Dynamic Analysis of Rumor Spreading Model Based on Three Recovery Modes

Jingping Lu, Qinlong Wang () and Wentao Huang ()
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Jingping Lu: Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China
Qinlong Wang: Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China
Wentao Huang: Center for Applied Mathematics of Guangxi (GUET), School of Mathematics and Computing Science, School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China

Mathematics, 2024, vol. 12, issue 23, 1-21

Abstract: In this paper, an SIR rumor propagation model is established with the three recovery modes that the spreader turns into a stifler under the influence of the spreader, stifler and media nonlinear rumor-refuting mechanism. Firstly, we calculate the basic regeneration number, and we determine the stability of the rumor-free equilibrium and the existence of the rumor-endemic equilibrium. Secondly, by applying the strict symbolic calculation methods of singular quantities, we investigate the Hopf bifurcation at the rumor-endemic equilibrium, and we determine the existence of single and double periodic solutions under certain parameter conditions. Thirdly, we discuss the practical dynamic behaviors of rumors spreading from the perspectives of the basic reproduction number and periodic solutions, especially the correlation between these two and multi-periodic oscillations. To our knowledge, such complex dynamic properties have rarely been analyzed in rumor models.

Keywords: rumor spreading; SIR model; rumor-refuting mechanism; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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