Dynamical behaviors and optimal control of delayed S2IS rumor propagation model with saturated conversion function over complex networks

• Published in: Communications in nonlinear science & numerical simulation 2024-01, Vol.128, p.107603, Article 107603
• Main Authors: Ding, Nana, Guan, Gui, Shen, Shuling, Zhu, Linhe
• Format: Article
• Language: English
• Subjects: Complex networks; Delay; Optimum control; Rumor propagation; Stability
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2023.107603

Nowadays, online information is disseminated in multiple languages on different platforms, and research on the dissemination trend and control of online rumors is a topic worth discussing. In the bilingual environment, we study the S2IS rumor propagation model with time delay and saturated conversion function which implies the limitation of resources in homogeneous and heterogeneous networks. First and foremost, the analysis of the boundedness of the solutions and the existence of the rumor-spreading equilibrium points is given in our work, and we figure out the basic reproduction number. Next, we conduct the local stability analysis of the rumor-free equilibrium point and the rumor-spreading equilibrium points according to the characteristic equation. The global stability of the rumor-free equilibrium point is shown based on the Lyapunov stability theory. Besides, we study the forward and backward bifurcation phenomenon and optimal control problem in theory, which is seldom discussed in the bilingual environment. Finally, numerical simulations are performed to verify the correctness of our main results. •This paper establishes a S2IS rumor propagation model with saturated conversion function.•Stability analysis and bifurcation phenomenon are investigated in theory.•Optimal control strategy is theoretically given by studying optimal system.