Caputo Fractional Rumor Propagation Model with Noise Interference

With the continuous development of social networks, netizens analyze and judge the credibility of information based on their accumulated knowledge, experience and other cognitive systems. Additionally, the presence of stochastic noise is inevitable in the actual network topology. In this paper, consider the memory effects represented by Caputo fractional derivatives, and noise interference represented by Gaussian white noise, simultaneously, a Caputo fractional order susceptible-infected-removed (CF-SIR) rumor propagation model with noise interference is established in social networks. Subsequently, the global existence and uniqueness of the solution are investigated by the Picard iteration method, and the extinction of rumor is explored in social networks. Simulation experiments on artificial and real networks verify the global existence and uniqueness of solutions. This discovery reveals that the enhancement of memory effects can suppress rumors, whereas the intensity of noise can promote the spread of rumors resulting in a stochastic resonance effect. Finally, the effectiveness of the proposed model is validated on a real dataset. Authoritative institutions can control rumors by continuously promoting knowledge and maintaining network stability.