Research on Rumor-Spreading Model with Holling Type III Functional Response

Yanhui Wei, Liang’an Huo and Hongguang He
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Yanhui Wei: Jiyang College, Zhejiang Agriculture & Forestry University, Zhuji 311800, China
Liang’an Huo: Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Hongguang He: Jiyang College, Zhejiang Agriculture & Forestry University, Zhuji 311800, China

Mathematics, 2022, vol. 10, issue 4, 1-13

Abstract: In this paper, a rumor-spreading model with Holling type III functional response was established. The existence of the equilibrium points was discussed. According to the Routh–Hurwitz criteria, the locally asymptotic stability of the equilibrium points was analyzed. The global stability of the equilibrium points was proven based on Lasalle’s invariance principle and generalized Bendixson–Dulac theorem. Numerical simulations were carried out to illustrate the impact of different parameters on the spread of rumors. When the stifling rate λ increases, or the predation capacity β or the system coming rate k decreases, the number of rumor-spreaders is reduced to extinction. The results provide theory, method and decision support for effectively controlling the spread of rumors.

Keywords: rumor-spreading model; Holling type III; generalized Bendixon–Dulac theorem; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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