Dynamical behavior of a stochastic SICR rumor model incorporating media coverage

Abstract

Rumor propagation in the new media era poses a huge threat to maintaining the normal order of social life. In this context, we put forth a nonlinear dynamics-based stochastic SICR rumor model that integrates media coverage with science education. First, the existence of a unique global positive solution is obtained. Second, sufficient conditions for extinction are constructed on the spread of rumors based on the Lyapunov function methods and Khasminskii’s theory. Finally, the theoretical analysis is verified through numerical simulations. Additionally, it demonstrates how rumor spreading can be hampered by media coverage.