Dynamical interplay between the dissemination of scientific knowledge and rumor spreading in emergency

Rumor is an important form of social interaction and its spreading has a significant impact on human lives. Accounting to rumors' spread, we present a way of analysis on interaction between two processes, and a frame about the dissemination of scientific knowledge in order to prevent rumor transition. Based on this analysis, a 4D dynamic model is established and numerical simulations are performed. Mathematical analysis of the system with regard to boundedness of solutions, local and global stability of the feasible equilibria and persistence of the system are presented. When the rate of scientific knowledge dissemination reaches a critical value, it can be concluded that the strictly positive interior equilibria undergoes Hopf-bifurcation. The rumor spreading rate also plays an important role on the dynamic behavior of our system, which can be showed from our simulation results that lower rumor spreading rate drives the rumormongers to extinction.