Dynamical analysis of two discrete-time rumor propagation models in online social networks

The main aim of this work is to propose and analyze two discrete-time rumor propagation models in online social networks. These models are discrete-time versions of two well-known continuous-time rumor propagation models constructed in recent studies. We perform a rigorous mathematical analysis for global dynamics of the proposed discrete-time models. More specifically, invariant sets, equilibrium points, and their local and global asymptotic stability are established. The obtained results indicate that the discrete-time models can capture essential dynamical properties of the continuous-time models under easily-verified conditions, but they are particularly advantageous in practical applications and real-life situations. Lastly, several illustrative numerical examples supporting the theoretical findings are reported and discussed.