Asymptotic Stability of a Rumor Spreading Model with Three Time Delays and Two Saturation Functions
Year: 2025
Type: article
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.
Source: Mathematics
DOI: 10.3390/math13122015
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4411457287