A rumor spreading multi-delay model with delay-dependent parameter

Shunjie Li, Xuebing Zhang and Qi An

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 223, issue C, 34-49

Abstract: This study presents a novel delayed rumor spreading model that incorporates a general contact function. We determine the reproduction number, denoted as ℛ0, and discuss its threshold properties. If ℛ0<1, the global asymptotic stability of the rumor-free equilibrium, denoted as E0, is ensured. Conversely, if ℛ0>1, the system exhibits a single rumor-endemic equilibrium, denoted as E∗, which is globally asymptotically stable under certain conditions. Furthermore, by considering the delay as a bifurcation parameter, we explore the Hopf bifurcation of the system. Our analysis indicates that the temporal dynamics of the system are significantly influenced by the delay, which can cause stability to transition into instability. Additionally, we introduce a control variable into the model, and derive an optimal solution.

Keywords: Reproduction number; Rumor; Delay; Hopf bifurcation; Global stability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:223:y:2024:i:c:p:34-49

DOI: 10.1016/j.matcom.2024.04.004

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