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

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.

Automated summary

This study explores the trends and control of online rumor dissemination. By analyzing the boundedness of solutions and the existence of rumor-spreading equilibrium points, as well as calculating the basic reproduction number, this study draws some fundamental conclusions. Furthermore, through the analysis of local stability and global stability, the equilibrium points of rumor spreading are thoroughly examined. In addition, this study discusses the forward and backward bifurcation phenomena and optimal control problem, which are seldom addressed in the bilingual environment. Numerical simulations are conducted to verify the accuracy of the main results.