Dynamics Analysis and Optimal Control for a Delayed Rumor-Spreading Model

Chunru Li () and Zujun Ma
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Chunru Li: Business School, Changshu Institute of Technology, Changshu 215500, China
Zujun Ma: School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China

Mathematics, 2022, vol. 10, issue 19, 1-25

Abstract: In this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium. By a Lyapunov functional technique, we examine the global asymptotically stability of the rumor-free and the rumor-endemic equilibria. We provide two control variables in the rumor-spreading model with time delay, and get the optimal solution via the optimal procedures. Finally, we present some numerical simulations to verify our theoretical predictions. They illustrate that the delay is a crucial issue for system, and it can lead to not just Hopf bifurcation but also chaos.

Keywords: rumor spreading model; delay; bifurcation; global stability; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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