Rumor spreading has become a critical social issue with the widespread use of social media platforms. This study develops a stochastic fractional delay differential equation (SFDDE) model to describe rumor propagation in a population divided into four compartments: susceptible \(\:S\left(t\right)\) , spreaders \(\:I\left(t\right)\) , counter-rumor spreaders \(\:C\left(t\right)\) , and stiflers \(\:R\left(t\right)\) . The proposed model ensures nonnegativity and boundedness of solutions for nonnegative initial conditions. Rigorous analytical investigations establish the local and global stability of both the Rumor-Free Equilibrium (RFE) and the Rumor-Present Equilibrium (RPE), with the reproduction number identified as a key threshold parameter. Supported by classical stability theorems, the model’s positivity, boundedness, local and global dynamics, and sensitivity around the reproduction number are systematically examined. Furthermore, the Generalized Nonstandard Finite Difference (GL-NSFD) method is employed to obtain accurate and dynamically consistent numerical approximations, demonstrating the model’s reliability and efficiency through simulations and graphical validation.
