rumor-Spreading Model with Three Identical Time Delays

Chunlong Fu, Guofang Liu, Xiaofan Yang (), Yang Qin and Luxing Yang
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Chunlong Fu: Department of Computer Science, Sichuan University Jinjiang College, Meishan 620860, China
Guofang Liu: 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 9, 1-26

Abstract: Understanding the effect of time delays on rumor spreading is of special importance to curbing the spread of rumors. This article proposes a rumor-spreading model with three identical time delays: a delay associated with the negative influence of a spreader on an exposed ignorant individual, a delay associated with the natural change from a spreader to a stifler, and a delay associated with the positive influence of a stifler on an exposed spreader. The basic reproduction number for the model is determined. A criterion for the existence of rumor-endemic equilibrium is provided. Interestingly, the model undergoes a conditional forward bifurcation. A collection of criteria for the asymptotic stability of the rumor-free equilibrium is derived. In the absence of a time delay, a criterion for the asymptotic stability of the rumor-endemic equilibrium is presented. By developing a novel technique for dealing with small time delays, a criterion for the asymptotic stability of the rumor-endemic equilibrium is established. Finally, the effect of some factors on the existence of rumor-endemic equilibrium is investigated. In particular, the effect of the time delay on rumor spreading is revealed. This work facilitates a deep understanding of the dynamics of rumor-spreading models with time delays.

Keywords: rumor-spreading model; time delay; equilibrium; local asymptotic stability; global asymptotic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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